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burgersInfer.m
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clear all
close all
%run('/home/eric/local/adimat-0.6.0-4971-GNU_Linux-x86_64/ADiMat_startup');
run('/Users/Eric/local/adimat-0.6.0-4971-GNU_Linux-x86_64/ADiMat_startup');
h = figure;
%% Grid
nx = 40;
L = 2.*pi;
dx = L/(nx);
x = linspace(0,2.*pi - dx,nx);
k = linspace(-nx/2,nx/2 - 1,nx)';
%% Initial Condition
%u = initialCondition(x,20,k);
%uhat = fftshift(fft(u))/1000.;
%% Filters
Delta = pi/20.;
kc = 20;
%Gf = exp(-k.^2*Delta^2./24.);%Gauss Filter
Gf = heaviside(pi/Delta - abs(k));%Sharp Spectral
%% Load DNS Data
LES = load('LESdata/LES.mat');
%% Initial Condition
%uhat = interp1(DNS.k,DNS.uhatsave(:,1),k);
%u = myifft(uhat,nx);
%u = sin(x)';%interp1(DNS.x,myifft(GfDNS.*DNS.uhatsave(:,1),length(DNS.x)),x)';
%uhat = myfft(u,nx);
%u = initialCondition(x,20,k);
%uhat = myfft(u,nx);
uhat = LES.uhatsave(:,1);
uhat_beta = zeros(size(uhat));
t = 0;
et = 0.1;
nu = 1e-2;
%dt = nu*dx^2*20;
dt0 = 1e-4;
dt = 1e-4;
iter = 1;
rk4const = [1./4,1./3,1./2,1.];
iter2 = 1;
uhatsave(:,iter) = uhat;
tauhatsave(:,iter) = EDQNM(k,kc,uhat);
Ehatsave(:,iter) = uhat.*conj(uhat);
tsave(:,iter) = 0;
mydraw = 1;
%%% Linear Tangent Info
assimilation_window = 1%length(LES.uhatsave(1,:));
nparams = 2; %number of inferred parameters
uhat_beta = zeros(nx,nparams);
M = eye(nx*assimilation_window);
Caa = eye(nparams);
Caa(2,2) = 1*Caa(1,1);
Wee = eye(nx*assimilation_window).*1./(1.e-10);
opt_its = 50;
gam = -6e-7;
beta0 = [0.1;0.9];
beta = beta0;
beta_save = beta0;
uhat_betasave = norm([uhat_beta]);
while (t < et)
iter = iter + 1;
uhat0 = uhat;
%uhat_beta = zeros(size(u));
uhat_beta0 = uhat_beta;%zeros(size(u));
for OPT_ITER=1:opt_its
[RHS1,tauhat] = convolutionRHS_LES_beta(uhat0,k,kc,nu,beta);
Jac = admDiffFD(@convolutionRHS_LES_beta,1,uhat0,k,kc,nu,beta,admOptions('i',1,'d',1));
dGdbeta = admDiffFD(@convolutionRHS_LES_beta,1,uhat0,k,kc,nu,beta,admOptions('i',5,'d',1));
uhat_beta = uhat_beta0 + dt*((Jac*uhat_beta) - dGdbeta);
A = eye(nx)./dt - Jac;
uhat = A\RHS1 + uhat0;
[val,LESind] = min(abs(t - LES.tsave));
obs_error = LES.uhatsave(:,LESind) - uhat;
%gam = -1./(norm(obs_error))*1e-8;
beta = beta - real(gam*( -Caa * (M * uhat_beta)'*Wee*obs_error));
end
uhat_betasave = [uhat_betasave;norm(uhat_beta(:,1))];
beta_save = [beta_save,beta];
t = t + dt;
if (mod(iter,10) == 0)
%% DNS Index:
[val,LESind] = min(abs(t - LES.tsave));
iter2 = iter2 + 1;
tauhatsave(:,iter2) = tauhat(:,1);
uhatsave(:,iter2) = uhat;
Ehatsave(:,iter2) = uhat.*conj(uhat);
tsave(iter2) = t;
if (mydraw == 1)
subplot(1,2,1)
plot(abs(k),abs(uhat))
%loglog(abs(k),abs(tauhat))
%hold on
%loglog(abs(LES.k),abs(LES.tauhatsave(:,LESind)),'o','color','red')
%%plot(ones(2,1)*kc,linspace(1e-10,1,2),'color','black','LineWidth',3)
%hold off
%xlabel('$k$','Interpreter','LaTex','FontSize',20)
%ylabel('$|\tau_{sgs}|$','Interpreter','LaTex','FontSize',20)
%legend('DNS','Filtered DNS','Filter Cutoff')
subplot(1,2,2)
plot(x,real(myifft(uhat,nx)))
%loglog(abs(k),uhat.*conj(uhat))
hold on
plot(LES.x,real(myifft(LES.uhatsave(:,LESind),length(LES.k))),'o')
%loglog(abs(LES.k),LES.Ehatsave(:,LESind),'color','red')
%plot(ones(2,1)*kc,linspace(1e-10,1,2),'o','color','black','LineWidth',3)
xlabel('$k$','Interpreter','LaTex','FontSize',20)
ylabel('$\hat{uu^{\ast}}$','Interpreter','LaTex','FontSize',20)
legend('LES','Filtered DNS')
%ylim([1e-10,1e8])
%xlim([1,5.*max(k)])
hold off
drawnow
end
t
beta
end
end
%close all
%plot_tau_vs_DNS(k,kc,tauhatsave,DNS,GfDNS,tsave,0,'LESFigures/edq_tau000.png',1)
%plot_tau_vs_DNS(k,kc,tauhatsave,DNS,GfDNS,tsave,0.1,'LESFigures/edq_tau010.png',1)
%plot_tau_vs_DNS(k,kc,tauhatsave,DNS,GfDNS,tsave,0.2,'LESFigures/edq_tau020.png',1)
%plot_tau_vs_DNS(k,kc,tauhatsave,DNS,GfDNS,tsave,0.3,'LESFigures/edq_tau030.png',1)
%plot_tau_vs_DNS(k,kc,tauhatsave,DNS,GfDNS,tsave,0.4,'LESFigures/edq_tau040.png',1)
%plot_tau_vs_DNS(k,kc,tauhatsave,DNS,GfDNS,tsave,0.5,'LESFigures/edq_tau050.png',1)
%plot_E_vs_DNS(k,kc,uhatsave,DNS,GfDNS,tsave,0,'LESFigures/edq_E000.png',1)
%plot_E_vs_DNS(k,kc,uhatsave,DNS,GfDNS,tsave,0.1,'LESFigures/edq_E010.png',1)
%plot_E_vs_DNS(k,kc,uhatsave,DNS,GfDNS,tsave,0.2,'LESFigures/edq_E020.png',1)
%plot_E_vs_DNS(k,kc,uhatsave,DNS,GfDNS,tsave,0.3,'LESFigures/edq_E030.png',1)
%plot_E_vs_DNS(k,kc,uhatsave,DNS,GfDNS,tsave,0.4,'LESFigures/edq_E040.png',1)
%plot_E_vs_DNS(k,kc,uhatsave,DNS,GfDNS,tsave,0.5,'LESFigures/edq_E050.png',1)