diff --git a/.gitignore b/.gitignore
index e32cd21..13d1290 100644
--- a/.gitignore
+++ b/.gitignore
@@ -16,3 +16,6 @@ deps/src/
 # Build artifacts for creating documentation generated by the Documenter package
 docs/build/
 docs/site/
+LotkaVolterra/.DS_Store
+*.DS_Store
+Project.toml
diff --git a/LotkaVolterra/Manifest.toml b/LotkaVolterra/Manifest.toml
index 502527d..b2f5419 100644
--- a/LotkaVolterra/Manifest.toml
+++ b/LotkaVolterra/Manifest.toml
@@ -1,21 +1,38 @@
 # This file is machine-generated - editing it directly is not advised
 
+[[AbstractAlgebra]]
+deps = ["GroupsCore", "InteractiveUtils", "LinearAlgebra", "MacroTools", "Markdown", "Random", "RandomExtensions", "SparseArrays", "Test"]
+git-tree-sha1 = "e1205b8ce43e3bf8102aa7416a3c1f0862c479a0"
+uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
+version = "0.27.0"
+
 [[AbstractFFTs]]
-deps = ["LinearAlgebra"]
-git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
+deps = ["ChainRulesCore", "LinearAlgebra"]
+git-tree-sha1 = "69f7020bd72f069c219b5e8c236c1fa90d2cb409"
 uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
-version = "1.0.1"
+version = "1.2.1"
 
 [[AbstractTrees]]
-git-tree-sha1 = "03e0550477d86222521d254b741d470ba17ea0b5"
+git-tree-sha1 = "5c0b629df8a5566a06f5fef5100b53ea56e465a0"
 uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
-version = "0.3.4"
+version = "0.4.2"
+
+[[Accessors]]
+deps = ["Compat", "CompositionsBase", "ConstructionBase", "Dates", "InverseFunctions", "LinearAlgebra", "MacroTools", "Requires", "Test"]
+git-tree-sha1 = "c877a35749324754d3c8fffb09fc1f9db144ff8f"
+uuid = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
+version = "0.1.18"
 
 [[Adapt]]
 deps = ["LinearAlgebra"]
-git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
+git-tree-sha1 = "af92965fb30777147966f58acb05da51c5616b5f"
 uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
-version = "3.3.1"
+version = "3.3.3"
+
+[[ArgCheck]]
+git-tree-sha1 = "a3a402a35a2f7e0b87828ccabbd5ebfbebe356b4"
+uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197"
+version = "2.3.0"
 
 [[ArgTools]]
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
@@ -27,74 +44,185 @@ uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
 version = "0.1.0"
 
 [[ArrayInterface]]
-deps = ["IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
-git-tree-sha1 = "045ff5e1bc8c6fb1ecb28694abba0a0d55b5f4f5"
+deps = ["ArrayInterfaceCore", "Compat", "IfElse", "LinearAlgebra", "Static"]
+git-tree-sha1 = "621913bff3923ff489e4268ba2b425bfacbb1759"
 uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
-version = "3.1.17"
+version = "6.0.21"
+
+[[ArrayInterfaceCore]]
+deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
+git-tree-sha1 = "8d9e48436c5589fbd51ae8c8165a299a219188c0"
+uuid = "30b0a656-2188-435a-8636-2ec0e6a096e2"
+version = "0.1.15"
+
+[[ArrayInterfaceGPUArrays]]
+deps = ["Adapt", "ArrayInterfaceCore", "GPUArraysCore", "LinearAlgebra"]
+git-tree-sha1 = "febba7add2873aecc0b6620b55969e73ec875bce"
+uuid = "6ba088a2-8465-4c0a-af30-387133b534db"
+version = "0.2.1"
+
+[[ArrayInterfaceOffsetArrays]]
+deps = ["ArrayInterface", "OffsetArrays", "Static"]
+git-tree-sha1 = "c49f6bad95a30defff7c637731f00934c7289c50"
+uuid = "015c0d05-e682-4f19-8f0a-679ce4c54826"
+version = "0.1.6"
+
+[[ArrayInterfaceStaticArrays]]
+deps = ["Adapt", "ArrayInterface", "ArrayInterfaceStaticArraysCore", "LinearAlgebra", "Static", "StaticArrays"]
+git-tree-sha1 = "efb000a9f643f018d5154e56814e338b5746c560"
+uuid = "b0d46f97-bff5-4637-a19a-dd75974142cd"
+version = "0.1.4"
+
+[[ArrayInterfaceStaticArraysCore]]
+deps = ["Adapt", "ArrayInterfaceCore", "LinearAlgebra", "StaticArraysCore"]
+git-tree-sha1 = "a1e2cf6ced6505cbad2490532388683f1e88c3ed"
+uuid = "dd5226c6-a4d4-4bc7-8575-46859f9c95b9"
+version = "0.1.0"
+
+[[ArrayInterfaceTracker]]
+deps = ["ArrayInterfaceCore", "Tracker"]
+git-tree-sha1 = "9600e1ef98f7067dc91c22c0759c60580a0320dd"
+uuid = "a2b0951a-f94f-4742-8780-617792921f9b"
+version = "0.1.1"
+
+[[ArrayLayouts]]
+deps = ["FillArrays", "LinearAlgebra", "SparseArrays"]
+git-tree-sha1 = "ebe4bbfc4de38ef88323f67d60a4e848fb550f0e"
+uuid = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
+version = "0.8.9"
 
 [[Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
 
+[[AutoHashEquals]]
+git-tree-sha1 = "45bb6705d93be619b81451bb2006b7ee5d4e4453"
+uuid = "15f4f7f2-30c1-5605-9d31-71845cf9641f"
+version = "0.2.0"
+
 [[AxisAlgorithms]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
-git-tree-sha1 = "a4d07a1c313392a77042855df46c5f534076fab9"
+git-tree-sha1 = "66771c8d21c8ff5e3a93379480a2307ac36863f7"
 uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
-version = "1.0.0"
+version = "1.0.1"
 
 [[BFloat16s]]
-deps = ["LinearAlgebra", "Test"]
-git-tree-sha1 = "4af69e205efc343068dc8722b8dfec1ade89254a"
+deps = ["LinearAlgebra", "Printf", "Random", "Test"]
+git-tree-sha1 = "a598ecb0d717092b5539dbbe890c98bac842b072"
 uuid = "ab4f0b2a-ad5b-11e8-123f-65d77653426b"
-version = "0.1.0"
+version = "0.2.0"
+
+[[BandedMatrices]]
+deps = ["ArrayLayouts", "FillArrays", "LinearAlgebra", "Random", "SparseArrays"]
+git-tree-sha1 = "0227886a3141dfbb9fab5bfbf2133ac57677c1f9"
+uuid = "aae01518-5342-5314-be14-df237901396f"
+version = "0.17.3"
+
+[[BangBang]]
+deps = ["Compat", "ConstructionBase", "Future", "InitialValues", "LinearAlgebra", "Requires", "Setfield", "Tables", "ZygoteRules"]
+git-tree-sha1 = "b15a6bc52594f5e4a3b825858d1089618871bf9d"
+uuid = "198e06fe-97b7-11e9-32a5-e1d131e6ad66"
+version = "0.3.36"
 
 [[Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
+[[Baselet]]
+git-tree-sha1 = "aebf55e6d7795e02ca500a689d326ac979aaf89e"
+uuid = "9718e550-a3fa-408a-8086-8db961cd8217"
+version = "0.1.1"
+
+[[Bijections]]
+git-tree-sha1 = "fe4f8c5ee7f76f2198d5c2a06d3961c249cce7bd"
+uuid = "e2ed5e7c-b2de-5872-ae92-c73ca462fb04"
+version = "0.1.4"
+
+[[BitTwiddlingConvenienceFunctions]]
+deps = ["Static"]
+git-tree-sha1 = "eaee37f76339077f86679787a71990c4e465477f"
+uuid = "62783981-4cbd-42fc-bca8-16325de8dc4b"
+version = "0.1.4"
+
+[[BlockArrays]]
+deps = ["ArrayLayouts", "FillArrays", "LinearAlgebra"]
+git-tree-sha1 = "43b09ac794ed8347592dd90539756d1c3416e5f2"
+uuid = "8e7c35d0-a365-5155-bbbb-fb81a777f24e"
+version = "0.16.19"
+
+[[BlockBandedMatrices]]
+deps = ["ArrayLayouts", "BandedMatrices", "BlockArrays", "FillArrays", "LinearAlgebra", "MatrixFactorizations", "SparseArrays", "Statistics"]
+git-tree-sha1 = "85c30bf983cb20748f126c235f0696dff8a83612"
+uuid = "ffab5731-97b5-5995-9138-79e8c1846df0"
+version = "0.11.7"
+
 [[Bzip2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "c3598e525718abcc440f69cc6d5f60dda0a1b61e"
+git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
 uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
-version = "1.0.6+5"
+version = "1.0.8+0"
 
 [[CEnum]]
-git-tree-sha1 = "215a9aa4a1f23fbd05b92769fdd62559488d70e9"
+git-tree-sha1 = "eb4cb44a499229b3b8426dcfb5dd85333951ff90"
 uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
-version = "0.4.1"
+version = "0.4.2"
+
+[[CPUSummary]]
+deps = ["CpuId", "IfElse", "Static"]
+git-tree-sha1 = "8a43595f7b3f7d6dd1e07ad9b94081e1975df4af"
+uuid = "2a0fbf3d-bb9c-48f3-b0a9-814d99fd7ab9"
+version = "0.1.25"
 
 [[CSTParser]]
 deps = ["Tokenize"]
-git-tree-sha1 = "9723e1c07c1727082e169ca50789644a552fb023"
+git-tree-sha1 = "3ddd48d200eb8ddf9cb3e0189fc059fd49b97c1f"
 uuid = "00ebfdb7-1f24-5e51-bd34-a7502290713f"
-version = "3.2.3"
+version = "3.3.6"
 
 [[CUDA]]
-deps = ["AbstractFFTs", "Adapt", "BFloat16s", "CEnum", "CompilerSupportLibraries_jll", "DataStructures", "ExprTools", "GPUArrays", "GPUCompiler", "LLVM", "LazyArtifacts", "Libdl", "LinearAlgebra", "Logging", "Printf", "Random", "Random123", "RandomNumbers", "Reexport", "Requires", "SparseArrays", "SpecialFunctions", "TimerOutputs"]
-git-tree-sha1 = "3e5a6cf59289a60202a0f63fdded29473544d553"
+deps = ["AbstractFFTs", "Adapt", "BFloat16s", "CEnum", "CompilerSupportLibraries_jll", "ExprTools", "GPUArrays", "GPUCompiler", "LLVM", "LazyArtifacts", "Libdl", "LinearAlgebra", "Logging", "Printf", "Random", "Random123", "RandomNumbers", "Reexport", "Requires", "SparseArrays", "SpecialFunctions", "TimerOutputs"]
+git-tree-sha1 = "49549e2c28ffb9cc77b3689dc10e46e6271e9452"
 uuid = "052768ef-5323-5732-b1bb-66c8b64840ba"
-version = "3.3.2"
+version = "3.12.0"
 
 [[Cairo_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
-git-tree-sha1 = "e2f47f6d8337369411569fd45ae5753ca10394c6"
+git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
 uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
-version = "1.16.0+6"
+version = "1.16.1+1"
+
+[[Calculus]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
+uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
+version = "0.5.1"
 
 [[Cassette]]
-git-tree-sha1 = "087e76b8d48c014112ba890892c33be42ad10504"
+git-tree-sha1 = "063b2e77c5537a548c5bf2f44161f1d3e1ab3227"
 uuid = "7057c7e9-c182-5462-911a-8362d720325c"
-version = "0.3.7"
+version = "0.3.10"
 
 [[ChainRules]]
-deps = ["ChainRulesCore", "Compat", "LinearAlgebra", "Random", "Statistics"]
-git-tree-sha1 = "4d6ed39877332d0e2157f703cb84f2619056292f"
+deps = ["ChainRulesCore", "Compat", "Distributed", "IrrationalConstants", "LinearAlgebra", "Random", "RealDot", "SparseArrays", "Statistics"]
+git-tree-sha1 = "e762b70af7c1d914f677d9588a1d3b32e5f832af"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "0.8.20"
+version = "1.39.1"
 
 [[ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra", "SparseArrays"]
-git-tree-sha1 = "be770c08881f7bb928dfd86d1ba83798f76cf62a"
+git-tree-sha1 = "80ca332f6dcb2508adba68f22f551adb2d00a624"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "0.10.9"
+version = "1.15.3"
+
+[[ChangesOfVariables]]
+deps = ["ChainRulesCore", "LinearAlgebra", "Test"]
+git-tree-sha1 = "38f7a08f19d8810338d4f5085211c7dfa5d5bdd8"
+uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
+version = "0.1.4"
+
+[[CloseOpenIntervals]]
+deps = ["ArrayInterface", "Static"]
+git-tree-sha1 = "5522c338564580adf5d58d91e43a55db0fa5fb39"
+uuid = "fb6a15b2-703c-40df-9091-08a04967cfa9"
+version = "0.1.10"
 
 [[CodecZlib]]
 deps = ["TranscodingStreams", "Zlib_jll"]
@@ -103,16 +231,22 @@ uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
 version = "0.7.0"
 
 [[ColorSchemes]]
-deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random", "StaticArrays"]
-git-tree-sha1 = "c8fd01e4b736013bc61b704871d20503b33ea402"
+deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "Random"]
+git-tree-sha1 = "1fd869cc3875b57347f7027521f561cf46d1fcd8"
 uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
-version = "3.12.1"
+version = "3.19.0"
 
 [[ColorTypes]]
 deps = ["FixedPointNumbers", "Random"]
-git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
+git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4"
 uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
-version = "0.11.0"
+version = "0.11.4"
+
+[[ColorVectorSpace]]
+deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"]
+git-tree-sha1 = "d08c20eef1f2cbc6e60fd3612ac4340b89fea322"
+uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
+version = "0.9.9"
 
 [[Colors]]
 deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
@@ -127,14 +261,14 @@ version = "1.0.2"
 
 [[CommonMark]]
 deps = ["Crayons", "JSON", "URIs"]
-git-tree-sha1 = "7632afc57f92720a01d9aedf23f413f4e5e21015"
+git-tree-sha1 = "4cd7063c9bdebdbd55ede1af70f3c2f48fab4215"
 uuid = "a80b9123-70ca-4bc0-993e-6e3bcb318db6"
-version = "0.8.1"
+version = "0.8.6"
 
 [[CommonSolve]]
-git-tree-sha1 = "68a0743f578349ada8bc911a5cbd5a2ef6ed6d1f"
+git-tree-sha1 = "332a332c97c7071600984b3c31d9067e1a4e6e25"
 uuid = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
-version = "0.2.0"
+version = "0.2.1"
 
 [[CommonSubexpressions]]
 deps = ["MacroTools", "Test"]
@@ -144,19 +278,30 @@ version = "0.3.0"
 
 [[Compat]]
 deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
-git-tree-sha1 = "dc7dedc2c2aa9faf59a55c622760a25cbefbe941"
+git-tree-sha1 = "9be8be1d8a6f44b96482c8af52238ea7987da3e3"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
-version = "3.31.0"
+version = "3.45.0"
 
 [[CompilerSupportLibraries_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
 
+[[ComponentArrays]]
+deps = ["ArrayInterface", "ChainRulesCore", "LinearAlgebra", "Requires"]
+git-tree-sha1 = "bdbd8f6d825682ba991b69842a4053ac0f588226"
+uuid = "b0b7db55-cfe3-40fc-9ded-d10e2dbeff66"
+version = "0.12.4"
+
 [[CompositeTypes]]
 git-tree-sha1 = "d5b014b216dc891e81fea299638e4c10c657b582"
 uuid = "b152e2b5-7a66-4b01-a709-34e65c35f657"
 version = "0.1.2"
 
+[[CompositionsBase]]
+git-tree-sha1 = "455419f7e328a1a2493cabc6428d79e951349769"
+uuid = "a33af91c-f02d-484b-be07-31d278c5ca2b"
+version = "0.1.1"
+
 [[ConsoleProgressMonitor]]
 deps = ["Logging", "ProgressMeter"]
 git-tree-sha1 = "3ab7b2136722890b9af903859afcf457fa3059e8"
@@ -165,43 +310,54 @@ version = "0.1.2"
 
 [[ConstructionBase]]
 deps = ["LinearAlgebra"]
-git-tree-sha1 = "f74e9d5388b8620b4cee35d4c5a618dd4dc547f4"
+git-tree-sha1 = "59d00b3139a9de4eb961057eabb65ac6522be954"
 uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
-version = "1.3.0"
+version = "1.4.0"
+
+[[ContextVariablesX]]
+deps = ["Compat", "Logging", "UUIDs"]
+git-tree-sha1 = "8ccaa8c655bc1b83d2da4d569c9b28254ababd6e"
+uuid = "6add18c4-b38d-439d-96f6-d6bc489c04c5"
+version = "0.1.2"
 
 [[Contour]]
-deps = ["StaticArrays"]
-git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
+git-tree-sha1 = "d05d9e7b7aedff4e5b51a029dced05cfb6125781"
 uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
-version = "0.5.7"
+version = "0.6.2"
+
+[[CpuId]]
+deps = ["Markdown"]
+git-tree-sha1 = "fcbb72b032692610bfbdb15018ac16a36cf2e406"
+uuid = "adafc99b-e345-5852-983c-f28acb93d879"
+version = "0.3.1"
 
 [[Crayons]]
-git-tree-sha1 = "3f71217b538d7aaee0b69ab47d9b7724ca8afa0d"
+git-tree-sha1 = "249fe38abf76d48563e2f4556bebd215aa317e15"
 uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
-version = "4.0.4"
+version = "4.1.1"
 
