JNotebooks/heat_eqn_tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\natal\\anaconda3\\envs\\deep_env\\lib\\site-packages\\tqdm\\auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
      "  from .autonotebook import tqdm as notebook_tqdm\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cuda\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "\n",
    "device = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n",
    "print(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving the 1D Heat Equation\n",
    "\n",
    "Let's solve the 1D heat equation! This partial differential equation describes the way heat diffuses throughout a region and is generally given by:\n",
    "$$\n",
    "u_t(x, t) = k u_{xx}(x, t)\n",
    "$$\n",
    "\n",
    "We will specifically be solving:\n",
    "$$\n",
    "u_t(x, t) = u_{xx}(x, t), \\quad t\\in[0,0.2], ~x\\in [0,1]\n",
    "$$\n",
    "\n",
    "with Dirichlet boundary conditions\n",
    "\n",
    "$$\n",
    "u(0, t) = u(1, t) = 0\n",
    "$$\n",
    "\n",
    "and the following initial condition\n",
    "\n",
    "$$\n",
    "u(x, 0) = \\text{sin}(\\pi x)\n",
    "$$\n",
    "\n",
    "Let's have a look at the initial condition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 1\n",
    "\n",
    "def ic_eqn(x):\n",
    "    return torch.sin(torch.pi * x)\n",
    "\n",
    "# Exact solution for the heat equation ut = u_xx with the IC above\n",
    "def exact_heat(x, t):\n",
    "    u = np.exp(-k * np.pi ** 2 * t) * np.sin(np.pi * x)\n",
    "    return u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.style.use('fivethirtyeight')\n",
    "x = torch.linspace(0, 1, 60)\n",
    "\n",
    "plt.plot(x, ic_eqn(x))\n",
    "plt.xlabel('Position')\n",
    "plt.ylabel('Temperature')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can imagine we have a rod that is warm at the center and we want to see how the heat will dissipate. Let's go ahead and train a model $u_{PINN}(x, t)$ to approximate the solution $u(x, t)$.\n",
    "\n",
    "## Task 1: Determine solution to heat equation\n",
    "\n",
    "We'll start by defining the neural network that we'll be using to approximate the solution. Notice that tanh is used instead of the popular ReLU! Why might this be?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class FCNN(nn.Module):\n",
    "    def __init__(self, input_size=2, output_size=1, num_layers=4, layer_depth=32) -> None:\n",
    "        super().__init__()\n",
    "        layers = [nn.Linear(input_size, layer_depth),\n",
    "                  nn.Tanh()]\n",
    "        \n",
    "        for i in range(num_layers - 2):\n",
    "            layers.append(nn.Linear(layer_depth, layer_depth))\n",
    "            layers.append(nn.Tanh())\n",
    "\n",
    "        layers.append(nn.Linear(layer_depth, output_size))\n",
    "\n",
    "        self.layers = nn.Sequential(*layers)\n",
    "        self.init_xavier()\n",
    "        \n",
    "    def forward(self, x):\n",
    "        return self.layers(x)\n",
    "\n",
    "    def init_xavier(self):\n",
    "        torch.manual_seed(42)\n",
    "\n",
    "        def init_weights(m):\n",
    "            if type(m) == nn.Linear and m.weight.requires_grad and m.bias.requires_grad:\n",
    "                g = nn.init.calculate_gain('tanh')\n",
    "                torch.nn.init.xavier_uniform_(m.weight, gain=g)\n",
    "                m.bias.data.fill_(0)\n",
    "\n",
    "        self.apply(init_weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's choose some collocation points and set our boundary and intial condition points. In this case, we want to select points over time AND space. Ultimately, we want the following points:\n",
    "* Randomly chosen points over time and space for assessing the PDE\n",
    "* Points at the boundaries (at x=0 and x=1 for all time) to assess the boundary conditions\n",
    "* Points at the intial state (all x at time=0) to assess the intial condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_collocation = 256\n",
    "num_ic = 64\n",
