Open ssp20190918 opened 4 years ago
masaaldosey
commented
4 years ago hi, from what i understood, the exact solution is generated in MATLAB using a suitable numerical method. i found one such implementation here.
i compared the difference (error) with the existing usol in the original burgers_shock.mat and found it to be of the order 1.e^(-10).
hope this helps.
ansh997
commented
2 years ago Can you also please make me understand x and t? Are these also Matlab generated for this particular problem or are random numbers are to be fed in the network to calculate any solution? Why do they use a .mat data table instead of using a randomly initialized array for x and t?
In discrete-time model (Allen cahn one), On changing the equation along with Initial condition. Run failed to converge and I got a F_tol error. I am confused right now if paper delivers what it promises, i.e. a universal solver for any PDE or what am I doing wrong.
Thanking you in anticipation.
efurlanm
commented
1 year ago I could be wrong, but as far as I can understand the exact solutions of the Burgers equation use estimated values calculated using Hermite's quadrature rule, as described in the Basdevant et al. article. Using Burkardt's Python code with parameters vtn=100, vxn=256, nu=0.01/numpy.pi, xlo=-1.0, xhi=1.0, tlo=0.0, thi=0.99, and qn=50 (order of the quadrature rule), it is possible to generate an array containing exact solutions, which passes the test numpy.allclose when compared to the original array of solutions contained in burgers_shock.mat. To illustrate, I created a Notebook with an example. Hope this helps.
iamsadia
commented
10 months ago If we change the conditions in the code(working Allen cahn equation), then reference should also be change?? how can we generate data file for allen cahn equation for other conditions? need help
iamsadia
commented
10 months ago Can you also please make me understand x and t? Are these also Matlab generated for this particular problem or are random numbers are to be fed in the network to calculate any solution? Why do they use a .mat data table instead of using a randomly initialized array for x and t?
In discrete-time model (Allen cahn one), On changing the equation along with Initial condition. Run failed to converge and I got a F_tol error. I am confused right now if paper delivers what it promises, i.e. a universal solver for any PDE or what am I doing wrong.
Thanking you in anticipation.
facing same problem.
In AppendixA.continuous_time_inference (Burgers) of PINN, The exact solution is mentioned in your code.But I don't quite understand what the exact solution you have here represent, and how those exact solution are calculated? Can you help me with this problem? thanks you.