 [[DataAPI]]
-git-tree-sha1 = "ee400abb2298bd13bfc3df1c412ed228061a2385"
+git-tree-sha1 = "fb5f5316dd3fd4c5e7c30a24d50643b73e37cd40"
 uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
-version = "1.7.0"
+version = "1.10.0"
 
 [[DataDrivenDiffEq]]
-deps = ["Compat", "DataInterpolations", "DiffEqBase", "DocStringExtensions", "LinearAlgebra", "ModelingToolkit", "ProgressMeter", "QuadGK", "Reexport", "Statistics", "StatsBase", "Symbolics", "Test"]
-git-tree-sha1 = "b0c8c835a78b4d906da052a8ad07a2157e9a13f9"
+deps = ["CommonSolve", "DataInterpolations", "DiffEqBase", "Distributions", "DocStringExtensions", "LinearAlgebra", "Literate", "Measurements", "ModelingToolkit", "Parameters", "ProgressMeter", "QuadGK", "Random", "RecipesBase", "Reexport", "Requires", "Statistics", "StatsBase", "SymbolicUtils", "Symbolics", "Test"]
+git-tree-sha1 = "f65c39707b06b2bb71344e10e9635d94ce5a5828"
 uuid = "2445eb08-9709-466a-b3fc-47e12bd697a2"
-version = "0.6.2"
+version = "0.8.5"
 
 [[DataInterpolations]]
-deps = ["ChainRulesCore", "LinearAlgebra", "Optim", "RecipesBase", "RecursiveArrayTools", "Reexport"]
-git-tree-sha1 = "2f20fd64fa6e5af06de832f42b2ce07beb4ade57"
+deps = ["ChainRulesCore", "LinearAlgebra", "Optim", "RecipesBase", "RecursiveArrayTools", "Reexport", "RegularizationTools", "Symbolics"]
+git-tree-sha1 = "e660731df2175355e573b55796ffb4d6d4f60093"
 uuid = "82cc6244-b520-54b8-b5a6-8a565e85f1d0"
-version = "3.4.1"
+version = "3.10.0"
 
 [[DataStructures]]
 deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
-git-tree-sha1 = "4437b64df1e0adccc3e5d1adbc3ac741095e4677"
+git-tree-sha1 = "d1fff3a548102f48987a52a2e0d114fa97d730f0"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
-version = "0.18.9"
+version = "0.18.13"
 
 [[DataValueInterfaces]]
 git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
@@ -212,45 +368,56 @@ version = "1.0.0"
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 
+[[DefineSingletons]]
+git-tree-sha1 = "0fba8b706d0178b4dc7fd44a96a92382c9065c2c"
+uuid = "244e2a9f-e319-4986-a169-4d1fe445cd52"
+version = "0.1.2"
+
 [[DelimitedFiles]]
 deps = ["Mmap"]
 uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 
+[[DensityInterface]]
+deps = ["InverseFunctions", "Test"]
+git-tree-sha1 = "80c3e8639e3353e5d2912fb3a1916b8455e2494b"
+uuid = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
+version = "0.4.0"
+
 [[DiffEqBase]]
-deps = ["ArrayInterface", "ChainRulesCore", "DataStructures", "DocStringExtensions", "FastBroadcast", "FunctionWrappers", "IterativeSolvers", "LabelledArrays", "LinearAlgebra", "Logging", "MuladdMacro", "NonlinearSolve", "Parameters", "Printf", "RecursiveArrayTools", "RecursiveFactorization", "Reexport", "Requires", "SciMLBase", "Setfield", "SparseArrays", "StaticArrays", "Statistics", "SuiteSparse", "ZygoteRules"]
-git-tree-sha1 = "cfd2c4f9357ade5db4a52041b1b2c97641aeb19c"
+deps = ["ArrayInterfaceCore", "ChainRulesCore", "DataStructures", "Distributions", "DocStringExtensions", "FastBroadcast", "ForwardDiff", "FunctionWrappers", "LinearAlgebra", "Logging", "MuladdMacro", "NonlinearSolve", "Parameters", "Printf", "RecursiveArrayTools", "Reexport", "Requires", "SciMLBase", "Setfield", "SparseArrays", "StaticArrays", "Statistics", "ZygoteRules"]
+git-tree-sha1 = "3fc96d4d32e5eed475c28a0e4762c6f558558fb6"
 uuid = "2b5f629d-d688-5b77-993f-72d75c75574e"
-version = "6.68.0"
+version = "6.94.4"
 
 [[DiffEqCallbacks]]
-deps = ["DataStructures", "DiffEqBase", "ForwardDiff", "LinearAlgebra", "NLsolve", "OrdinaryDiffEq", "RecipesBase", "RecursiveArrayTools", "StaticArrays"]
-git-tree-sha1 = "0972ca167952dc426b5438fc188b846b7a66a1f3"
+deps = ["DataStructures", "DiffEqBase", "ForwardDiff", "LinearAlgebra", "NLsolve", "Parameters", "RecipesBase", "RecursiveArrayTools", "SciMLBase", "StaticArrays"]
+git-tree-sha1 = "cfef2afe8d73ed2d036b0e4b14a3f9b53045c534"
 uuid = "459566f4-90b8-5000-8ac3-15dfb0a30def"
-version = "2.16.1"
-
-[[DiffEqFlux]]
-deps = ["Adapt", "Cassette", "ConsoleProgressMonitor", "DataInterpolations", "DiffEqBase", "DiffEqSensitivity", "DiffResults", "Distributions", "DistributionsAD", "Flux", "ForwardDiff", "GalacticOptim", "LinearAlgebra", "Logging", "LoggingExtras", "Optim", "Printf", "ProgressLogging", "RecursiveArrayTools", "Reexport", "Requires", "StaticArrays", "TerminalLoggers", "Zygote", "ZygoteRules"]
-git-tree-sha1 = "e0059d6e9b8fbe02aef4a51ba32a7ed63d98e32a"
-uuid = "aae7a2af-3d4f-5e19-a356-7da93b79d9d0"
-version = "1.41.0"
+version = "2.23.1"
 
 [[DiffEqJump]]
-deps = ["ArrayInterface", "Compat", "DataStructures", "DiffEqBase", "FunctionWrappers", "LinearAlgebra", "PoissonRandom", "Random", "RandomNumbers", "RecursiveArrayTools", "StaticArrays", "TreeViews", "UnPack"]
-git-tree-sha1 = "210ae4148a9b687680c74d13f415cc190fb2c101"
+deps = ["ArrayInterfaceCore", "DataStructures", "DiffEqBase", "DocStringExtensions", "FunctionWrappers", "Graphs", "LinearAlgebra", "Markdown", "PoissonRandom", "Random", "RandomNumbers", "RecursiveArrayTools", "Reexport", "SciMLBase", "StaticArrays", "TreeViews", "UnPack"]
+git-tree-sha1 = "de3014a7c8b4f84d22715a43fe6c58e1c35dc998"
 uuid = "c894b116-72e5-5b58-be3c-e6d8d4ac2b12"
-version = "6.14.2"
+version = "8.6.3"
 
 [[DiffEqNoiseProcess]]
-deps = ["DiffEqBase", "Distributions", "LinearAlgebra", "Optim", "PoissonRandom", "QuadGK", "Random", "Random123", "RandomNumbers", "RecipesBase", "RecursiveArrayTools", "Requires", "ResettableStacks", "StaticArrays", "Statistics"]
-git-tree-sha1 = "3d8842936fdb1d3d95929fcb99645a48d08fd0d7"
+deps = ["DiffEqBase", "Distributions", "GPUArraysCore", "LinearAlgebra", "Markdown", "Optim", "PoissonRandom", "QuadGK", "Random", "Random123", "RandomNumbers", "RecipesBase", "RecursiveArrayTools", "ResettableStacks", "SciMLBase", "StaticArrays", "Statistics"]
+git-tree-sha1 = "6f3fe6ebe1b6e6e3a9b72739ada313aa17c9bb66"
 uuid = "77a26b50-5914-5dd7-bc55-306e6241c503"
-version = "5.8.0"
+version = "5.12.0"
+
+[[DiffEqOperators]]
+deps = ["BandedMatrices", "BlockBandedMatrices", "DiffEqBase", "DomainSets", "ForwardDiff", "LazyArrays", "LazyBandedMatrices", "LinearAlgebra", "LoopVectorization", "NNlib", "NonlinearSolve", "Requires", "RuntimeGeneratedFunctions", "SciMLBase", "SparseArrays", "SparseDiffTools", "StaticArrays", "SuiteSparse"]
+git-tree-sha1 = "403d101caee42ba504f2ee74ae6e8413b765605b"
+uuid = "9fdde737-9c7f-55bf-ade8-46b3f136cc48"
+version = "4.43.1"
 
 [[DiffEqSensitivity]]
-deps = ["Adapt", "ArrayInterface", "Cassette", "ChainRulesCore", "DiffEqBase", "DiffEqCallbacks", "DiffEqNoiseProcess", "DiffRules", "Distributions", "Enzyme", "FFTW", "FiniteDiff", "ForwardDiff", "GlobalSensitivity", "LinearAlgebra", "Parameters", "QuadGK", "QuasiMonteCarlo", "Random", "RandomNumbers", "RecursiveArrayTools", "Reexport", "Requires", "ReverseDiff", "SharedArrays", "Statistics", "StochasticDiffEq", "Tracker", "Zygote", "ZygoteRules"]
-git-tree-sha1 = "0b1d851eccc4e7431dff5bb9c3a24c2b63075413"
+deps = ["Adapt", "ArrayInterfaceCore", "ArrayInterfaceTracker", "Cassette", "ChainRulesCore", "DiffEqBase", "DiffEqCallbacks", "DiffEqNoiseProcess", "DiffEqOperators", "DiffRules", "Distributions", "EllipsisNotation", "Enzyme", "FiniteDiff", "ForwardDiff", "GPUArrays", "LinearAlgebra", "LinearSolve", "Markdown", "OrdinaryDiffEq", "Parameters", "QuadGK", "Random", "RandomNumbers", "RecursiveArrayTools", "Reexport", "ReverseDiff", "SciMLBase", "Statistics", "StochasticDiffEq", "Tracker", "Zygote", "ZygoteRules"]
+git-tree-sha1 = "87fd2c08bd8749906cdf253a240b21a5c92b7214"
 uuid = "41bf760c-e81c-5289-8e54-58b1f1f8abe2"
-version = "6.55.0"
+version = "6.79.0"
 
 [[DiffResults]]
 deps = ["StaticArrays"]
@@ -259,95 +426,101 @@ uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
 version = "1.0.3"
 
 [[DiffRules]]
-deps = ["NaNMath", "Random", "SpecialFunctions"]
-git-tree-sha1 = "214c3fcac57755cfda163d91c58893a8723f93e9"
+deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
+git-tree-sha1 = "28d605d9a0ac17118fe2c5e9ce0fbb76c3ceb120"
 uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
-version = "1.0.2"
+version = "1.11.0"
 
 [[Distances]]
-deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
-git-tree-sha1 = "abe4ad222b26af3337262b8afb28fab8d215e9f8"
+deps = ["LinearAlgebra", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "3258d0659f812acde79e8a74b11f17ac06d0ca04"
 uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
-version = "0.10.3"
+version = "0.10.7"
 
 [[Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
 [[Distributions]]
-deps = ["FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"]
-git-tree-sha1 = "465bac778ecf06edf09e6b649246f819d5e136dd"
+deps = ["ChainRulesCore", "DensityInterface", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Test"]
+git-tree-sha1 = "aafa0665e3db0d3d0890cdc8191ea03dc279b042"
 uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
-version = "0.25.7"
+version = "0.25.66"
 
 [[DistributionsAD]]
 deps = ["Adapt", "ChainRules", "ChainRulesCore", "Compat", "DiffRules", "Distributions", "FillArrays", "LinearAlgebra", "NaNMath", "PDMats", "Random", "Requires", "SpecialFunctions", "StaticArrays", "StatsBase", "StatsFuns", "ZygoteRules"]
-git-tree-sha1 = "1c0ef4fe9eaa9596aca50b15a420e987b8447e56"
+git-tree-sha1 = "ec811a2688b3504ce5b315fe7bc86464480d5964"
 uuid = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
-version = "0.6.28"
+version = "0.6.41"
 
 [[DocStringExtensions]]
 deps = ["LibGit2"]
-git-tree-sha1 = "a32185f5428d3986f47c2ab78b1f216d5e6cc96f"
+git-tree-sha1 = "b19534d1895d702889b219c382a6e18010797f0b"
 uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
-version = "0.8.5"
+version = "0.8.6"
 
 [[DomainSets]]
-deps = ["CompositeTypes", "IntervalSets", "LinearAlgebra", "StaticArrays", "Statistics", "Test"]
-git-tree-sha1 = "6cdd99d0b7b555f96f7cb05aa82067ee79e7aef4"
+deps = ["CompositeTypes", "IntervalSets", "LinearAlgebra", "StaticArrays", "Statistics"]
+git-tree-sha1 = "ac425eea956013b51e7891bef3c33684b7d37029"
 uuid = "5b8099bc-c8ec-5219-889f-1d9e522a28bf"
-version = "0.5.2"
+version = "0.5.11"
 
 [[Downloads]]
-deps = ["ArgTools", "LibCURL", "NetworkOptions"]
+deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
 
+[[DualNumbers]]
+deps = ["Calculus", "NaNMath", "SpecialFunctions"]
+git-tree-sha1 = "5837a837389fccf076445fce071c8ddaea35a566"
+uuid = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"
+version = "0.6.8"
+
 [[DynamicPolynomials]]
 deps = ["DataStructures", "Future", "LinearAlgebra", "MultivariatePolynomials", "MutableArithmetics", "Pkg", "Reexport", "Test"]
-git-tree-sha1 = "b17c665e4994b1e0f30148ffdd16188cae4e9d1b"
+git-tree-sha1 = "d0fa82f39c2a5cdb3ee385ad52bc05c42cb4b9f0"
 uuid = "7c1d4256-1411-5781-91ec-d7bc3513ac07"
-version = "0.3.17"
+version = "0.4.5"
 
 [[EarCut_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "92d8f9f208637e8d2d28c664051a00569c01493d"
+git-tree-sha1 = "3f3a2501fa7236e9b911e0f7a588c657e822bb6d"
 uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
-version = "2.1.5+1"
+version = "2.2.3+0"
 
 [[EllipsisNotation]]
 deps = ["ArrayInterface"]
-git-tree-sha1 = "8041575f021cba5a099a456b4163c9a08b566a02"
+git-tree-sha1 = "03b753748fd193a7f2730c02d880da27c5a24508"
 uuid = "da5c29d0-fa7d-589e-88eb-ea29b0a81949"
-version = "1.1.0"
+version = "1.6.0"
 
 [[Enzyme]]
-deps = ["Adapt", "CEnum", "Enzyme_jll", "GPUCompiler", "LLVM", "Libdl", "ObjectFile"]
-git-tree-sha1 = "51e96577a19733d0002d4ae35bdefc1f493fc40c"
+deps = ["Adapt", "CEnum", "Enzyme_jll", "GPUCompiler", "LLVM", "Libdl", "LinearAlgebra", "ObjectFile", "Printf", "Random"]
+git-tree-sha1 = "8ab9eb44fbcfc9161b3f81be7814a7618f2a3460"
 uuid = "7da242da-08ed-463a-9acd-ee780be4f1d9"
-version = "0.6.1"
+version = "0.10.4"
 
 [[Enzyme_jll]]
-deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "8cf42ef2e322d9464c69ef994ee17b8e45a719c0"
+deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg", "TOML"]
+git-tree-sha1 = "722aa3b554e883118e0e3111629ec40e176cee2c"
 uuid = "7cc45869-7501-5eee-bdea-0790c847d4ef"
-version = "0.0.13+2"
+version = "0.0.33+0"
 
 [[Expat_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
+git-tree-sha1 = "bad72f730e9e91c08d9427d5e8db95478a3c323d"
 uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
-version = "2.2.10+0"
+version = "2.4.8+0"
 
 [[ExponentialUtilities]]
-deps = ["ArrayInterface", "LinearAlgebra", "Printf", "Requires", "SparseArrays"]
-git-tree-sha1 = "ad435656c49da7615152b856c0f9abe75b0b5dc9"
+deps = ["ArrayInterfaceCore", "GPUArraysCore", "GenericSchur", "LinearAlgebra", "Printf", "SparseArrays", "libblastrampoline_jll"]
+git-tree-sha1 = "b40c9037e1a33990466bc5d224ced34b34eebdb0"
 uuid = "d4d017d3-3776-5f7e-afef-a10c40355c18"
-version = "1.8.4"
+version = "1.18.0"
 
 [[ExprTools]]
-git-tree-sha1 = "555eab1f7c501166ba87eeb5d561e9f5e7d167d3"
+git-tree-sha1 = "56559bbef6ca5ea0c0818fa5c90320398a6fbf8d"
 uuid = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
-version = "0.1.4"
+version = "0.1.8"
 
 [[FFMPEG]]
 deps = ["FFMPEG_jll"]
@@ -356,51 +529,72 @@ uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
 version = "0.4.1"
 
 [[FFMPEG_jll]]
-deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "LibVPX_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
-git-tree-sha1 = "3cc57ad0a213808473eafef4845a74766242e05f"
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
+git-tree-sha1 = "ccd479984c7838684b3ac204b716c89955c76623"
 uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
-version = "4.3.1+4"
+version = "4.4.2+0"
 
 [[FFTW]]
 deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
-git-tree-sha1 = "f985af3b9f4e278b1d24434cbb546d6092fca661"
+git-tree-sha1 = "90630efff0894f8142308e334473eba54c433549"
 uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
-version = "1.4.3"
+version = "1.5.0"
 