    "num_bc = 64\n",
    "\n",
    "torch.manual_seed(128)\n",
    "\n",
    "# The last dimension will hold the position and time for each collocation sample\n",
    "# Since we are going from time 0 to 1 and position 0 to 1, we are good to go\n",
    "xt_collocation = torch.rand(num_collocation, 2)\n",
    "xt_collocation[..., 1] = xt_collocation[..., 1] * 0.2\n",
    "\n",
    "# For the IC, we want t=0 and a variety of x points\n",
    "xt_ic = torch.empty((num_ic, 2))\n",
    "xt_ic[..., 0] = torch.linspace(0, 1, num_ic)\n",
    "xt_ic[..., 1] = 0\n",
    "\n",
    "# Right boundary condition: set x=1, and a variety of times\n",
    "xt_bc_right = torch.empty((num_bc, 2))\n",
    "xt_bc_right[..., 0] = 1\n",
    "xt_bc_right[..., 1] = torch.linspace(0, 0.2, num_bc)\n",
    "\n",
    "# Left boundary condition: set x=0, and a variety of times\n",
    "xt_bc_left = torch.empty((num_bc, 2))\n",
    "xt_bc_left[..., 0] = 0\n",
    "xt_bc_left[..., 1] = torch.linspace(0, 0.2, num_bc)\n",
    "\n",
    "plt.scatter(xt_collocation[..., 1], xt_collocation[..., 0], label='Collocation')\n",
    "plt.scatter(xt_ic[..., 1], xt_ic[..., 0], label='Initial condition')\n",
    "plt.scatter(xt_bc_right[..., 1], xt_bc_right[..., 0], label='Right boundary condition')\n",
    "plt.scatter(xt_bc_left[..., 1], xt_bc_left[..., 0], label='Left boundary condition')\n",
    "\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Position')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can start training! In our loss function, we will have a few terms to minimize:\n",
    "* The PDE, or physics term: $u_t(x_{\\text{col}}, t_{\\text{col}}) - u_{xx}(x_{\\text{col}}, t_{\\text{col}})$\n",
    "* The initial condition term: $u(x_{\\text{IC}}, 0) - \\text{sin}(\\pi x)$\n",
    "* The right boundary condition term: $u(1, t_{\\text{BC}})$\n",
    "* The left boundary condition term: $u(0, t_{\\text{BC}})$\n",
    "\n",
    "You'll notice we won't do any normalizing or scaling of the data. Why might that be?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0:, Loss: 56.52262\n",
      "Epoch 1000:, Loss: 0.37508\n",
      "Epoch 2000:, Loss: 0.02780\n",
      "Epoch 3000:, Loss: 0.00649\n",
      "Epoch 4000:, Loss: 0.00280\n",
      "Epoch 5000:, Loss: 0.00132\n",
      "Epoch 6000:, Loss: 0.00067\n",
      "Epoch 7000:, Loss: 0.00042\n",
      "Epoch 8000:, Loss: 0.00038\n",
      "Epoch 9000:, Loss: 0.00022\n",
      "Epoch 10000:, Loss: 0.01835\n",
      "Epoch 11000:, Loss: 0.00014\n",
      "Epoch 12000:, Loss: 0.00015\n",
      "Epoch 13000:, Loss: 0.00016\n",
      "Epoch 14000:, Loss: 0.00008\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fix up torch inputs to require gradients\n",
    "xt_collocation = xt_collocation.to(device).requires_grad_()\n",
    "xt_ic = xt_ic.to(device).requires_grad_()\n",
    "xt_bc_right = xt_bc_right.to(device).requires_grad_()\n",
    "xt_bc_left = xt_bc_left.to(device).requires_grad_()\n",
    "\n",
    "# set model and optimizer\n",
    "model = FCNN(num_layers=5, layer_depth=20)\n",
    "model.to(device)\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=0.001)\n",
    "\n",
    "# weights for balancing our loss terms\n",
    "weights = [1, 10, 5, 5]\n",
    "losses = []\n",
    "\n",
    "for i in range(15000):\n",
    "    optimizer.zero_grad()\n",
    "\n",
    "    ## PDE loss ##\n",
    "    u_pde = model(xt_collocation)\n",
    "\n",
    "    grad_u = torch.autograd.grad(u_pde, xt_collocation, grad_outputs=torch.ones_like(u_pde),create_graph=True)[0]\n",
    "    grad_u_t = grad_u[:, 1]\n",
    "    grad_u_x = grad_u[:, 0]\n",
    "    grad_u_xx = torch.autograd.grad(grad_u_x, xt_collocation, grad_outputs=torch.ones_like(grad_u_x), create_graph=True)[0][:, 0]\n",
    "\n",
    "    pde_term = torch.mean((grad_u_t - k * grad_u_xx) ** 2)\n",
    "\n",
    "    ## IC loss ##\n",
    "    u_ic = model(xt_ic)\n",
    "    ic_exact = ic_eqn(xt_ic[..., 0])\n",
    "\n",
    "    ic_term = torch.mean((u_ic.squeeze() - ic_exact) ** 2)\n",
    "\n",
    "    ## BC right loss ##\n",
