How to use the chebfun package to solve the Burgers equation? Is there any MATLAB code? I have been trying for a few days and have been experiencing problems

[dyanoo]

No description provided.

[sifanexisted]

Thank you for reaching out to us. We mainly follow the matlab implemention from Fourier nerual operator paper. Please see https://github.com/neuraloperator/neuraloperator/tree/master/data_generation/burgers. But please note that we used different hyper-parameters to get the shock developed. Here we present a demo showing how we generate the dataset for the Burger's equation. The function GRF and Burgers are the same as in the shared link. Hope this may resolve your quesiton.

% number of realizations to generate
N = 1000;

% parameters for the Gaussian random field
gamma = 4;
tau = 5;
sigma = 25^(2);

% viscosity
visc = 0.0001;

% grid size
s = 4096;
steps = 200;
nn = 256;

inputs = zeros(N, nn);
if steps == 1
outputs = zeros(N, s);
else
outputs = zeros(N, steps, nn);
end

tspan = linspace(0,1,steps+1);
x = linspace(0,1, s+1);
X = linspace(0,1, nn);

for j=1:N
u0 = GRF(s/2, 0, gamma, tau, sigma, "periodic");
u = Burgers(u0, tspan, s, visc);

u0_eval = u0(X);
inputs(j,:) = u0_eval;

if steps == 1
    outputs(j,:) = u.values;
else
    for k=1:(steps+1)
        outputs(j,k,:) = u{k}(X);
    end
end

disp(j);

end

[dyanoo]

thanks you