 [[FFTW_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "3676abafff7e4ff07bbd2c42b3d8201f31653dcc"
+git-tree-sha1 = "c6033cc3892d0ef5bb9cd29b7f2f0331ea5184ea"
 uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
-version = "3.3.9+8"
+version = "3.3.10+0"
+
+[[FLoops]]
+deps = ["BangBang", "Compat", "FLoopsBase", "InitialValues", "JuliaVariables", "MLStyle", "Serialization", "Setfield", "Transducers"]
+git-tree-sha1 = "4391d3ed58db9dc5a9883b23a0578316b4798b1f"
+uuid = "cc61a311-1640-44b5-9fba-1b764f453329"
+version = "0.2.0"
+
+[[FLoopsBase]]
+deps = ["ContextVariablesX"]
+git-tree-sha1 = "656f7a6859be8673bf1f35da5670246b923964f7"
+uuid = "b9860ae5-e623-471e-878b-f6a53c775ea6"
+version = "0.1.1"
 
 [[FastBroadcast]]
-deps = ["LinearAlgebra"]
-git-tree-sha1 = "26be48918640ce002f5833e8fc537b2ba7ed0234"
+deps = ["ArrayInterface", "ArrayInterfaceCore", "LinearAlgebra", "Polyester", "Static", "StrideArraysCore"]
+git-tree-sha1 = "21cdeff41e5a1822c2acd7fc7934c5f450588e00"
 uuid = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
-version = "0.1.8"
+version = "0.2.1"
 
 [[FastClosures]]
 git-tree-sha1 = "acebe244d53ee1b461970f8910c235b259e772ef"
 uuid = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
 version = "0.3.2"
 
+[[FastLapackInterface]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "9c77a18eddbc4f7b5edbd2f1c28467ba4ba787bd"
+uuid = "29a986be-02c6-4525-aec4-84b980013641"
+version = "1.1.0"
+
 [[FileIO]]
 deps = ["Pkg", "Requires", "UUIDs"]
-git-tree-sha1 = "256d8e6188f3f1ebfa1a5d17e072a0efafa8c5bf"
+git-tree-sha1 = "9267e5f50b0e12fdfd5a2455534345c4cf2c7f7a"
 uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
-version = "1.10.1"
+version = "1.14.0"
+
+[[FileWatching]]
+uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
 
 [[FillArrays]]
-deps = ["LinearAlgebra", "Random", "SparseArrays"]
-git-tree-sha1 = "a603e79b71bb3c1efdb58f0ee32286efe2d1a255"
+deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
+git-tree-sha1 = "246621d23d1f43e3b9c368bf3b72b2331a27c286"
 uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
-version = "0.11.8"
+version = "0.13.2"
 
 [[FiniteDiff]]
-deps = ["ArrayInterface", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays"]
-git-tree-sha1 = "f6f80c8f934efd49a286bb5315360be66956dfc4"
+deps = ["ArrayInterfaceCore", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays"]
+git-tree-sha1 = "e3af8444c9916abed11f4357c2f59b6801e5b376"
 uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
-version = "2.8.0"
+version = "2.13.1"
 
 [[FixedPointNumbers]]
 deps = ["Statistics"]
@@ -409,16 +603,22 @@ uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
 version = "0.8.4"
 
 [[Flux]]
-deps = ["AbstractTrees", "Adapt", "CUDA", "CodecZlib", "Colors", "DelimitedFiles", "Functors", "Juno", "LinearAlgebra", "MacroTools", "NNlib", "NNlibCUDA", "Pkg", "Printf", "Random", "Reexport", "SHA", "Statistics", "StatsBase", "Test", "ZipFile", "Zygote"]
-git-tree-sha1 = "0b3c6d0ce57d3b793eabd346ccc8f605035ef079"
+deps = ["Adapt", "ArrayInterface", "CUDA", "ChainRulesCore", "Functors", "LinearAlgebra", "MLUtils", "MacroTools", "NNlib", "NNlibCUDA", "Optimisers", "ProgressLogging", "Random", "Reexport", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "Test", "Zygote"]
+git-tree-sha1 = "96dc065bf4a998e8adeebc0ff1302902b6e59362"
 uuid = "587475ba-b771-5e3f-ad9e-33799f191a9c"
-version = "0.12.4"
+version = "0.13.4"
+
+[[FoldsThreads]]
+deps = ["Accessors", "FunctionWrappers", "InitialValues", "SplittablesBase", "Transducers"]
+git-tree-sha1 = "eb8e1989b9028f7e0985b4268dabe94682249025"
+uuid = "9c68100b-dfe1-47cf-94c8-95104e173443"
+version = "0.1.1"
 
 [[Fontconfig_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
-git-tree-sha1 = "35895cf184ceaab11fd778b4590144034a167a2f"
+git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
 uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
-version = "2.13.1+14"
+version = "2.13.93+0"
 
 [[Formatting]]
 deps = ["Printf"]
@@ -427,16 +627,16 @@ uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
 version = "0.4.2"
 
 [[ForwardDiff]]
-deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "NaNMath", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "e2af66012e08966366a43251e1fd421522908be6"
+deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
+git-tree-sha1 = "2f18915445b248731ec5db4e4a17e451020bf21e"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
-version = "0.10.18"
+version = "0.10.30"
 
 [[FreeType2_jll]]
 deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
-git-tree-sha1 = "cbd58c9deb1d304f5a245a0b7eb841a2560cfec6"
+git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
 uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
-version = "2.10.1+5"
+version = "2.10.4+0"
 
 [[FriBidi_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -450,10 +650,9 @@ uuid = "069b7b12-0de2-55c6-9aab-29f3d0a68a2e"
 version = "1.1.2"
 
 [[Functors]]
-deps = ["MacroTools"]
-git-tree-sha1 = "a7bb2af991c43dcf5c3455d276dd83976799634f"
+git-tree-sha1 = "223fffa49ca0ff9ce4f875be001ffe173b2b7de4"
 uuid = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
-version = "0.2.1"
+version = "0.2.8"
 
 [[Future]]
 deps = ["Random"]
@@ -461,45 +660,57 @@ uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
 
 [[GLFW_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
-git-tree-sha1 = "dba1e8614e98949abfa60480b13653813d8f0157"
+git-tree-sha1 = "51d2dfe8e590fbd74e7a842cf6d13d8a2f45dc01"
 uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
-version = "3.3.5+0"
+version = "3.3.6+0"
 
 [[GPUArrays]]
-deps = ["AbstractFFTs", "Adapt", "LinearAlgebra", "Printf", "Random", "Serialization", "Statistics"]
-git-tree-sha1 = "ececbf05f8904c92814bdbd0aafd5540b0bf2e9a"
+deps = ["Adapt", "GPUArraysCore", "LLVM", "LinearAlgebra", "Printf", "Random", "Reexport", "Serialization", "Statistics"]
+git-tree-sha1 = "73145f1d724b5ee0e90098aec39a65e9697429a6"
 uuid = "0c68f7d7-f131-5f86-a1c3-88cf8149b2d7"
-version = "7.0.1"
+version = "8.4.2"
+
+[[GPUArraysCore]]
+deps = ["Adapt"]
+git-tree-sha1 = "d88b17a38322e153c519f5a9ed8d91e9baa03d8f"
+uuid = "46192b85-c4d5-4398-a991-12ede77f4527"
+version = "0.1.1"
 
 [[GPUCompiler]]
-deps = ["DataStructures", "ExprTools", "InteractiveUtils", "LLVM", "Libdl", "Logging", "TimerOutputs", "UUIDs"]
-git-tree-sha1 = "03c3fb77362c08c3722bcef8dec488b708a95d52"
+deps = ["ExprTools", "InteractiveUtils", "LLVM", "Libdl", "Logging", "TimerOutputs", "UUIDs"]
+git-tree-sha1 = "1067cd05184719ba86f19cf1d49d57f0bcbabbf6"
 uuid = "61eb1bfa-7361-4325-ad38-22787b887f55"
-version = "0.12.4"
+version = "0.16.2"
 
 [[GR]]
-deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
-git-tree-sha1 = "b83e3125048a9c3158cbb7ca423790c7b1b57bea"
+deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "RelocatableFolders", "Serialization", "Sockets", "Test", "UUIDs"]
+git-tree-sha1 = "037a1ca47e8a5989cc07d19729567bb71bfabd0c"
 uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
-version = "0.57.5"
+version = "0.66.0"
 
 [[GR_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
-git-tree-sha1 = "e14907859a1d3aee73a019e7b3c98e9e7b8b5b3e"
+git-tree-sha1 = "c8ab731c9127cd931c93221f65d6a1008dad7256"
 uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
-version = "0.57.3+0"
+version = "0.66.0+0"
 
 [[GalacticOptim]]
-deps = ["ArrayInterface", "ConsoleProgressMonitor", "DiffResults", "DocStringExtensions", "Logging", "LoggingExtras", "Printf", "ProgressLogging", "Reexport", "Requires", "SciMLBase", "TerminalLoggers"]
-git-tree-sha1 = "fd355a5e3657d4159fb8dbf9d04138b115ac1442"
+deps = ["ArrayInterfaceCore", "ConsoleProgressMonitor", "DiffResults", "DocStringExtensions", "Logging", "LoggingExtras", "Pkg", "Printf", "ProgressLogging", "Reexport", "Requires", "SciMLBase", "TerminalLoggers"]
+git-tree-sha1 = "6725ceb3d9afbbae9ad08aa7ef206a6ab9559600"
 uuid = "a75be94c-b780-496d-a8a9-0878b188d577"
-version = "2.0.3"
+version = "3.4.0"
+
+[[GenericSchur]]
+deps = ["LinearAlgebra", "Printf"]
+git-tree-sha1 = "fb69b2a645fa69ba5f474af09221b9308b160ce6"
+uuid = "c145ed77-6b09-5dd9-b285-bf645a82121e"
+version = "0.5.3"
 
 [[GeometryBasics]]
 deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
-git-tree-sha1 = "15ff9a14b9e1218958d3530cc288cf31465d9ae2"
+git-tree-sha1 = "83ea630384a13fc4f002b77690bc0afeb4255ac9"
 uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
-version = "0.3.13"
+version = "0.4.2"
 
 [[Gettext_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
@@ -509,26 +720,62 @@ version = "0.21.0+0"
 
 [[Glib_jll]]
 deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
-git-tree-sha1 = "47ce50b742921377301e15005c96e979574e130b"
+git-tree-sha1 = "a32d672ac2c967f3deb8a81d828afc739c838a06"
 uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
-version = "2.68.1+0"
+version = "2.68.3+2"
 
 [[GlobalSensitivity]]
 deps = ["Distributions", "FFTW", "ForwardDiff", "KernelDensity", "LinearAlgebra", "Parameters", "QuasiMonteCarlo", "Random", "RecursiveArrayTools", "Statistics", "StatsBase", "Trapz"]
-git-tree-sha1 = "01ad95275c8578acd7cf6cdf987501e23f0a9830"
+git-tree-sha1 = "a083eb2d419b80e0c9edbf39ad8fad00eead152d"
 uuid = "af5da776-676b-467e-8baf-acd8249e4f0f"
-version = "1.1.0"
+version = "2.0.0"
+
+[[Graphite2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
+uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
+version = "1.3.14+0"
+
+[[Graphs]]
+deps = ["ArnoldiMethod", "Compat", "DataStructures", "Distributed", "Inflate", "LinearAlgebra", "Random", "SharedArrays", "SimpleTraits", "SparseArrays", "Statistics"]
+git-tree-sha1 = "db5c7e27c0d46fd824d470a3c32a4fc6c935fa96"
+uuid = "86223c79-3864-5bf0-83f7-82e725a168b6"
+version = "1.7.1"
 
 [[Grisu]]
 git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
 uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
 version = "1.0.2"
 
+[[Groebner]]
+deps = ["AbstractAlgebra", "Combinatorics", "Logging", "MultivariatePolynomials", "Primes", "Random"]
+git-tree-sha1 = "5531337afa01d679c8ce97ff751291fd4760e962"
+uuid = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
+version = "0.2.8"
+
+[[GroupsCore]]
+deps = ["Markdown", "Random"]
+git-tree-sha1 = "9e1a5e9f3b81ad6a5c613d181664a0efc6fe6dd7"
+uuid = "d5909c97-4eac-4ecc-a3dc-fdd0858a4120"
+version = "0.4.0"
+
 [[HTTP]]
-deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
-git-tree-sha1 = "c6a1fff2fd4b1da29d3dccaffb1e1001244d844e"
+deps = ["Base64", "CodecZlib", "Dates", "IniFile", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
+git-tree-sha1 = "ed47af35905b7cc8f1a522ca684b35a212269bd8"
 uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
-version = "0.9.12"
+version = "1.2.0"
+
+[[HarfBuzz_jll]]
+deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
+git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
+uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
+version = "2.8.1+1"
+
+[[HostCPUFeatures]]
+deps = ["BitTwiddlingConvenienceFunctions", "IfElse", "Libdl", "Static"]
+git-tree-sha1 = "b7b88a4716ac33fe31d6556c02fc60017594343c"
+uuid = "3e5b6fbb-0976-4d2c-9146-d79de83f2fb0"
+version = "0.1.8"
 
 [[Hwloc]]
 deps = ["Hwloc_jll"]
@@ -538,20 +785,32 @@ version = "2.0.0"
 
 [[Hwloc_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "3395d4d4aeb3c9d31f5929d32760d8baeee88aaf"
+git-tree-sha1 = "303d70c961317c4c20fafaf5dbe0e6d610c38542"
 uuid = "e33a78d0-f292-5ffc-b300-72abe9b543c8"
-version = "2.5.0+0"
+version = "2.7.1+0"
+
+[[HypergeometricFunctions]]
+deps = ["DualNumbers", "LinearAlgebra", "OpenLibm_jll", "SpecialFunctions", "Test"]
+git-tree-sha1 = "709d864e3ed6e3545230601f94e11ebc65994641"
+uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
+version = "0.3.11"
+
+[[IOCapture]]
+deps = ["Logging", "Random"]
+git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a"
+uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
+version = "0.2.2"
 
 [[IRTools]]
 deps = ["InteractiveUtils", "MacroTools", "Test"]
-git-tree-sha1 = "95215cd0076a150ef46ff7928892bc341864c73c"
+git-tree-sha1 = "af14a478780ca78d5eb9908b263023096c2b9d64"
 uuid = "7869d1d1-7146-5819-86e3-90919afe41df"
-version = "0.4.3"
+version = "0.4.6"
 
 [[IfElse]]
-git-tree-sha1 = "28e837ff3e7a6c3cdb252ce49fb412c8eb3caeef"
+git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
 uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
-version = "0.1.0"
+version = "0.1.1"
 
 [[Inflate]]
 git-tree-sha1 = "f5fc07d4e706b84f72d54eedcc1c13d92fb0871c"
@@ -559,10 +818,19 @@ uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
 version = "0.1.2"
 
 [[IniFile]]
-deps = ["Test"]
-git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
+git-tree-sha1 = "f550e6e32074c939295eb5ea6de31849ac2c9625"
 uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
-version = "0.5.0"
+version = "0.5.1"
+
+[[InitialValues]]
+git-tree-sha1 = "4da0f88e9a39111c2fa3add390ab15f3a44f3ca3"
+uuid = "22cec73e-a1b8-11e9-2c92-598750a2cf9c"
+version = "0.3.1"
+
+[[IntegerMathUtils]]
+git-tree-sha1 = "f366daebdfb079fd1fe4e3d560f99a0c892e15bc"
+uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235"
+version = "0.1.0"
 
 [[IntelOpenMP_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -576,26 +844,37 @@ uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
 [[Interpolations]]
 deps = ["AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
-git-tree-sha1 = "1470c80592cf1f0a35566ee5e93c5f8221ebc33a"
+git-tree-sha1 = "b7bc05649af456efc75d178846f47006c2c4c3c7"
 uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
-version = "0.13.3"
+version = "0.13.6"
 
 [[IntervalSets]]
-deps = ["Dates", "EllipsisNotation", "Statistics"]
-git-tree-sha1 = "3cc368af3f110a767ac786560045dceddfc16758"
+deps = ["Dates", "Random", "Statistics"]
+git-tree-sha1 = "57af5939800bce15980bddd2426912c4f83012d8"
 uuid = "8197267c-284f-5f27-9208-e0e47529a953"
-version = "0.5.3"
+version = "0.7.1"
+
+[[InverseFunctions]]
+deps = ["Test"]
+git-tree-sha1 = "b3364212fb5d870f724876ffcd34dd8ec6d98918"
+uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
+version = "0.1.7"
+
+[[IrrationalConstants]]
+git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
+uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
+version = "0.1.1"
 
 [[IterTools]]
-git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
+git-tree-sha1 = "fa6287a4469f5e048d763df38279ee729fbd44e5"
 uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
-version = "1.3.0"
+version = "1.4.0"
 
 [[IterativeSolvers]]
 deps = ["LinearAlgebra", "Printf", "Random", "RecipesBase", "SparseArrays"]
-git-tree-sha1 = "1a8c6237e78b714e901e406c096fc8a65528af7d"
+git-tree-sha1 = "1169632f425f79429f245113b775a0e3d121457c"
 uuid = "42fd0dbc-a981-5370-80f2-aaf504508153"
-version = "0.9.1"
+version = "0.9.2"
 
 [[IteratorInterfaceExtensions]]
 git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
@@ -603,34 +882,46 @@ uuid = "82899510-4779-5014-852e-03e436cf321d"
 version = "1.0.0"
 