    "    u_bc_right = model(xt_bc_right)\n",
    "    bc_right_term = torch.mean((u_bc_right) ** 2)\n",
    "\n",
    "    ## BC left loss ##\n",
    "    u_bc_left = model(xt_bc_left)\n",
    "    bc_left_term = torch.mean((u_bc_left) ** 2)\n",
    "\n",
    "    # Total loss\n",
    "    loss = weights[0] * pde_term + weights[1] * ic_term \\\n",
    "        + weights[2] * bc_right_term + weights[3] * bc_left_term\n",
    "    \n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    losses.append(loss.item())\n",
    "\n",
    "    if i % 1000 == 0:\n",
    "        print(f'Epoch {i}:, Loss: {loss.item():.5f}')\n",
    "\n",
    "plt.plot(losses)\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Loss')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing \n",
    "\n",
    "Now we can test our model! \n",
    "\n",
    "We'll look at the following to assess our perfomance:\n",
    "* Relative absolute error to get a general sense of our performance\n",
    "* Predicted heat\n",
    "* Exact heat\n",
    "* The absolute error map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, t = torch.linspace(0, 1, 100), torch.linspace(0, 0.2, 100)\n",
    "x_grid, t_grid = torch.meshgrid(x, t)\n",
    "exact = exact_heat(x_grid, t_grid)\n",
    "\n",
    "xt = torch.stack([x_grid.flatten(), t_grid.flatten()], dim=-1).to(device)\n",
    "model.eval()\n",
    "\n",
    "with torch.no_grad():\n",
    "    u = model(xt)\n",
    "    u = u.cpu().detach()\n",
    "    u = u.reshape(x_grid.shape)\n",
    "\n",
    "error_map = abs((u - exact))\n",
    "relative_absolute_error= (torch.mean(abs(u - exact)) / torch.mean(torch.abs(exact))) * 100\n",
    "print(f\"Relative absolute error: {relative_absolute_error.item():.3f}%\",)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_map(map_data, title='', cmap='inferno', vmin=None, vmax=None):\n",
    "    plt.style.use('fivethirtyeight')\n",
    "    plt.imshow(map_data, cmap=cmap, extent=(0, 2, 0, 1), vmin=vmin, vmax=vmax)\n",
    "    plt.xlabel('Time')\n",
    "    plt.ylabel('Position')\n",
    "    plt.title(title)\n",
    "    ax = plt.gca()\n",
    "    ax.set_xticks([0.0, 0.5, 1, 1.5, 2])\n",
    "    ax.set_xticklabels([0.0, 0.05, 0.1, 0.15, 0.2])\n",
    "    ax.grid(False)\n",
    "    cbar = plt.colorbar(shrink=0.8)\n",
    "    cbar.set_label('Temperature')\n",
    "    plt.show()\n",
    "\n",
    "    return\n",
    "\n",
    "vmin = min(u.min(), exact.min())\n",
    "vmax = max(u.max(), exact.max())\n",
    "plot_map(u, title='PINN Prediction', vmin=vmin, vmax=vmax)\n",
    "plot_map(exact, title='Exact Solution', vmin=vmin, vmax=vmax)\n",
    "plot_map(error_map, cmap='viridis', title='Absolute Error')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 2: Learn parameters of the heat equation\n",
    "\n",
    "\n",
    "In the previous task, we trained our model to approximate the solution to the heat equation. To do this, we used the exact value of $k$ in our PDE loss term, as well as the exact values of the boundary and initial conditions. Now, let's approach it from the other way around: given some noisy data, can we determine the paramters of the PDE? i.e.) Can we learn $k$?\n",
    "\n",
    "Let's start by generating some noisy data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_data = 256\n",
    "\n",
    "xt_data = torch.rand(num_data, 2)\n",
    "xt_data[..., 1] = xt_data[..., 1] * 0.2\n",
    "u_data_true = exact_heat(xt_data[..., 0], xt_data[..., 1]) + torch.randn(num_data) * 0.01\n",
    "plt.scatter(xt_data[..., 1], xt_data[..., 0], c=u_data_true, cmap='inferno')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Position')\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('Temperature')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we're going to train our model. Our loss terms look a bit different this time around. We want to minimize\n",
    "\n",
    "* The PDE, or physics term: $u_t(x_{\\text{col}}, t_{\\text{col}}) - ku_{xx}(x_{\\text{col}}, t_{\\text{col}})$.\n",
    "* The supervised, or data loss: $u(x_{\\text{data}}, t_{\\text{data}}) - u_{\\text{exact}}(x_{\\text{data}}, t_{\\text{data}})$\n",
