This is a project for the inviscid Burgers’ equation. We use SVV (the spectral vanishing viscosity method) and DL (deep learning) to solve the equation. The documents in the repository are described below:
(1) Burgers_Exact_Solution.m
This is a Matlab code to calculate the exact solution of the inviscid Burgers’ equation.
(2) exact solution.txt
The exact solution of the equation generated by Matlab.
(3) method_SVV.ipynb
This is a code for solving the inviscid Burgers’ equation and its automatic optimizer. We employ SVV(The spectral vanishing viscosity method) to solve the PDE problem. Then we use Sequential Least Squares Programming(SLSQP) to optimize parameters(Qk) and find the best Qk for the equation.
(4) method_DL.ipynb
This is a code for solving the inviscid Burgers’ equation and its automatic optimizer. We employ DL (deepxde) to solve the PDE problem. While training, we use the Adam optimizer to update parameters and find the smallest error between the exact resolution and the network's output.
(5) result
This is the folder where the output of the code is stored.
The red line represents the exact solution, while the blue 'x' represents the result.
- The result of SVV in 0.9s
- The result of SVV with optimizer in 0.9s
- The result of deepxde in 0.9s