 [[JLD2]]
-deps = ["DataStructures", "FileIO", "MacroTools", "Mmap", "Pkg", "Printf", "Reexport", "TranscodingStreams", "UUIDs"]
-git-tree-sha1 = "4813826871754cf52607e76ad37acb36ccf52719"
+deps = ["FileIO", "MacroTools", "Mmap", "OrderedCollections", "Pkg", "Printf", "Reexport", "TranscodingStreams", "UUIDs"]
+git-tree-sha1 = "81b9477b49402b47fbe7f7ae0b252077f53e4a08"
 uuid = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
-version = "0.4.11"
+version = "0.4.22"
 
 [[JLLWrappers]]
 deps = ["Preferences"]
-git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
+git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1"
 uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
-version = "1.3.0"
+version = "1.4.1"
 
 [[JSON]]
 deps = ["Dates", "Mmap", "Parsers", "Unicode"]
-git-tree-sha1 = "81690084b6198a2e1da36fcfda16eeca9f9f24e4"
+git-tree-sha1 = "3c837543ddb02250ef42f4738347454f95079d4e"
 uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
-version = "0.21.1"
+version = "0.21.3"
 
 [[JpegTurbo_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
+git-tree-sha1 = "b53380851c6e6664204efb2e62cd24fa5c47e4ba"
 uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
-version = "2.1.0+0"
+version = "2.1.2+0"
 
 [[JuliaFormatter]]
 deps = ["CSTParser", "CommonMark", "DataStructures", "Pkg", "Tokenize"]
-git-tree-sha1 = "9e7476b5e1dc749e525497eef53809893cb6c898"
+git-tree-sha1 = "6f13ba89febc5c12f882902e1f5dcd11a8913fa5"
 uuid = "98e50ef6-434e-11e9-1051-2b60c6c9e899"
-version = "0.14.8"
+version = "1.0.7"
+
+[[JuliaVariables]]
+deps = ["MLStyle", "NameResolution"]
+git-tree-sha1 = "49fb3cb53362ddadb4415e9b73926d6b40709e70"
+uuid = "b14d175d-62b4-44ba-8fb7-3064adc8c3ec"
+version = "0.2.4"
+
+[[JumpProcesses]]
+deps = ["ArrayInterfaceCore", "DataStructures", "DiffEqBase", "DocStringExtensions", "FunctionWrappers", "Graphs", "LinearAlgebra", "Markdown", "PoissonRandom", "Random", "RandomNumbers", "RecursiveArrayTools", "Reexport", "SciMLBase", "StaticArrays", "TreeViews", "UnPack"]
+git-tree-sha1 = "4aa139750616fee7216ddcb30652357c60c3683e"
+uuid = "ccbc3e58-028d-4f4c-8cd5-9ae44345cda5"
+version = "9.0.1"
 
 [[Juno]]
 deps = ["Base64", "Logging", "Media", "Profile"]
@@ -638,11 +929,29 @@ git-tree-sha1 = "07cb43290a840908a771552911a6274bc6c072c7"
 uuid = "e5e0dc1b-0480-54bc-9374-aad01c23163d"
 version = "0.8.4"
 
+[[KLU]]
+deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse_jll"]
+git-tree-sha1 = "cae5e3dfd89b209e01bcd65b3a25e74462c67ee0"
+uuid = "ef3ab10e-7fda-4108-b977-705223b18434"
+version = "0.3.0"
+
 [[KernelDensity]]
 deps = ["Distributions", "DocStringExtensions", "FFTW", "Interpolations", "StatsBase"]
-git-tree-sha1 = "591e8dc09ad18386189610acafb970032c519707"
+git-tree-sha1 = "0a7ca818440ce8c70ebb5d42ac4ebf3205675f04"
 uuid = "5ab0869b-81aa-558d-bb23-cbf5423bbe9b"
-version = "0.6.3"
+version = "0.6.4"
+
+[[Krylov]]
+deps = ["LinearAlgebra", "Printf", "SparseArrays"]
+git-tree-sha1 = "a2327039e1c84615e22d662adb3df113caf44b70"
+uuid = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
+version = "0.8.3"
+
+[[KrylovKit]]
+deps = ["LinearAlgebra", "Printf"]
+git-tree-sha1 = "49b0c1dd5c292870577b8f58c51072bd558febb9"
+uuid = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
+version = "0.5.4"
 
 [[LAME_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -650,11 +959,23 @@ git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
 uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
 version = "3.100.1+0"
 
+[[LERC_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434"
+uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
+version = "3.0.0+1"
+
 [[LLVM]]
-deps = ["CEnum", "Libdl", "Printf", "Unicode"]
-git-tree-sha1 = "f57ac3fd2045b50d3db081663837ac5b4096947e"
+deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Printf", "Unicode"]
+git-tree-sha1 = "e7e9184b0bf0158ac4e4aa9daf00041b5909bf1a"
 uuid = "929cbde3-209d-540e-8aea-75f648917ca0"
-version = "3.9.0"
+version = "4.14.0"
+
+[[LLVMExtra_jll]]
+deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg", "TOML"]
+git-tree-sha1 = "771bfe376249626d3ca12bcd58ba243d3f961576"
+uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
+version = "0.0.16+0"
 
 [[LZO_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -663,21 +984,21 @@ uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
 version = "2.10.1+0"
 
 [[LaTeXStrings]]
-git-tree-sha1 = "c7f1c695e06c01b95a67f0cd1d34994f3e7db104"
+git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
 uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
-version = "1.2.1"
+version = "1.3.0"
 
 [[LabelledArrays]]
-deps = ["ArrayInterface", "LinearAlgebra", "MacroTools", "StaticArrays"]
-git-tree-sha1 = "248a199fa42ec62922225334131c9330e1dd72f6"
+deps = ["ArrayInterfaceCore", "ArrayInterfaceStaticArrays", "ChainRulesCore", "LinearAlgebra", "MacroTools", "PreallocationTools", "RecursiveArrayTools", "StaticArrays"]
+git-tree-sha1 = "b86aeff13358dfef82efd9f66a9d44705c9a4746"
 uuid = "2ee39098-c373-598a-b85f-a56591580800"
-version = "1.6.1"
+version = "1.11.1"
 
 [[Latexify]]
 deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
-git-tree-sha1 = "a4b12a1bd2ebade87891ab7e36fdbce582301a92"
+git-tree-sha1 = "1a43be956d433b5d0321197150c2f94e16c0aaa0"
 uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
-version = "0.15.6"
+version = "0.15.16"
 
 [[LatinHypercubeSampling]]
 deps = ["Random", "StableRNGs", "StatsBase", "Test"]
@@ -691,15 +1012,51 @@ git-tree-sha1 = "7f5b02258a3ca0221a6a9710b0a0a2e8fb4957fe"
 uuid = "73f95e8e-ec14-4e6a-8b18-0d2e271c4e55"
 version = "0.0.1"
 
+[[LayoutPointers]]
+deps = ["ArrayInterface", "ArrayInterfaceOffsetArrays", "ArrayInterfaceStaticArrays", "LinearAlgebra", "ManualMemory", "SIMDTypes", "Static"]
+git-tree-sha1 = "b67e749fb35530979839e7b4b606a97105fe4f1c"
+uuid = "10f19ff3-798f-405d-979b-55457f8fc047"
+version = "0.1.10"
+
+[[Lazy]]
+deps = ["MacroTools"]
+git-tree-sha1 = "1370f8202dac30758f3c345f9909b97f53d87d3f"
+uuid = "50d2b5c4-7a5e-59d5-8109-a42b560f39c0"
+version = "0.15.1"
+
+[[LazyArrays]]
+deps = ["ArrayLayouts", "FillArrays", "LinearAlgebra", "MacroTools", "MatrixFactorizations", "SparseArrays", "StaticArrays"]
+git-tree-sha1 = "d9a962fac652cc6b0224622b18199f0ed46d316a"
+uuid = "5078a376-72f3-5289-bfd5-ec5146d43c02"
+version = "0.22.11"
+
 [[LazyArtifacts]]
 deps = ["Artifacts", "Pkg"]
 uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
 
+[[LazyBandedMatrices]]
+deps = ["ArrayLayouts", "BandedMatrices", "BlockArrays", "BlockBandedMatrices", "FillArrays", "LazyArrays", "LinearAlgebra", "MatrixFactorizations", "SparseArrays", "StaticArrays"]
+git-tree-sha1 = "034d371419140f14a986ab7325d11f90f30b0c6d"
+uuid = "d7e5e226-e90b-4449-9968-0f923699bf6f"
+version = "0.7.17"
+
+[[LeastSquaresOptim]]
+deps = ["FiniteDiff", "ForwardDiff", "LinearAlgebra", "Optim", "Printf", "SparseArrays", "Statistics", "SuiteSparse"]
+git-tree-sha1 = "06ea4a7c438f434dc0dc8d03c72e61ee0bf3629d"
+uuid = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
+version = "0.8.3"
+
 [[LeftChildRightSiblingTrees]]
 deps = ["AbstractTrees"]
-git-tree-sha1 = "71be1eb5ad19cb4f61fa8c73395c0338fd092ae0"
+git-tree-sha1 = "fb6803dafae4a5d62ea5cab204b1e657d9737e7f"
 uuid = "1d6d02ad-be62-4b6b-8a6d-2f90e265016e"
-version = "0.1.2"
+version = "0.2.0"
+
+[[LevyArea]]
+deps = ["LinearAlgebra", "Random", "SpecialFunctions"]
+git-tree-sha1 = "56513a09b8e0ae6485f34401ea9e2f31357958ec"
+uuid = "2d8b4e74-eb68-11e8-0fb9-d5eb67b50637"
+version = "1.0.0"
 
 [[LibCURL]]
 deps = ["LibCURL_jll", "MozillaCACerts_jll"]
@@ -728,9 +1085,9 @@ uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 
 [[Libffi_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "761a393aeccd6aa92ec3515e428c26bf99575b3b"
+git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
 uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
-version = "3.2.2+0"
+version = "3.2.2+1"
 
 [[Libgcrypt_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
@@ -763,10 +1120,10 @@ uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
 version = "2.35.0+0"
 
 [[Libtiff_jll]]
-deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
-git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
+deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
+git-tree-sha1 = "3eb79b0ca5764d4799c06699573fd8f533259713"
 uuid = "89763e89-9b03-5906-acba-b20f662cd828"
-version = "4.3.0+0"
+version = "4.4.0+0"
 
 [[Libuuid_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -787,56 +1144,102 @@ uuid = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
 version = "7.1.1"
 
 [[LinearAlgebra]]
-deps = ["Libdl"]
+deps = ["Libdl", "libblastrampoline_jll"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
+[[LinearSolve]]
+deps = ["ArrayInterfaceCore", "DocStringExtensions", "FastLapackInterface", "GPUArraysCore", "IterativeSolvers", "KLU", "Krylov", "KrylovKit", "LinearAlgebra", "RecursiveFactorization", "Reexport", "SciMLBase", "Setfield", "SparseArrays", "SuiteSparse", "UnPack"]
+git-tree-sha1 = "92cc95b66f1459d230af9e67089eeeea6c6b2ee9"
+uuid = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
+version = "1.23.0"
+
+[[Literate]]
+deps = ["Base64", "IOCapture", "JSON", "REPL"]
+git-tree-sha1 = "5b5ec7696d40868945c407f28a6672a230448b70"
+uuid = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
+version = "2.13.4"
+
 [[LogExpFunctions]]
-deps = ["DocStringExtensions", "LinearAlgebra"]
-git-tree-sha1 = "7bd5f6565d80b6bf753738d2bc40a5dfea072070"
+deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
+git-tree-sha1 = "7c88f63f9f0eb5929f15695af9a4d7d3ed278a91"
 uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
-version = "0.2.5"
+version = "0.3.16"
 
 [[Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
 [[LoggingExtras]]
 deps = ["Dates", "Logging"]
-git-tree-sha1 = "dfeda1c1130990428720de0024d4516b1902ce98"
+git-tree-sha1 = "5d4d2d9904227b8bd66386c1138cf4d5ffa826bf"
 uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
-version = "0.4.7"
+version = "0.4.9"
 
 [[LoopVectorization]]
-deps = ["ArrayInterface", "DocStringExtensions", "IfElse", "LinearAlgebra", "OffsetArrays", "Polyester", "Requires", "SLEEFPirates", "Static", "StrideArraysCore", "ThreadingUtilities", "UnPack", "VectorizationBase"]
-git-tree-sha1 = "20316f08f70fae085ed90c7169ae318c036ee83b"
+deps = ["ArrayInterface", "ArrayInterfaceCore", "ArrayInterfaceOffsetArrays", "ArrayInterfaceStaticArrays", "CPUSummary", "ChainRulesCore", "CloseOpenIntervals", "DocStringExtensions", "ForwardDiff", "HostCPUFeatures", "IfElse", "LayoutPointers", "LinearAlgebra", "OffsetArrays", "PolyesterWeave", "SIMDDualNumbers", "SIMDTypes", "SLEEFPirates", "SpecialFunctions", "Static", "ThreadingUtilities", "UnPack", "VectorizationBase"]
+git-tree-sha1 = "adc9421494fd93e31a18a66e49d79615ad6b2efa"
 uuid = "bdcacae8-1622-11e9-2a5c-532679323890"
-version = "0.12.49"
+version = "0.12.120"
+
+[[Lux]]
+deps = ["Adapt", "CUDA", "ChainRulesCore", "ComponentArrays", "FillArrays", "Functors", "LinearAlgebra", "Markdown", "NNlib", "NNlibCUDA", "Optimisers", "Random", "Requires", "Setfield", "SparseArrays", "Statistics", "Zygote"]
+git-tree-sha1 = "94dc5071b0a99368ec4588b90046016db86f702d"
+uuid = "b2108857-7c20-44ae-9111-449ecde12c47"
+version = "0.4.11"
 
 [[MKL_jll]]
 deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
-git-tree-sha1 = "c253236b0ed414624b083e6b72bfe891fbd2c7af"
+git-tree-sha1 = "e595b205efd49508358f7dc670a940c790204629"
 uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
-version = "2021.1.1+1"
+version = "2022.0.0+0"
+
+[[MLStyle]]
+git-tree-sha1 = "c4f433356372cc8838da59e3608be4b0c4c2c280"
+uuid = "d8e11817-5142-5d16-987a-aa16d5891078"
+version = "0.4.13"
+
+[[MLUtils]]
+deps = ["ChainRulesCore", "DelimitedFiles", "FLoops", "FoldsThreads", "Random", "ShowCases", "Statistics", "StatsBase", "Transducers"]
+git-tree-sha1 = "79cc42c45972b176339988fffdcb5360ef841bbc"
+uuid = "f1d291b0-491e-4a28-83b9-f70985020b54"
+version = "0.2.9"
 
 [[MacroTools]]
 deps = ["Markdown", "Random"]
-git-tree-sha1 = "6a8a2a625ab0dea913aba95c11370589e0239ff0"
+git-tree-sha1 = "3d3e902b31198a27340d0bf00d6ac452866021cf"
 uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
-version = "0.5.6"
+version = "0.5.9"
+
+[[ManualMemory]]
+git-tree-sha1 = "bcaef4fc7a0cfe2cba636d84cda54b5e4e4ca3cd"
+uuid = "d125e4d3-2237-4719-b19c-fa641b8a4667"
+version = "0.1.8"
 
 [[Markdown]]
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
+[[MatrixFactorizations]]
+deps = ["ArrayLayouts", "LinearAlgebra", "Printf", "Random"]
+git-tree-sha1 = "2212d36f97e01347adb1460a6914e20f2feee853"
+uuid = "a3b82374-2e81-5b9e-98ce-41277c0e4c87"
+version = "0.9.1"
+
 [[MbedTLS]]
-deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
-git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
+deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "Random", "Sockets"]
+git-tree-sha1 = "9f4f5a42de3300439cb8300236925670f844a555"
 uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
-version = "1.0.3"
+version = "1.1.1"
 
 [[MbedTLS_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
 
+[[Measurements]]
+deps = ["Calculus", "LinearAlgebra", "Printf", "RecipesBase", "Requires"]
+git-tree-sha1 = "dd8b9e6d7be9731fdaecc813acc5c3083496a251"
+uuid = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
+version = "2.7.2"
+
 [[Measures]]
 git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
 uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
@@ -848,20 +1251,38 @@ git-tree-sha1 = "75a54abd10709c01f1b86b84ec225d26e840ed58"
 uuid = "e89f7d12-3494-54d1-8411-f7d8b9ae1f27"
 version = "0.5.0"
 
+[[Memoize]]
+deps = ["MacroTools"]
+git-tree-sha1 = "2b1dfcba103de714d31c033b5dacc2e4a12c7caa"
+uuid = "c03570c3-d221-55d1-a50c-7939bbd78826"
+version = "0.4.4"
+
+[[Metatheory]]
+deps = ["AutoHashEquals", "DataStructures", "Dates", "DocStringExtensions", "Parameters", "Reexport", "TermInterface", "ThreadsX", "TimerOutputs"]
+git-tree-sha1 = "a160e323d3684889e6026914576f1f4288de131d"
+uuid = "e9d8d322-4543-424a-9be4-0cc815abe26c"
+version = "1.3.4"
+
+[[MicroCollections]]
+deps = ["BangBang", "InitialValues", "Setfield"]
+git-tree-sha1 = "6bb7786e4f24d44b4e29df03c69add1b63d88f01"
+uuid = "128add7d-3638-4c79-886c-908ea0c25c34"
+version = "0.1.2"
+
 [[Missings]]
 deps = ["DataAPI"]
-git-tree-sha1 = "4ea90bd5d3985ae1f9a908bd4500ae88921c5ce7"
+git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
 uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
-version = "1.0.0"
+version = "1.0.2"
 