    "\n",
    "The first term is the same as before, except this time, k is a trainable parameter! The second term will minimize the difference between our model output and the observed data. Note that for this task, the model needs to learn the solution to the heat equation AND the parameter $k$ that governs the heat equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fix up torch inputs to require gradients\n",
    "xt_collocation = xt_collocation.to(device).requires_grad_()\n",
    "xt_data = xt_data.to(device)\n",
    "u_data_true = u_data_true.to(device)\n",
    "\n",
    "# set model and optimizer\n",
    "model = FCNN(num_layers=5, layer_depth=20)\n",
    "model.to(device)\n",
    "# K is set as a trainable parameter and added to the optimizer alongside the model\n",
    "k_model = torch.nn.Parameter(torch.zeros(1, requires_grad=True, device=device))\n",
    "optimizer = torch.optim.Adam(list(model.parameters()) + [k_model], lr=0.001)\n",
    "\n",
    "weights = [1, 10]\n",
    "losses = []\n",
    "ks = []\n",
    "\n",
    "for i in range(10000):\n",
    "    optimizer.zero_grad()\n",
    "\n",
    "    ## PDE loss ##\n",
    "    u_pde = model(xt_collocation)\n",
    "\n",
    "    grad_u = torch.autograd.grad(u_pde, xt_collocation, grad_outputs=torch.ones_like(u_pde),create_graph=True)[0]\n",
    "    grad_u_t = grad_u[:, 1]\n",
    "    grad_u_x = grad_u[:, 0]\n",
    "    grad_u_xx = torch.autograd.grad(grad_u_x, xt_collocation, grad_outputs=torch.ones_like(grad_u_x), create_graph=True)[0][:, 0]\n",
    "\n",
    "    pde_term = torch.mean((grad_u_t - k_model * grad_u_xx) ** 2)\n",
    "\n",
    "    ## Data loss ##\n",
    "    u_data_pred = model(xt_data)\n",
    "    data_term = torch.mean((u_data_pred.squeeze() - u_data_true) ** 2)\n",
    "\n",
    "    # Total loss\n",
    "    loss = weights[0] * pde_term + weights[1] * data_term\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    losses.append(loss.item())\n",
    "    ks.append(k_model.item())\n",
    "\n",
    "    if i % 1000 == 0:\n",
    "        print(f'Epoch {i}:, Loss: {loss.item():.5f}')\n",
    "\n",
    "plt.plot(losses)\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Loss')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see whether we converged to the correct value of k."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(ks, color='C5', label='Predicted k')\n",
    "plt.axhline(1, linestyle='--', c='C0', label=r'True k')\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('k')\n",
    "plt.legend()\n",
    "relative_absolute_error= (abs(ks[-1] - k) / k) * 100\n",
    "\n",
    "plt.title(f\"Relative absolute error: {relative_absolute_error:.3f}%\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also have a look at the solution our model learnt. Even though this wasn't necessarily our goal to find the PDE solution, we get it as a bonus when we solve the inverse problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, t = torch.linspace(0, 1, 100), torch.linspace(0, 0.2, 100)\n",
    "x_grid, t_grid = torch.meshgrid(x, t)\n",
    "exact = exact_heat(x_grid, t_grid)\n",
    "\n",
    "xt = torch.stack([x_grid.flatten(), t_grid.flatten()], dim=-1).to(device)\n",
    "model.eval()\n",
    "\n",
    "with torch.no_grad():\n",
    "    u = model(xt)\n",
    "    u = u.cpu().detach()\n",
    "    u = u.reshape(x_grid.shape)\n",
    "\n",
    "error_map = abs((u - exact))\n",
    "relative_absolute_error= (torch.mean(abs(u - exact)) / torch.mean(torch.abs(exact))) * 100\n",
    "print(f\"Relative absolute error: {relative_absolute_error.item():.3f}%\",)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vmin = min(u.min(), exact.min())\n",
    "vmax = max(u.max(), exact.max())\n",
    "plot_map(u, title='PINN Prediction', vmin=vmin, vmax=vmax)\n",
    "plot_map(exact, title='Exact Solution', vmin=vmin, vmax=vmax)\n",
    "plot_map(error_map, cmap='viridis', title='Absolute Error')"
   ]
  }
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