 [[Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
 [[ModelingToolkit]]
-deps = ["AbstractTrees", "ArrayInterface", "ConstructionBase", "DataStructures", "DiffEqBase", "DiffEqJump", "DiffRules", "Distributed", "Distributions", "DocStringExtensions", "DomainSets", "IfElse", "JuliaFormatter", "LabelledArrays", "Latexify", "Libdl", "LightGraphs", "LinearAlgebra", "MacroTools", "NaNMath", "NonlinearSolve", "RecursiveArrayTools", "Reexport", "Requires", "RuntimeGeneratedFunctions", "SafeTestsets", "SciMLBase", "Serialization", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicUtils", "Symbolics", "UnPack", "Unitful"]
-git-tree-sha1 = "7344cc0ba1e2c4933f9b2545b8860483a9acf0d4"
+deps = ["AbstractTrees", "ArrayInterfaceCore", "Combinatorics", "ConstructionBase", "DataStructures", "DiffEqBase", "DiffEqCallbacks", "DiffRules", "Distributed", "Distributions", "DocStringExtensions", "DomainSets", "ForwardDiff", "Graphs", "IfElse", "InteractiveUtils", "JuliaFormatter", "JumpProcesses", "LabelledArrays", "Latexify", "Libdl", "LinearAlgebra", "MacroTools", "NaNMath", "NonlinearSolve", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLBase", "Serialization", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicUtils", "Symbolics", "UnPack", "Unitful"]
+git-tree-sha1 = "98919c7f37fee67d7f625f8c453a85673706ea89"
 uuid = "961ee093-0014-501f-94e3-6117800e7a78"
-version = "5.21.0"
+version = "8.18.1"
 
 [[MozillaCACerts_jll]]
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
@@ -872,22 +1293,22 @@ uuid = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221"
 version = "0.2.2"
 
 [[MultivariatePolynomials]]
-deps = ["DataStructures", "LinearAlgebra", "MutableArithmetics"]
-git-tree-sha1 = "db4718c1b40e0b0ff739159c7230d5266bbfc7db"
+deps = ["ChainRulesCore", "DataStructures", "LinearAlgebra", "MutableArithmetics"]
+git-tree-sha1 = "393fc4d82a73c6fe0e2963dd7c882b09257be537"
 uuid = "102ac46a-7ee4-5c85-9060-abc95bfdeaa3"
-version = "0.3.17"
+version = "0.4.6"
 
 [[MutableArithmetics]]
 deps = ["LinearAlgebra", "SparseArrays", "Test"]
-git-tree-sha1 = "3927848ccebcc165952dc0d9ac9aa274a87bfe01"
+git-tree-sha1 = "4e675d6e9ec02061800d6cfb695812becbd03cdf"
 uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
-version = "0.2.20"
+version = "1.0.4"
 
 [[NLSolversBase]]
 deps = ["DiffResults", "Distributed", "FiniteDiff", "ForwardDiff"]
-git-tree-sha1 = "50608f411a1e178e0129eab4110bd56efd08816f"
+git-tree-sha1 = "50310f934e55e5ca3912fb941dec199b49ca9b68"
 uuid = "d41bc354-129a-5804-8e4c-c37616107c6c"
-version = "7.8.0"
+version = "7.8.2"
 
 [[NLsolve]]
 deps = ["Distances", "LineSearches", "LinearAlgebra", "NLSolversBase", "Printf", "Reexport"]
@@ -896,30 +1317,36 @@ uuid = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 version = "4.5.1"
 
 [[NNlib]]
-deps = ["Adapt", "ChainRulesCore", "Compat", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
-git-tree-sha1 = "7e6f31cfa39b1ff1c541cc8580b14b0ff4ba22d0"
+deps = ["Adapt", "ChainRulesCore", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
+git-tree-sha1 = "415108fd88d6f55cedf7ee940c7d4b01fad85421"
 uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
-version = "0.7.23"
+version = "0.8.9"
 
 [[NNlibCUDA]]
-deps = ["CUDA", "LinearAlgebra", "NNlib", "Random", "Statistics"]
-git-tree-sha1 = "5c970b9fd6098e5f04349b4d1a43fdd3e69c9e97"
+deps = ["Adapt", "CUDA", "LinearAlgebra", "NNlib", "Random", "Statistics"]
+git-tree-sha1 = "4429261364c5ea5b7308aecaa10e803ace101631"
 uuid = "a00861dc-f156-4864-bf3c-e6376f28a68d"
-version = "0.1.6"
+version = "0.2.4"
 
 [[NaNMath]]
-git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
+git-tree-sha1 = "b086b7ea07f8e38cf122f5016af580881ac914fe"
 uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
-version = "0.3.5"
+version = "0.3.7"
+
+[[NameResolution]]
+deps = ["PrettyPrint"]
+git-tree-sha1 = "1a0fa0e9613f46c9b8c11eee38ebb4f590013c5e"
+uuid = "71a1bf82-56d0-4bbc-8a3c-48b961074391"
+version = "0.1.5"
 
 [[NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 
 [[NonlinearSolve]]
-deps = ["ArrayInterface", "FiniteDiff", "ForwardDiff", "IterativeSolvers", "LinearAlgebra", "RecursiveArrayTools", "RecursiveFactorization", "Reexport", "SciMLBase", "Setfield", "StaticArrays", "UnPack"]
-git-tree-sha1 = "ef18e47df4f3917af35be5e5d7f5d97e8a83b0ec"
+deps = ["ArrayInterfaceCore", "FiniteDiff", "ForwardDiff", "IterativeSolvers", "LinearAlgebra", "RecursiveArrayTools", "RecursiveFactorization", "Reexport", "SciMLBase", "Setfield", "StaticArrays", "UnPack"]
+git-tree-sha1 = "932bbdc22e6a2e0bae8dec35d32e4c8cb6c50f98"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
-version = "0.3.8"
+version = "0.3.21"
 
 [[ObjectFile]]
 deps = ["Reexport", "StructIO"]
@@ -929,21 +1356,29 @@ version = "0.3.7"
 
 [[OffsetArrays]]
 deps = ["Adapt"]
-git-tree-sha1 = "2bf78c5fd7fa56d2bbf1efbadd45c1b8789e6f57"
+git-tree-sha1 = "1ea784113a6aa054c5ebd95945fa5e52c2f378e7"
 uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
-version = "1.10.2"
+version = "1.12.7"
 
 [[Ogg_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
+git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
 uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
-version = "1.3.5+0"
+version = "1.3.5+1"
+
+[[OpenBLAS_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
+uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
+
+[[OpenLibm_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
 
 [[OpenSSL_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
+git-tree-sha1 = "e60321e3f2616584ff98f0a4f18d98ae6f89bbb3"
 uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
-version = "1.1.10+0"
+version = "1.1.17+0"
 
 [[OpenSpecFun_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
@@ -952,10 +1387,34 @@ uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
 version = "0.5.5+0"
 
 [[Optim]]
-deps = ["Compat", "FillArrays", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "SparseArrays", "StatsBase"]
-git-tree-sha1 = "d34366a3abc25c41f88820762ef7dfdfe9306711"
+deps = ["Compat", "FillArrays", "ForwardDiff", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "SparseArrays", "StatsBase"]
+git-tree-sha1 = "7351d1daa3dad1bcf67c79d1ba34dd3f6136c9aa"
 uuid = "429524aa-4258-5aef-a3af-852621145aeb"
-version = "1.3.0"
+version = "1.7.1"
+
+[[Optimisers]]
+deps = ["ChainRulesCore", "Functors", "LinearAlgebra", "Random", "Statistics"]
+git-tree-sha1 = "62844c5525c3f13b3107aa2c25a06208ecadde88"
+uuid = "3bd65402-5787-11e9-1adc-39752487f4e2"
+version = "0.2.8"
+
+[[Optimization]]
+deps = ["ArrayInterfaceCore", "ConsoleProgressMonitor", "DiffResults", "DocStringExtensions", "Logging", "LoggingExtras", "Pkg", "Printf", "ProgressLogging", "Reexport", "Requires", "SciMLBase", "SparseArrays", "TerminalLoggers"]
+git-tree-sha1 = "34e947f0cdb8172f25533279d6abc28d03b29584"
+uuid = "7f7a1694-90dd-40f0-9382-eb1efda571ba"
+version = "3.8.0"
+
+[[OptimizationOptimJL]]
+deps = ["Optim", "Optimization", "Reexport", "SparseArrays"]
+git-tree-sha1 = "76ac41f9e82ba98a600d8a380532adef76b27e15"
+uuid = "36348300-93cb-4f02-beb5-3c3902f8871e"
+version = "0.1.2"
+
+[[OptimizationOptimisers]]
+deps = ["Optimisers", "Optimization", "Printf", "ProgressLogging", "Reexport"]
+git-tree-sha1 = "e2f152fc4adc9a634ca6ec00de2f2500d8642789"
+uuid = "42dfb2eb-d2b4-4451-abcd-913932933ac1"
+version = "0.1.0"
 
 [[Opus_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -969,10 +1428,10 @@ uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
 version = "1.4.1"
 
 [[OrdinaryDiffEq]]
-deps = ["Adapt", "ArrayInterface", "DataStructures", "DiffEqBase", "DocStringExtensions", "ExponentialUtilities", "FastClosures", "FiniteDiff", "ForwardDiff", "LinearAlgebra", "Logging", "MacroTools", "MuladdMacro", "NLsolve", "Polyester", "RecursiveArrayTools", "Reexport", "SparseArrays", "SparseDiffTools", "StaticArrays", "UnPack"]
-git-tree-sha1 = "f865c198eb4041535c9d27e0835c5b59cdb759d4"
+deps = ["Adapt", "ArrayInterface", "ArrayInterfaceGPUArrays", "ArrayInterfaceStaticArrays", "DataStructures", "DiffEqBase", "DocStringExtensions", "ExponentialUtilities", "FastBroadcast", "FastClosures", "FiniteDiff", "ForwardDiff", "LinearAlgebra", "LinearSolve", "Logging", "LoopVectorization", "MacroTools", "MuladdMacro", "NLsolve", "NonlinearSolve", "Polyester", "PreallocationTools", "RecursiveArrayTools", "Reexport", "SciMLBase", "SparseArrays", "SparseDiffTools", "StaticArrays", "UnPack"]
+git-tree-sha1 = "c3b30b0c3ec02849cd30001e3de3f63e5842bbfd"
 uuid = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
-version = "5.59.2"
+version = "6.19.2"
 
 [[PCRE_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -982,21 +1441,21 @@ version = "8.44.0+0"
 
 [[PDMats]]
 deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
-git-tree-sha1 = "4dd403333bcf0909341cfe57ec115152f937d7d8"
+git-tree-sha1 = "cf494dca75a69712a72b80bc48f59dcf3dea63ec"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
-version = "0.11.1"
+version = "0.11.16"
 
 [[Parameters]]
 deps = ["OrderedCollections", "UnPack"]
-git-tree-sha1 = "2276ac65f1e236e0a6ea70baff3f62ad4c625345"
+git-tree-sha1 = "34c0e9ad262e5f7fc75b10a9952ca7692cfc5fbe"
 uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
-version = "0.12.2"
+version = "0.12.3"
 
 [[Parsers]]
 deps = ["Dates"]
-git-tree-sha1 = "c8abc88faa3f7a3950832ac5d6e690881590d6dc"
+git-tree-sha1 = "0044b23da09b5608b4ecacb4e5e6c6332f833a7e"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
-version = "1.1.0"
+version = "2.3.2"
 
 [[Pixman_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -1009,34 +1468,40 @@ deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markd
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 
 [[PlotThemes]]
-deps = ["PlotUtils", "Requires", "Statistics"]
-git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d"
+deps = ["PlotUtils", "Statistics"]
+git-tree-sha1 = "8162b2f8547bc23876edd0c5181b27702ae58dce"
 uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
-version = "2.0.1"
+version = "3.0.0"
 
 [[PlotUtils]]
 deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
-git-tree-sha1 = "ae9a295ac761f64d8c2ec7f9f24d21eb4ffba34d"
+git-tree-sha1 = "9888e59493658e476d3073f1ce24348bdc086660"
 uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
-version = "1.0.10"
+version = "1.3.0"
 
 [[Plots]]
-deps = ["Base64", "Contour", "Dates", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs"]
-git-tree-sha1 = "67db176835858a8e51be8a027e97665f95b4a38b"
+deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "Unzip"]
+git-tree-sha1 = "0a0da27969e8b6b2ee67c112dcf7001a659049a0"
 uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
-version = "1.16.8"
+version = "1.31.4"
 
 [[PoissonRandom]]
-deps = ["Random", "Statistics", "Test"]
-git-tree-sha1 = "44d018211a56626288b5d3f8c6497d28c26dc850"
+deps = ["Random"]
+git-tree-sha1 = "9ac1bb7c15c39620685a3a7babc0651f5c64c35b"
 uuid = "e409e4f3-bfea-5376-8464-e040bb5c01ab"
-version = "0.4.0"
+version = "0.4.1"
 
 [[Polyester]]
-deps = ["ArrayInterface", "IfElse", "Requires", "Static", "StrideArraysCore", "ThreadingUtilities", "VectorizationBase"]
-git-tree-sha1 = "04a03d3f8ae906f4196b9085ed51506c4b466340"
+deps = ["ArrayInterface", "BitTwiddlingConvenienceFunctions", "CPUSummary", "IfElse", "ManualMemory", "PolyesterWeave", "Requires", "Static", "StrideArraysCore", "ThreadingUtilities"]
+git-tree-sha1 = "94e20822bd7427b1b1b843a3980003f5d5e8696b"
 uuid = "f517fe37-dbe3-4b94-8317-1923a5111588"
-version = "0.3.1"
+version = "0.6.14"
+
+[[PolyesterWeave]]
+deps = ["BitTwiddlingConvenienceFunctions", "CPUSummary", "IfElse", "Static", "ThreadingUtilities"]
+git-tree-sha1 = "cf82af4e114b0da31c4896aef6c5b8be3fe0916d"
+uuid = "1d0040c9-8b98-4ee7-8388-3f51789ca0ad"
+version = "0.1.7"
 
 [[PositiveFactorizations]]
 deps = ["LinearAlgebra"]
@@ -1044,11 +1509,28 @@ git-tree-sha1 = "17275485f373e6673f7e7f97051f703ed5b15b20"
 uuid = "85a6dd25-e78a-55b7-8502-1745935b8125"
 version = "0.2.4"
 
+[[PreallocationTools]]
+deps = ["Adapt", "ArrayInterfaceCore", "ForwardDiff"]
+git-tree-sha1 = "ba66bf03b84ca3bd0a26aa2bbe96cd9df2f4f9b9"
+uuid = "d236fae5-4411-538c-8e31-a6e3d9e00b46"
+version = "0.4.0"
+
 [[Preferences]]
 deps = ["TOML"]
-git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
+git-tree-sha1 = "47e5f437cc0e7ef2ce8406ce1e7e24d44915f88d"
 uuid = "21216c6a-2e73-6563-6e65-726566657250"
-version = "1.2.2"
+version = "1.3.0"
+
+[[PrettyPrint]]
+git-tree-sha1 = "632eb4abab3449ab30c5e1afaa874f0b98b586e4"
+uuid = "8162dcfd-2161-5ef2-ae6c-7681170c5f98"
+version = "0.2.0"
+
+[[Primes]]
+deps = ["IntegerMathUtils"]
+git-tree-sha1 = "311a2aa90a64076ea0fac2ad7492e914e6feeb81"
+uuid = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae"
+version = "0.5.3"
 
 [[Printf]]
 deps = ["Unicode"]
@@ -1066,98 +1548,129 @@ version = "0.1.4"
 
 [[ProgressMeter]]
 deps = ["Distributed", "Printf"]
-git-tree-sha1 = "afadeba63d90ff223a6a48d2009434ecee2ec9e8"
+git-tree-sha1 = "d7a7aef8f8f2d537104f170139553b14dfe39fe9"
 uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
-version = "1.7.1"
+version = "1.7.2"
 
 [[Qt5Base_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
-git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8"
+git-tree-sha1 = "c6c0f690d0cc7caddb74cef7aa847b824a16b256"
 uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
-version = "5.15.3+0"
+version = "5.15.3+1"
 
 [[QuadGK]]
 deps = ["DataStructures", "LinearAlgebra"]
-git-tree-sha1 = "12fbe86da16df6679be7521dfb39fbc861e1dc7b"
+git-tree-sha1 = "78aadffb3efd2155af139781b8a8df1ef279ea39"
 uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
-version = "2.4.1"
+version = "2.4.2"
 
 [[QuasiMonteCarlo]]
 deps = ["Distributions", "LatinHypercubeSampling", "LatticeRules", "Sobol"]
-git-tree-sha1 = "e1ffcdd1f7a81db4376b474a441691084d5b7a82"
+git-tree-sha1 = "3c4082632b3eddac3eaa7e1d476637101a5e76c5"
 uuid = "8a4e6c94-4038-4cdc-81c3-7e6ffdb2a71b"
-version = "0.2.3"
+version = "0.2.9"
 
 [[REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 
 [[Random]]
-deps = ["Serialization"]
+deps = ["SHA", "Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
 [[Random123]]
-deps = ["Libdl", "Random", "RandomNumbers"]
-git-tree-sha1 = "0e8b146557ad1c6deb1367655e052276690e71a3"
+deps = ["Random", "RandomNumbers"]
+git-tree-sha1 = "afeacaecf4ed1649555a19cb2cad3c141bbc9474"
 uuid = "74087812-796a-5b5d-8853-05524746bad3"
-version = "1.4.2"
+version = "1.5.0"
+
+[[RandomExtensions]]
+deps = ["Random", "SparseArrays"]
+git-tree-sha1 = "062986376ce6d394b23d5d90f01d81426113a3c9"
+uuid = "fb686558-2515-59ef-acaa-46db3789a887"
+version = "0.4.3"
 
 [[RandomNumbers]]
 deps = ["Random", "Requires"]
-git-tree-sha1 = "441e6fc35597524ada7f85e13df1f4e10137d16f"
+git-tree-sha1 = "043da614cc7e95c703498a491e2c21f58a2b8111"
 uuid = "e6cf234a-135c-5ec9-84dd-332b85af5143"
-version = "1.4.0"
+version = "1.5.3"
 
 [[Ratios]]
-git-tree-sha1 = "37d210f612d70f3f7d57d488cb3b6eff56ad4e41"
+deps = ["Requires"]
+git-tree-sha1 = "dc84268fe0e3335a62e315a3a7cf2afa7178a734"
 uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
-version = "0.4.0"
+version = "0.4.3"
+
+[[RealDot]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "9f0a1b71baaf7650f4fa8a1d168c7fb6ee41f0c9"
+uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
+version = "0.1.0"
 
 [[RecipesBase]]
-git-tree-sha1 = "b3fb709f3c97bfc6e948be68beeecb55a0b340ae"
+git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
 uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
-version = "1.1.1"
+version = "1.2.1"
 
 [[RecipesPipeline]]
 deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
-git-tree-sha1 = "9b8e57e3cca8828a1bc759840bfe48d64db9abfb"
+git-tree-sha1 = "2690681814016887462cf5ac37102b51cd9ec781"
 uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
-version = "0.3.3"
+version = "0.6.2"
 
 [[RecursiveArrayTools]]
-deps = ["ArrayInterface", "ChainRulesCore", "DocStringExtensions", "LinearAlgebra", "RecipesBase", "Requires", "StaticArrays", "Statistics", "ZygoteRules"]
-git-tree-sha1 = "b20384ee84f3e0e89cee36dbcb9c44b8bd61e133"
+deps = ["Adapt", "ArrayInterfaceCore", "ArrayInterfaceStaticArraysCore", "ChainRulesCore", "DocStringExtensions", "FillArrays", "GPUArraysCore", "LinearAlgebra", "RecipesBase", "StaticArraysCore", "Statistics", "ZygoteRules"]
+git-tree-sha1 = "4ce7584604489e537b2ab84ed92b4107d03377f0"
 uuid = "731186ca-8d62-57ce-b412-fbd966d074cd"
-version = "2.14.3"
+version = "2.31.2"
 
 [[RecursiveFactorization]]
-deps = ["LinearAlgebra", "LoopVectorization"]
-git-tree-sha1 = "2e1a88c083ebe8ba69bc0b0084d4b4ba4aa35ae0"
+deps = ["LinearAlgebra", "LoopVectorization", "Polyester", "StrideArraysCore", "TriangularSolve"]
+git-tree-sha1 = "3ee71214057e29a8466f5d70cfe745236aa1d9d7"
 uuid = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
-version = "0.1.13"
+version = "0.2.11"
 
 [[Reexport]]
-git-tree-sha1 = "5f6c21241f0f655da3952fd60aa18477cf96c220"
+git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
 uuid = "189a3867-3050-52da-a836-e630ba90ab69"
-version = "1.1.0"
+version = "1.2.2"
+
+[[Referenceables]]
+deps = ["Adapt"]
+git-tree-sha1 = "e681d3bfa49cd46c3c161505caddf20f0e62aaa9"
+uuid = "42d2dcc6-99eb-4e98-b66c-637b7d73030e"
+version = "0.1.2"
+
+[[RegularizationTools]]
+deps = ["Calculus", "Lazy", "LeastSquaresOptim", "LinearAlgebra", "MLStyle", "Memoize", "Optim", "Random", "Underscores"]
+git-tree-sha1 = "d445316cca15281a4b36b63c520123baa256a545"
+uuid = "29dad682-9a27-4bc3-9c72-016788665182"
+version = "0.6.0"
+
+[[RelocatableFolders]]
+deps = ["SHA", "Scratch"]
+git-tree-sha1 = "22c5201127d7b243b9ee1de3b43c408879dff60f"
+uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
+version = "0.3.0"
 
 [[Requires]]
 deps = ["UUIDs"]
-git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
+git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
 uuid = "ae029012-a4dd-5104-9daa-d747884805df"
-version = "1.1.3"
+version = "1.3.0"
 
 [[ResettableStacks]]
 deps = ["StaticArrays"]
-git-tree-sha1 = "622b3e491fb0a85fbfeed6f17dc320a9f46d8929"
+git-tree-sha1 = "256eeeec186fa7f26f2801732774ccf277f05db9"
 uuid = "ae5879a3-cd67-5da8-be7f-38c6eb64a37b"
-version = "1.1.0"
+version = "1.1.1"
 
 [[ReverseDiff]]
-deps = ["DiffResults", "DiffRules", "ForwardDiff", "FunctionWrappers", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "SpecialFunctions", "StaticArrays", "Statistics"]
-git-tree-sha1 = "63ee24ea0689157a1113dbdab10c6cb011d519c4"
+deps = ["ChainRulesCore", "DiffResults", "DiffRules", "ForwardDiff", "FunctionWrappers", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NaNMath", "Random", "SpecialFunctions", "StaticArrays", "Statistics"]
+git-tree-sha1 = "b8e2eb3d8e1530acb73d8949eab3cedb1d43f840"
 uuid = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
-version = "1.9.0"
+version = "1.14.1"
 
 [[Rmath]]
 deps = ["Random", "Rmath_jll"]
@@ -1173,18 +1686,29 @@ version = "0.3.0+0"
 
 [[RuntimeGeneratedFunctions]]
 deps = ["ExprTools", "SHA", "Serialization"]
-git-tree-sha1 = "5975a4f824533fa4240f40d86f1060b9fc80d7cc"
+git-tree-sha1 = "cdc1e4278e91a6ad530770ebb327f9ed83cf10c4"
 uuid = "7e49a35a-f44a-4d26-94aa-eba1b4ca6b47"
-version = "0.5.2"
+version = "0.5.3"
 
 [[SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 
+[[SIMDDualNumbers]]
+deps = ["ForwardDiff", "IfElse", "SLEEFPirates", "VectorizationBase"]
+git-tree-sha1 = "dd4195d308df24f33fb10dde7c22103ba88887fa"
+uuid = "3cdde19b-5bb0-4aaf-8931-af3e248e098b"
+version = "0.1.1"
+
+[[SIMDTypes]]
+git-tree-sha1 = "330289636fb8107c5f32088d2741e9fd7a061a5c"
+uuid = "94e857df-77ce-4151-89e5-788b33177be4"
+version = "0.1.0"
+
 [[SLEEFPirates]]
 deps = ["IfElse", "Static", "VectorizationBase"]
-git-tree-sha1 = "da6d214ffc85b1292f300649ef86d3c4f9aaf25d"
+git-tree-sha1 = "7ee0e13ac7cd77f2c0e93bff8c40c45f05c77a5a"
 uuid = "476501e8-09a2-5ece-8869-fb82de89a1fa"
-version = "0.6.22"
+version = "0.6.33"
 
 [[SafeTestsets]]
 deps = ["Test"]
@@ -1193,41 +1717,51 @@ uuid = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 version = "0.0.1"
 
 [[SciMLBase]]
-deps = ["ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "RecipesBase", "RecursiveArrayTools", "StaticArrays", "Statistics", "Tables", "TreeViews"]
-git-tree-sha1 = "7d60436171978e9b4f73790ebf436fccd307df51"
+deps = ["ArrayInterfaceCore", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "Markdown", "RecipesBase", "RecursiveArrayTools", "StaticArraysCore", "Statistics", "Tables"]
+git-tree-sha1 = "7cb46ff55af945a8b68e148bf22f9325f7221d8d"
 uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
-version = "1.14.0"
+version = "1.45.0"
 
 [[Scratch]]
 deps = ["Dates"]
-git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
+git-tree-sha1 = "f94f779c94e58bf9ea243e77a37e16d9de9126bd"
 uuid = "6c6a2e73-6563-6170-7368-637461726353"
-version = "1.1.0"
+version = "1.1.1"
 
 [[Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
 [[Setfield]]
 deps = ["ConstructionBase", "Future", "MacroTools", "Requires"]
-git-tree-sha1 = "d5640fc570fb1b6c54512f0bd3853866bd298b3e"
+git-tree-sha1 = "38d88503f695eb0301479bc9b0d4320b378bafe5"
 uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
-version = "0.7.0"
+version = "0.8.2"
 
 [[SharedArrays]]
 deps = ["Distributed", "Mmap", "Random", "Serialization"]
 uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
 
+[[ShowCases]]
+git-tree-sha1 = "7f534ad62ab2bd48591bdeac81994ea8c445e4a5"
+uuid = "605ecd9f-84a6-4c9e-81e2-4798472b76a3"
+version = "0.1.0"
+
 [[Showoff]]
 deps = ["Dates", "Grisu"]
 git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
 uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
 version = "1.0.3"
 
+[[SimpleBufferStream]]
+git-tree-sha1 = "874e8867b33a00e784c8a7e4b60afe9e037b74e1"
+uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
+version = "1.1.0"
+
 [[SimpleTraits]]
 deps = ["InteractiveUtils", "MacroTools"]
-git-tree-sha1 = "daf7aec3fe3acb2131388f93a4c409b8c7f62226"
+git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
 uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
-version = "0.9.3"
+version = "0.9.4"
 
 [[Sobol]]
 deps = ["DelimitedFiles", "Random"]
@@ -1240,25 +1774,31 @@ uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
 [[SortingAlgorithms]]
 deps = ["DataStructures"]
-git-tree-sha1 = "2ec1962eba973f383239da22e75218565c390a96"
+git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
 uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
-version = "1.0.0"
+version = "1.0.1"
 
 [[SparseArrays]]
 deps = ["LinearAlgebra", "Random"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [[SparseDiffTools]]
-deps = ["Adapt", "ArrayInterface", "Compat", "DataStructures", "FiniteDiff", "ForwardDiff", "LightGraphs", "LinearAlgebra", "Requires", "SparseArrays", "VertexSafeGraphs"]
-git-tree-sha1 = "be20320958ccd298c98312137a5ebe75a654ebc8"
+deps = ["Adapt", "ArrayInterfaceCore", "ArrayInterfaceStaticArrays", "Compat", "DataStructures", "FiniteDiff", "ForwardDiff", "Graphs", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays", "VertexSafeGraphs"]
+git-tree-sha1 = "32025c052719c6353f22f7c6de7d7b97b7cd2c88"
 uuid = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
-version = "1.13.2"
+version = "1.24.0"
 
 [[SpecialFunctions]]
-deps = ["ChainRulesCore", "LogExpFunctions", "OpenSpecFun_jll"]
-git-tree-sha1 = "a50550fa3164a8c46747e62063b4d774ac1bcf49"
+deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
+git-tree-sha1 = "d75bda01f8c31ebb72df80a46c88b25d1c79c56d"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
-version = "1.5.1"
+version = "2.1.7"
+
+[[SplittablesBase]]
+deps = ["Setfield", "Test"]
+git-tree-sha1 = "39c9f91521de844bad65049efd4f9223e7ed43f9"
+uuid = "171d559e-b47b-412a-8079-5efa626c420e"
+version = "0.1.14"
 
 [[StableRNGs]]
 deps = ["Random", "Test"]
@@ -1268,54 +1808,60 @@ version = "1.0.0"
 
 [[Static]]
 deps = ["IfElse"]
-git-tree-sha1 = "2740ea27b66a41f9d213561a04573da5d3823d4b"
+git-tree-sha1 = "f94f9d627ba3f91e41a815b9f9f977d729e2e06f"
 uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
-version = "0.2.5"
+version = "0.7.6"
 
 [[StaticArrays]]
-deps = ["LinearAlgebra", "Random", "Statistics"]
-git-tree-sha1 = "896d55218776ab8f23fb7b222a5a4a946d4aafc2"
+deps = ["LinearAlgebra", "Random", "StaticArraysCore", "Statistics"]
+git-tree-sha1 = "23368a3313d12a2326ad0035f0db0c0966f438ef"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "1.2.5"
+version = "1.5.2"
+
+[[StaticArraysCore]]
+git-tree-sha1 = "66fe9eb253f910fe8cf161953880cfdaef01cdf0"
+uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+version = "1.0.1"
 
 [[Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [[StatsAPI]]
-git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "2c11d7290036fe7aac9038ff312d3b3a2a5bf89e"
 uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
-version = "1.0.0"
+version = "1.4.0"
 
 [[StatsBase]]
-deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
-git-tree-sha1 = "2f6792d523d7448bbe2fec99eca9218f06cc746d"
+deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "0005d75f43ff23688914536c5e9d5ac94f8077f7"
 uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
-version = "0.33.8"
+version = "0.33.20"
 
 [[StatsFuns]]
-deps = ["LogExpFunctions", "Rmath", "SpecialFunctions"]
-git-tree-sha1 = "30cd8c360c54081f806b1ee14d2eecbef3c04c49"
+deps = ["ChainRulesCore", "HypergeometricFunctions", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "5783b877201a82fc0014cbf381e7e6eb130473a4"
 uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
-version = "0.9.8"
+version = "1.0.1"
 
 [[StochasticDiffEq]]
-deps = ["ArrayInterface", "DataStructures", "DiffEqBase", "DiffEqJump", "DiffEqNoiseProcess", "DocStringExtensions", "FillArrays", "FiniteDiff", "ForwardDiff", "LinearAlgebra", "Logging", "MuladdMacro", "NLsolve", "OrdinaryDiffEq", "Random", "RandomNumbers", "RecursiveArrayTools", "Reexport", "SparseArrays", "SparseDiffTools", "StaticArrays", "UnPack"]
-git-tree-sha1 = "aee830c3b2c96d0e2e9fa40c5cae30d281db0dbd"
+deps = ["Adapt", "ArrayInterface", "DataStructures", "DiffEqBase", "DiffEqNoiseProcess", "DocStringExtensions", "FillArrays", "FiniteDiff", "ForwardDiff", "JumpProcesses", "LevyArea", "LinearAlgebra", "Logging", "MuladdMacro", "NLsolve", "OrdinaryDiffEq", "Random", "RandomNumbers", "RecursiveArrayTools", "Reexport", "SciMLBase", "SparseArrays", "SparseDiffTools", "StaticArrays", "UnPack"]
+git-tree-sha1 = "a518b59fe62a07e007c8f7913e14e2fae697c8a7"
 uuid = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0"
-version = "6.35.0"
+version = "6.51.0"
 
 [[StrideArraysCore]]
-deps = ["ArrayInterface", "Requires", "ThreadingUtilities", "VectorizationBase"]
-git-tree-sha1 = "efcdfcbb8cf91e859f61011de1621be34b550e69"
+deps = ["ArrayInterface", "CloseOpenIntervals", "IfElse", "LayoutPointers", "ManualMemory", "SIMDTypes", "Static", "ThreadingUtilities"]
+git-tree-sha1 = "ac730bd978bf35f9fe45daa0bd1f51e493e97eb4"
 uuid = "7792a7ef-975c-4747-a70f-980b88e8d1da"
-version = "0.1.13"
+version = "0.3.15"
 
 [[StructArrays]]
 deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
-git-tree-sha1 = "000e168f5cc9aded17b6999a560b7c11dda69095"
+git-tree-sha1 = "ec47fb6069c57f1cee2f67541bf8f23415146de7"
 uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
-version = "0.6.0"
+version = "0.6.11"
 
 [[StructIO]]
 deps = ["Test"]
@@ -1327,17 +1873,21 @@ version = "0.3.0"
 deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
 uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
 
+[[SuiteSparse_jll]]
+deps = ["Artifacts", "Libdl", "Pkg", "libblastrampoline_jll"]
+uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
+
 [[SymbolicUtils]]
-deps = ["AbstractTrees", "ChainRulesCore", "Combinatorics", "ConstructionBase", "DataStructures", "DynamicPolynomials", "IfElse", "LabelledArrays", "LinearAlgebra", "MultivariatePolynomials", "NaNMath", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "TimerOutputs"]
-git-tree-sha1 = "91659406d1c4a06bcbf074a11727dff49c35240c"
+deps = ["AbstractTrees", "Bijections", "ChainRulesCore", "Combinatorics", "ConstructionBase", "DataStructures", "DocStringExtensions", "DynamicPolynomials", "IfElse", "LabelledArrays", "LinearAlgebra", "Metatheory", "MultivariatePolynomials", "NaNMath", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "TermInterface", "TimerOutputs"]
+git-tree-sha1 = "027b43d312f6d52187bb16c2d4f0588ddb8c4bb2"
 uuid = "d1185830-fcd6-423d-90d6-eec64667417b"
-version = "0.13.0"
+version = "0.19.11"
 
 [[Symbolics]]
-deps = ["ConstructionBase", "DiffRules", "Distributions", "DocStringExtensions", "DomainSets", "IfElse", "Latexify", "Libdl", "LinearAlgebra", "MacroTools", "NaNMath", "RecipesBase", "Reexport", "Requires", "RuntimeGeneratedFunctions", "SciMLBase", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicUtils", "TreeViews"]
-git-tree-sha1 = "713685972c3991b23a430fea59e32136140f2528"
+deps = ["ArrayInterfaceCore", "ConstructionBase", "DataStructures", "DiffRules", "Distributions", "DocStringExtensions", "DomainSets", "Groebner", "IfElse", "Latexify", "Libdl", "LinearAlgebra", "MacroTools", "Markdown", "Metatheory", "NaNMath", "RecipesBase", "Reexport", "Requires", "RuntimeGeneratedFunctions", "SciMLBase", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicUtils", "TermInterface", "TreeViews"]
+git-tree-sha1 = "0ea9acaf00f81da959a568f5f43d503decce2ca1"
 uuid = "0c5d862f-8b57-4792-8d23-62f2024744c7"
-version = "1.2.2"
+version = "4.10.2"
 
 [[TOML]]
 deps = ["Dates"]
@@ -1350,58 +1900,81 @@ uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
 version = "1.0.1"
 
 [[Tables]]
-deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
-git-tree-sha1 = "8ed4a3ea724dac32670b062be3ef1c1de6773ae8"
+deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "OrderedCollections", "TableTraits", "Test"]
+git-tree-sha1 = "5ce79ce186cc678bbb5c5681ca3379d1ddae11a1"
 uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
-version = "1.4.4"
+version = "1.7.0"
 
 [[Tar]]
 deps = ["ArgTools", "SHA"]
 uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
 
+[[TensorCore]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
+uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
+version = "0.1.1"
+
+[[TermInterface]]
+git-tree-sha1 = "7aa601f12708243987b88d1b453541a75e3d8c7a"
+uuid = "8ea1fca8-c5ef-4a55-8b96-4e9afe9c9a3c"
+version = "0.2.3"
+
 [[TerminalLoggers]]
-deps = ["LeftChildRightSiblingTrees", "Logging", "Markdown", "Printf", "ProgressLogging", "UUIDs"]
-git-tree-sha1 = "d620a061cb2a56930b52bdf5cf908a5c4fa8e76a"
+deps = ["Logging", "Printf"]
+git-tree-sha1 = "987a3ebb20307530775f4def7eb9109cfa881748"
 uuid = "5d786b92-1e48-4d6f-9151-6b4477ca9bed"
-version = "0.1.4"
+version = "0.1.0"
 
 [[Test]]
 deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [[ThreadingUtilities]]
-deps = ["VectorizationBase"]
-git-tree-sha1 = "28f4295cd761ce98db2b5f8c1fe6e5c89561efbe"
+deps = ["ManualMemory"]
+git-tree-sha1 = "f8629df51cab659d70d2e5618a430b4d3f37f2c3"
 uuid = "8290d209-cae3-49c0-8002-c8c24d57dab5"
-version = "0.4.4"
+version = "0.5.0"
+
+[[ThreadsX]]
+deps = ["ArgCheck", "BangBang", "ConstructionBase", "InitialValues", "MicroCollections", "Referenceables", "Setfield", "SplittablesBase", "Transducers"]
+git-tree-sha1 = "d223de97c948636a4f34d1f84d92fd7602dc555b"
+uuid = "ac1d9e8a-700a-412c-b207-f0111f4b6c0d"
+version = "0.1.10"
 
 [[TimerOutputs]]
 deps = ["ExprTools", "Printf"]
-git-tree-sha1 = "209a8326c4f955e2442c07b56029e88bb48299c7"
+git-tree-sha1 = "464d64b2510a25e6efe410e7edab14fffdc333df"
 uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
-version = "0.5.12"
+version = "0.5.20"
 
 [[Tokenize]]
-git-tree-sha1 = "37018506dc445ad7db288442fbb846105f26c43f"
+git-tree-sha1 = "2b3af135d85d7e70b863540160208fa612e736b9"
 uuid = "0796e94c-ce3b-5d07-9a54-7f471281c624"
-version = "0.5.17"
+version = "0.5.24"
 
 [[Tracker]]
-deps = ["Adapt", "DiffRules", "ForwardDiff", "LinearAlgebra", "MacroTools", "NNlib", "NaNMath", "Printf", "Random", "Requires", "SpecialFunctions", "Statistics"]
-git-tree-sha1 = "bf4adf36062afc921f251af4db58f06235504eff"
+deps = ["Adapt", "DiffRules", "ForwardDiff", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NNlib", "NaNMath", "Printf", "Random", "Requires", "SpecialFunctions", "Statistics"]
+git-tree-sha1 = "0874c1b5de1b5529b776cfeca3ec0acfada97b1b"
 uuid = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
-version = "0.2.16"
+version = "0.2.20"
 
 [[TranscodingStreams]]
 deps = ["Random", "Test"]
-git-tree-sha1 = "7c53c35547de1c5b9d46a4797cf6d8253807108c"
+git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
 uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
-version = "0.9.5"
+version = "0.9.6"
+
+[[Transducers]]
+deps = ["Adapt", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "Setfield", "SplittablesBase", "Tables"]
+git-tree-sha1 = "c76399a3bbe6f5a88faa33c8f8a65aa631d95013"
+uuid = "28d57a85-8fef-5791-bfe6-a80928e7c999"
+version = "0.4.73"
 
 [[Trapz]]
-git-tree-sha1 = "aff96deaaa38e3b52a5af1dd3da376d49bf6ec9a"
+git-tree-sha1 = "79eb0ed763084a3e7de81fe1838379ac6a23b6a0"
 uuid = "592b5752-818d-11e9-1e9a-2b8ca4a44cd1"
-version = "2.0.2"
+version = "2.0.3"
 
 [[TreeViews]]
 deps = ["Test"]
@@ -1409,10 +1982,16 @@ git-tree-sha1 = "8d0d7a3fe2f30d6a7f833a5f19f7c7a5b396eae6"
 uuid = "a2a6695c-b41b-5b7d-aed9-dbfdeacea5d7"
 version = "0.3.0"
 
+[[TriangularSolve]]
+deps = ["CloseOpenIntervals", "IfElse", "LayoutPointers", "LinearAlgebra", "LoopVectorization", "Polyester", "Static", "VectorizationBase"]
+git-tree-sha1 = "caf797b6fccbc0d080c44b4cb2319faf78c9d058"
+uuid = "d5829a12-d9aa-46ab-831f-fb7c9ab06edf"
+version = "0.1.12"
+
 [[URIs]]
-git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
+git-tree-sha1 = "e59ecc5a41b000fa94423a578d29290c7266fc10"
 uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
-version = "1.3.0"
+version = "1.4.0"
 
 [[UUIDs]]
 deps = ["Random", "SHA"]
@@ -1423,26 +2002,42 @@ git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
 uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
 version = "1.0.2"
 
+[[Underscores]]
+git-tree-sha1 = "6e6de5a5e7116dcff8effc99f6f55230c61f6862"
+uuid = "d9a01c3f-67ce-4d8c-9b55-35f6e4050bb1"
+version = "3.0.0"
+
 [[Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 
+[[UnicodeFun]]
+deps = ["REPL"]
+git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
+uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
+version = "0.4.1"
+
 [[Unitful]]
 deps = ["ConstructionBase", "Dates", "LinearAlgebra", "Random"]
-git-tree-sha1 = "b3682a0559219355f1e3c8024e9f97adce2d4623"
+git-tree-sha1 = "b649200e887a487468b71821e2644382699f1b0f"
 uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
-version = "1.8.0"
+version = "1.11.0"
+
+[[Unzip]]
+git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
+uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
+version = "0.1.2"
 
 [[VectorizationBase]]
-deps = ["ArrayInterface", "Hwloc", "IfElse", "Libdl", "LinearAlgebra", "Static"]
-git-tree-sha1 = "0ba060e248edfacacafd764926cdd6de51af1343"
+deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static"]
+git-tree-sha1 = "81d19dae338dd4cf3ecd6331fb4763a1002f9580"
 uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
-version = "0.20.19"
+version = "0.21.43"
 
 [[VertexSafeGraphs]]
-deps = ["LightGraphs"]
-git-tree-sha1 = "b9b450c99a3ca1cc1c6836f560d8d887bcbe356e"
+deps = ["Graphs"]
+git-tree-sha1 = "8351f8d73d7e880bfc042a8b6922684ebeafb35c"
 uuid = "19fa3120-7c27-5ec5-8db8-b0b0aa330d6f"
-version = "0.1.2"
+version = "0.2.0"
 
 [[Wayland_jll]]
 deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
@@ -1451,22 +2046,22 @@ uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
 version = "1.19.0+0"
 
 [[Wayland_protocols_jll]]
-deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"]
-git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
 uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
-version = "1.18.0+4"
+version = "1.25.0+0"
 
 [[WoodburyMatrices]]
 deps = ["LinearAlgebra", "SparseArrays"]
-git-tree-sha1 = "59e2ad8fd1591ea019a5259bd012d7aee15f995c"
+git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
 uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
-version = "0.5.3"
+version = "0.5.5"
 
 [[XML2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
-git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
+git-tree-sha1 = "58443b63fb7e465a8a7210828c91c08b92132dff"
 uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
-version = "2.9.12+0"
+version = "2.9.14+0"
 
 [[XSLT_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
@@ -1602,9 +2197,9 @@ version = "1.4.0+3"
 
 [[ZipFile]]
 deps = ["Libdl", "Printf", "Zlib_jll"]
-git-tree-sha1 = "c3a5637e27e914a7a445b8d0ad063d701931e9f7"
+git-tree-sha1 = "ef4f23ffde3ee95114b461dc667ea4e6906874b2"
 uuid = "a5390f91-8eb1-5f08-bee0-b1d1ffed6cea"
-version = "0.9.3"
+version = "0.10.0"
 
 [[Zlib_jll]]
 deps = ["Libdl"]
@@ -1612,33 +2207,43 @@ uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
 
 [[Zstd_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
+git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
 uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
-version = "1.5.0+0"
+version = "1.5.2+0"
 
 [[Zygote]]
-deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
-git-tree-sha1 = "531474afbc343c3c7cb9b71c2771813c6defd550"
+deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NaNMath", "Random", "Requires", "SparseArrays", "SpecialFunctions", "Statistics", "ZygoteRules"]
+git-tree-sha1 = "3cfdb31b517eec4173584fba2b1aa65daad46e09"
 uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
-version = "0.6.14"
+version = "0.6.41"
 
 [[ZygoteRules]]
 deps = ["MacroTools"]
-git-tree-sha1 = "9e7a1e8ca60b742e508a315c17eef5211e7fbfd7"
+git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
 uuid = "700de1a5-db45-46bc-99cf-38207098b444"
-version = "0.2.1"
+version = "0.2.2"
+
+[[libaom_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
+uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
+version = "3.4.0+0"
 
 [[libass_jll]]
-deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
-git-tree-sha1 = "acc685bcf777b2202a904cdcb49ad34c2fa1880c"
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
 uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
-version = "0.14.0+4"
+version = "0.15.1+0"
+
+[[libblastrampoline_jll]]
+deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
 
 [[libfdk_aac_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "7a5780a0d9c6864184b3a2eeeb833a0c871f00ab"
+git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
 uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
-version = "0.1.6+4"
+version = "2.0.2+0"
 
 [[libpng_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
@@ -1648,9 +2253,9 @@ version = "1.6.38+0"
 
 [[libvorbis_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
-git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
+git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
 uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
-version = "1.3.7+0"
+version = "1.3.7+1"
 
 [[nghttp2_jll]]
 deps = ["Artifacts", "Libdl"]
@@ -1662,15 +2267,15 @@ uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
 
 [[x264_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f"
+git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
 uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
-version = "2020.7.14+2"
+version = "2021.5.5+0"
 
 [[x265_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab"
+git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
 uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
-version = "3.0.0+3"
+version = "3.5.0+0"
 
 [[xkbcommon_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
diff --git a/LotkaVolterra/plots/Scenario_1__losses.pdf b/LotkaVolterra/plots/Scenario_1__losses.pdf
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diff --git a/LotkaVolterra/scenario_1.jl b/LotkaVolterra/scenario_1.jl
index dae1e87..22ca14f 100644
--- a/LotkaVolterra/scenario_1.jl
+++ b/LotkaVolterra/scenario_1.jl
@@ -6,8 +6,8 @@ using Pkg; Pkg.activate("."); Pkg.instantiate()
 using OrdinaryDiffEq
 using ModelingToolkit
 using DataDrivenDiffEq
-using LinearAlgebra, Optim
-using Optimization, OptimizationFlux, OptimizationOptimJL #OptimizationFlux for ADAM and OptimizationOptimJL for BFGS
+using LinearAlgebra, ComponentArrays
+using Optimization, OptimizationOptimisers, OptimizationOptimJL #OptimizationFlux for ADAM and OptimizationOptimJL for BFGS
 using DiffEqSensitivity
 using Lux
 using Plots
@@ -34,19 +34,22 @@ function lotka!(du, u, p, t)
 end
 
 # Define the experimental parameter
-tspan = (0.0f0,3.0f0)
-u0 = Float32[0.44249296,4.6280594]
-p_ = Float32[1.3, 0.9, 0.8, 1.8]
+tspan = (0.0,3.0)
+u0 = [0.44249296,4.6280594]
+p_ = [1.3, 0.9, 0.8, 1.8]
 prob = ODEProblem(lotka!, u0,tspan, p_)
 solution = solve(prob, Vern7(), abstol=1e-12, reltol=1e-12, saveat = 0.1)
 
 # Ideal data
 X = Array(solution)
 t = solution.t
+DX = Array(solution(solution.t, Val{1}))
+
+full_problem = DataDrivenProblem(X, t = t, DX = DX)
 
 # Add noise in terms of the mean
 x̄ = mean(X, dims = 2)
-noise_magnitude = Float32(5e-3)
+noise_magnitude = 5e-3
 Xₙ = X .+ (noise_magnitude*x̄) .* randn(eltype(X), size(X))
 
 plot(solution, alpha = 0.75, color = :black, label = ["True Data" nothing])
@@ -77,8 +80,8 @@ prob_nn = ODEProblem(nn_dynamics!,Xₙ[:, 1], tspan, p)
 ## Function to train the network
 # Define a predictor
 function predict(θ, X = Xₙ[:,1], T = t)
-    Array(solve(prob_nn, Vern7(), u0 = X, p=θ,
-                saveat = T,
+    _prob = remake(prob_nn, u0 = X, tspan = (T[1], T[end]), p = θ)
+    Array(solve(_prob, Vern7(), saveat = T,
                 abstol=1e-6, reltol=1e-6,
                 sensealg = ForwardDiffSensitivity()
                 ))
@@ -91,7 +94,7 @@ function loss(θ)
 end
 
 # Container to track the losses
-losses = Float32[]
+losses = Float64[]
 
 callback = function (p, l)
   push!(losses, l)
@@ -107,7 +110,7 @@ end
 # favourable starting positing for BFGS
 adtype = Optimization.AutoZygote()
 optf = Optimization.OptimizationFunction((x,p)->loss(x), adtype)
-optprob = Optimization.OptimizationProblem(optf, Lux.ComponentArray(p))
+optprob = Optimization.OptimizationProblem(optf, ComponentVector{Float64}(p))
 res1 = Optimization.solve(optprob, ADAM(0.1), callback=callback, maxiters = 200)
 println("Training loss after $(length(losses)) iterations: $(losses[end])")
 # Train with BFGS
@@ -156,18 +159,17 @@ b = [polynomial_basis(u, 5); sin.(u)]
 basis = Basis(b,u);
 
 # Create the thresholds which should be used in the search process
-λ = Float32.(exp10.(-7:0.1:0))
+λ = exp10.(-3:0.01:5)
 # Create an optimizer for the SINDy problem
 opt = STLSQ(λ)
 # Define different problems for the recovery
-full_problem = ContinuousDataDrivenProblem(X, t)
-ideal_problem = ContinuousDataDrivenProblem(X̂, ts, DX = Ȳ)
-nn_problem = ContinuousDataDrivenProblem(X̂, ts, DX = Ŷ)
+ideal_problem = DirectDataDrivenProblem(X̂, Ȳ)
+nn_problem = DirectDataDrivenProblem(X̂, Ŷ)
 # Test on ideal derivative data for unknown function ( not available )
 println("Sparse regression")
 full_res = solve(full_problem, basis, opt, maxiter = 10000, progress = true)
 ideal_res = solve(ideal_problem, basis, opt, maxiter = 10000, progress = true)
-nn_res = solve(nn_problem, basis, opt, maxiter = 10000, progress = true)
+nn_res = solve(nn_problem, basis, opt, maxiter = 10000, progress = true, sampler = DataSampler(Batcher(n = 4, shuffle = true)))
 # Store the results
 results = [full_res; ideal_res; nn_res]
 # Show the results
@@ -195,7 +197,7 @@ plot!(estimate)
 ## Simulation
 
 # Look at long term prediction
-t_long = (0.0f0, 50.0f0)
+t_long = (0.0, 50.0)
 estimation_prob = ODEProblem(recovered_dynamics!, u0, t_long, parameters(nn_res))
 estimate_long = solve(estimation_prob, Tsit5(), saveat = 0.1) # Using higher tolerances here results in exit of julia
 plot(estimate_long)
diff --git a/LotkaVolterra/scenario_2.jl b/LotkaVolterra/scenario_2.jl
index 4780d2e..eb764d7 100644
--- a/LotkaVolterra/scenario_2.jl
+++ b/LotkaVolterra/scenario_2.jl
@@ -1,3 +1,4 @@
+
 ## Environment and packages
 cd(@__DIR__)
 using Pkg; Pkg.activate("."); Pkg.instantiate()
@@ -5,14 +6,18 @@ using Pkg; Pkg.activate("."); Pkg.instantiate()
 using OrdinaryDiffEq
 using ModelingToolkit
 using DataDrivenDiffEq
-using LinearAlgebra, Optim
-using DiffEqFlux, Flux
+using LinearAlgebra
+using Optimization, OptimizationOptimisers, OptimizationOptimJL #OptimizationFlux for ADAM and OptimizationOptimJL for BFGS
+using DiffEqSensitivity
+using Lux
+using ComponentArrays
 using Plots
 gr()
 using JLD2, FileIO
 using Statistics
 # Set a random seed for reproduceable behaviour
 using Random
+rng = Random.default_rng()
 Random.seed!(2345)
 
 #### NOTE
@@ -31,30 +36,31 @@ function lotka!(du, u, p, t)
 end
 
 # Define the experimental parameter
-tspan = (0.0f0,6.0f0)
-u0 = Float32[0.44249296,4.6280594]
-p_ = Float32[1.3, 0.9, 0.8, 1.8]
+tspan = (0.0,6.0)
+u0 = [0.44249296,4.6280594]
+p_ = [1.3, 0.9, 0.8, 1.8]
 prob = ODEProblem(lotka!, u0,tspan, p_)
 solution = solve(prob, Vern7(), abstol=1e-6, reltol=1e-6, saveat = 0.1)
 
-scatter(solution, alpha = 0.25)
-plot!(solution, alpha = 0.5)
-
 # Ideal data
 X = Array(solution)
 t = solution.t
+DX = Array(solution(solution.t, Val{1}))
+
+full_problem = DataDrivenProblem(X, t = t, DX = DX)
+
 # Add noise in terms of the mean
 x̄ = mean(X, dims = 2)
-noise_magnitude = Float32(1e-2)
+noise_magnitude = 5e-3
 Xₙ = X .+ (noise_magnitude*x̄) .* randn(eltype(X), size(X))
 
 # Subsample the data in y
 # We assume we have only 5 measurements in y, evenly distributed
-ty = collect(t[1]:Float32(6/5):t[end])
+ty = collect(t[1]:Float64(6/5):t[end])
 # Create datasets for the different measurements
 round(Int64, mean(diff(ty))/mean(diff(t)))
-XS = zeros(eltype(X), length(ty)-1, floor(Int64, mean(diff(ty))/mean(diff(t)))+1) # All x data
-TS = zeros(eltype(t), length(ty)-1, floor(Int64, mean(diff(ty))/mean(diff(t)))+1) # Time data
+XS = zeros(eltype(X), length(ty)-1, ceil(Int64, mean(diff(ty))/mean(diff(t)))+1) # All x data
+TS = zeros(eltype(t), length(ty)-1, ceil(Int64, mean(diff(ty))/mean(diff(t)))+1) # Time data
 YS = zeros(eltype(X), length(ty)-1, 2) # Just two measurements in y
 
 for i in 1:length(ty)-1
@@ -64,26 +70,28 @@ for i in 1:length(ty)-1
     YS[i, :] = [Xₙ[2, t .== ty[i]]'; Xₙ[2, t .== ty[i+1]]]
 end
 
-XS
-
 scatter!(t, transpose(Xₙ))
 ## Define the network
 # Gaussian RBF as activation
 rbf(x) = exp.(-(x.^2))
 
-# Define the network 2->5->5->5->2
-U = FastChain(
-    FastDense(2,5,rbf), FastDense(5,5, rbf), FastDense(5,5, rbf), FastDense(5,2)
+# Multilayer FeedForward
+U = Lux.Chain(
+    Lux.Dense(2,5,rbf), Lux.Dense(5,5, rbf), Lux.Dense(5,5, rbf), Lux.Dense(5,2)
 )
-# Get the initial parameters, first is linear decay
-p = [rand(Float32); initial_params(U)]
 
+# Get the initial parameters and state variables of the model
+p_nn, st_nn = Lux.setup(rng, U) 
+
+# Merge the parameters
+p = (;δ = rand(rng), ude = p_nn)
+p = ComponentVector{Float64}(p)
 # Define the hybrid model
 function ude_dynamics!(du,u, p, t, p_true)
-    û = U(u, p[2:end]) # Network prediction
+    û = U(u, p.ude, st_nn)[1] # Network prediction
     du[1] = p_true[1]*u[1] + û[1]
     # We assume a linear decay rate for the predator
-    du[2] = -p[1]*u[2] + û[2]
+    du[2] = -p.δ*u[2] + û[2]
 end
 
 # Closure with the known parameter
@@ -94,8 +102,8 @@ prob_nn = ODEProblem(nn_dynamics!,Xₙ[:, 1], tspan, p)
 ## Function to train the network
 # Define a predictor
 function predict(θ, X = Xₙ[:,1], T = t)
-    Array(solve(prob_nn, Vern7(), u0 = X, p=θ,
-                tspan = (T[1], T[end]), saveat = T,
+    _prob = remake(prob_nn, u0 = X, tspan = (T[1], T[end]), p = θ)
+    Array(solve(_prob, Vern7(), saveat = T,
                 abstol=1e-6, reltol=1e-6,
                 sensealg = ForwardDiffSensitivity()
                 ))
@@ -116,32 +124,34 @@ function loss(θ)
 end
 
 # Container to track the losses
-losses = Float32[]
-
-# Callback to show the loss during training
-callback(θ,l) = begin
-    push!(losses, l)
-    if length(losses)%50==0
-        println("Current loss after $(length(losses)) iterations: $(losses[end])")
-    end
-    false
+losses = Float64[]
+
+callback = function (p, l)
+  push!(losses, l)
+  if length(losses)%50==0
+      println("Current loss after $(length(losses)) iterations: $(losses[end])")
+  end
+  return false
 end
 
 ## Training
 
 # First train with ADAM for better convergence -> move the parameters into a
 # favourable starting positing for BFGS
-res1 = DiffEqFlux.sciml_train(loss, p, ADAM(0.1f0), cb=callback, maxiters = 300)
+adtype = Optimization.AutoZygote()
+optf = Optimization.OptimizationFunction((x,p)->loss(x), adtype)
+optprob = Optimization.OptimizationProblem(optf, p)
+res1 = Optimization.solve(optprob, ADAM(0.1), callback=callback, maxiters = 200)
 println("Training loss after $(length(losses)) iterations: $(losses[end])")
 # Train with BFGS
-res2 = DiffEqFlux.sciml_train(loss, res1.minimizer, BFGS(initial_stepnorm=0.01f0), cb=callback, maxiters = 10000, g_tol = 1e-10)
+optprob2 = Optimization.OptimizationProblem(optf, res1.minimizer)
+res2 = Optimization.solve(optprob2, Optim.BFGS(initial_stepnorm=0.01), callback=callback, maxiters = 10000)
 println("Final training loss after $(length(losses)) iterations: $(losses[end])")
 
 # Plot the losses
-pl_losses = plot(1:300, losses[1:300], yaxis = :log10, xaxis = :log10, xlabel = "Iterations", ylabel = "Loss", label = "ADAM", color = :blue)
-plot!(301:length(losses), losses[301:end], yaxis = :log10, xaxis = :log10, xlabel = "Iterations", ylabel = "Loss", label = "BFGS", color = :red)
+pl_losses = plot(1:200, losses[1:200], yaxis = :log10, xaxis = :log10, xlabel = "Iterations", ylabel = "Loss", label = "ADAM", color = :blue)
+plot!(201:length(losses), losses[201:end], yaxis = :log10, xaxis = :log10, xlabel = "Iterations", ylabel = "Loss", label = "BFGS", color = :red)
 savefig(pl_losses, joinpath(pwd(), "plots", "$(svname)_losses.pdf"))
-
 # Rename the best candidate
 p_trained = res2.minimizer
 
@@ -160,7 +170,7 @@ savefig(pl_trajectory, joinpath(pwd(), "plots", "$(svname)_trajectory_reconstruc
 # Ideal unknown interactions of the predictor
 Ȳ = [-p_[2]*(X̂[1,:].*X̂[2,:])';p_[3]*(X̂[1,:].*X̂[2,:])']
 # Neural network guess
-Ŷ = U(X̂,p_trained[2:end])
+Ŷ = U(X̂,p_trained.ude, st_nn)[1]
 
 pl_reconstruction = plot(ts, transpose(Ŷ), xlabel = "t", ylabel ="U(x,y)", color = :red, label = ["UDE Approximation" nothing])
 plot!(ts, transpose(Ȳ), color = :black, label = ["True Interaction" nothing], legend = :topleft)
@@ -182,21 +192,22 @@ b = [polynomial_basis(u, 5); sin.(u)]
 basis = Basis(b, u)
 
 # Create the thresholds which should be used in the search process
-λ = Float32.(exp10.(-3:0.01:5))
+λ = exp10.(-3:0.01:5)
 # Create an optimizer for the SINDy problem
 opt = STLSQ(λ)
 # Target function to choose the results from; x = L0 of coefficients and L2-Error of the model
 g(x) = x[1] <= 1 ? Inf : 2*x[1]-2*log(x[2])
 
 # Define different problems for the recovery
-full_problem = ContinuousDataDrivenProblem(solution)
-ideal_problem = ContinuousDataDrivenProblem(X̂, ts, DX = Ȳ)
-nn_problem = ContinuousDataDrivenProblem(X̂, ts, DX = Ŷ)
+ideal_problem = DirectDataDrivenProblem(X̂, Ȳ)
+nn_problem = DirectDataDrivenProblem(X̂,Ŷ)
+
 # Test on ideal derivative data for unknown function ( not available )
 println("Sparse regression")
 full_res = solve(full_problem, basis, opt, maxiter = 10000, progress = true)
 ideal_res = solve(ideal_problem, basis, opt, maxiter = 10000, progress = true)
 nn_res = solve(nn_problem, basis, opt, maxiter = 10000, progress = true)
+
 # Store the results
 results = [full_res; ideal_res; nn_res]
 # Show the results
@@ -226,7 +237,7 @@ plot!(estimate)
 ## Simulation
 
 # Look at long term prediction
-t_long = (0.0f0, 50.0f0)
+t_long = (0.0, 50.0)
 estimation_prob = ODEProblem(estimated_dynamics!, u0, t_long, parameters(nn_res))
 estimate_long = solve(estimation_prob, Tsit5(), saveat = 0.1) # Using higher tolerances here results in exit of julia
 plot(estimate_long)
diff --git a/LotkaVolterra/scenario_3.jl b/LotkaVolterra/scenario_3.jl
index 8945db7..9290888 100644
--- a/LotkaVolterra/scenario_3.jl
+++ b/LotkaVolterra/scenario_3.jl
@@ -5,14 +5,17 @@ using Pkg; Pkg.activate("."); Pkg.instantiate()
 using OrdinaryDiffEq
 using ModelingToolkit
 using DataDrivenDiffEq
-using LinearAlgebra, Optim
-using DiffEqFlux, Flux
+using LinearAlgebra, ComponentArrays
+using Optimization, OptimizationOptimisers, OptimizationOptimJL #OptimizationFlux for ADAM and OptimizationOptimJL for BFGS
+using DiffEqSensitivity
+using Lux
 using Plots
 gr()
 using JLD2, FileIO
 using Statistics
 # Set a random seed for reproduceable behaviour
 using Random
+rng = Random.default_rng()
 Random.seed!(1235)
 
 # Create a name for saving ( basically a prefix )
@@ -59,7 +62,7 @@ t = solution.t
 
 # Add noise in terms of the mean
 x̄ = mean(X, dims = 2)
-noise_magnitude = Float32(2.5e-2)
+noise_magnitude = Float32(5e-3)
 Xₙ = X .+ (noise_magnitude*x̄) .* randn(eltype(X), size(X))
 
 
@@ -77,41 +80,53 @@ savefig(pl_initial_data, joinpath(pwd(), "plots","$(svname)full_data_$(noise_mag
 rbf(x) = exp.(-(x.^2))
 
 # Create the network to recover the reaction
-rx_nn = FastChain(
-    FastDense(1, 5, rbf),
-    FastDense(5, 5, rbf),
-    FastDense(5, 5, rbf),
-    FastDense(5, 1)
+rx_nn = Lux.Chain(
+    Lux.Dense(1, 5, rbf),
+    Lux.Dense(5, 5, rbf),
+    Lux.Dense(5, 5, rbf),
+    Lux.Dense(5, 1)
 )
 
 #initialize D0 close to D/dx^2
 D0 = Float32[6.5]
-p1s = initial_params(rx_nn)
+
+# Get the initial parameters and state variables of the model
+p_nn, st_nn = Lux.setup(rng, rx_nn)
 p2s = zeros(Float32, 4)
-p = [p1s;p2s;D0]
+p = ComponentVector(;
+    ude = p_nn,
+    p2s = p2s,
+    D0 = D0
+)
+
 
 function nn_ode(u,p,t)
     # This is the dircetional derivative
-    u_cnn_1   = [p[end-4] * u[end] + p[end-3] * u[1] + p[end-2] * u[2]]
-    u_cnn     = [p[end-4] * u[i-1] + p[end-3] * u[i] + p[end-2] * u[i+1] for i in 2:size(u, 1)-1]
-    u_cnn_end = [p[end-4] * u[end-1] + p[end-3] * u[end] + p[end-2] * u[1]]
 
-    [rx_nn([ui], p[1:length(p1s)])[1] for ui in u] + p[end] * vcat(u_cnn_1, u_cnn, u_cnn_end)
+    ps_ = p.p2s
+    u_cnn_1   = [ps_[end-3] * u[end] + ps_[end-2] * u[1] + ps_[end-1] * u[2]]
+    u_cnn     = [ps_[end-3] * u[i-1] + ps_[end-2] * u[i] + ps_[end-1] * u[i+1] for i in 2:size(u, 1)-1]
+    u_cnn_end = [ps_[end-3] * u[end-1] + ps_[end-2] * u[end] + ps_[end-1] * u[1]]
+
+    reduce(vcat, map(u) do ui 
+        rx_nn([ui], p.ude, st_nn)[1]
+    end) + p.D0 .* vcat(u_cnn_1, u_cnn, u_cnn_end)
 end
 
 prob_nn = ODEProblem(nn_ode, Xₙ[:, 1], (t[1], t[end]), p)
-
+nn_ode(rho_ic(Delta), p, 0.0)
 
 ## Necessary functions
 
 function predict_pde(θ, X = Xₙ[:, 1], T = t)
-  # No ReverseDiff if using Flux
-  Array(solve(prob_nn, Vern7(),
-        u0 = X, p = θ, tspan = (T[1], T[end]), saveat=T,
-        sensealg=ForwardDiffSensitivity(convert_tspan = false)#, reltol = 1e-4, abstol = 1e-4
-        ))
+    _prob = remake(prob_nn, u0 = X, tspan = (T[1], T[end]), p = θ)
+    Array(solve(_prob, Vern7(), saveat = T,
+                sensealg = ForwardDiffSensitivity(convert_tspan = false)
+                ))
 end
 
+predict_pde(p)
+
 #match data and force the weights of the CNN to add up to zero
 function objective_pde(p)
     pred = predict_pde(p)
@@ -130,18 +145,24 @@ callback(θ,l) = begin
     false
 end
 
-## Train the model
-# First train with ADAM
-res1 = DiffEqFlux.sciml_train(objective_pde, p, ADAM(0.1f0), cb=callback, maxiters = 40)
+# First train with ADAM for better convergence -> move the parameters into a
+# favourable starting positing for BFGS
+adtype = Optimization.AutoZygote()
+optf = Optimization.OptimizationFunction((x,p)->objective_pde(x), adtype)
+optprob = Optimization.OptimizationProblem(optf, p)
+res1 = Optimization.solve(optprob, ADAM(0.1), callback=callback, maxiters = 10)
+println("Training loss after $(length(losses)) iterations: $(losses[end])")
 # Train with BFGS
-res2 = DiffEqFlux.sciml_train(objective_pde, res1.minimizer, BFGS(initial_stepnorm=0.1f0), cb=callback, maxiters = 10000)
+optprob2 = Optimization.OptimizationProblem(optf, res1.minimizer)
+res2 = Optimization.solve(optprob2, Optim.BFGS(initial_stepnorm=0.001), callback=callback, maxiters = 100)
+println("Final training loss after $(length(losses)) iterations: $(losses[end])")
+
 p_trained = res2.minimizer
 
 ## Data evaluation -> we subsample here!
-tsample = t[1]:1.0*mean(diff(t)):t[end]
-X̂ = predict_pde(p_trained, Xₙ[:,1], tsample)
+X̂ = predict_pde(p_trained)
 # Trained on noisy data vs real solution
-pl_trajectory = plot(tsample, transpose(X̂), xlabel = "t", ylabel ="rho(x,t)", color = :red,
+pl_trajectory = plot(t, transpose(X̂), xlabel = "t", ylabel ="rho(x,t)", color = :red,
  label = ["UDE Approximation" [nothing for i in 1:25]...])
 scatter!(t, transpose(Xₙ), color = :black, label = ["Measurements"  [nothing for i in 1:25]...], legend = :bottomright)
 savefig(pl_trajectory, joinpath(pwd(), "plots", "$(svname)_trajectory_reconstruction.pdf"))
@@ -151,7 +172,7 @@ savefig(pl_trajectory, joinpath(pwd(), "plots", "$(svname)_trajectory_reconstruc
 R̂ = similar(X̂)
 R̄ = similar(X̂)
 for i in 1:size(X̂, 1), j in 1:size(X̂, 2)
-    R̂[i,j] = rx_nn(X̂[i,j], p_trained[1:length(p1s)])[1]
+    R̂[i,j] = rx_nn([X̂[i,j]], p_trained.ude, st_nn)[1][1]
     R̄[i,j] = reaction(X̂[i,j])
 end
 
@@ -175,7 +196,7 @@ Rs = Matrix(vcat(eachrow(R̂[1:end, :])...)')
 
 # Technically this is cheating until a general DataDrivenProblem is defined properly.
 # we work with the continuous form
-nn_prob = ContinuousDataDrivenProblem(Xs, zeros(Float32, size(Xs, 2)), DX = Rs)
+nn_prob = DirectDataDrivenProblem(Xs, Rs)
 
 λs = Float32.(exp10.(-3:0.01:5))
 opt = STLSQ(λs)
diff --git a/Manifest.toml b/Manifest.toml
new file mode 100644
index 0000000..6d5c0ad
--- /dev/null
+++ b/Manifest.toml
@@ -0,0 +1,6 @@
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.7.3"
+manifest_format = "2.0"
+
+[deps]