# Demos of Forward Problems

Here are some demos of solving forward problems of PDEs.

## ODEs

## Time-independent PDEs

- Poisson equation in 1D with Dirichlet boundary conditions
- Poisson equation in 1D with Dirichlet/Neumann boundary conditions
- Poisson equation in 1D with Dirichlet/Robin boundary conditions
- Poisson equation in 1D with Dirichlet/Periodic boundary conditions
- Poisson equation in 1D with Dirichlet/PointSetOperator boundary conditions
- Poisson equation in 1D with hard boundary conditions
- Poisson equation in 1D with Multi-scale Fourier feature networks
- Poisson equation over L-shaped domain
- Laplace equation on a disk
- Euler beam
- Linear elastostatic equation over a 2D square domain
- Helmholtz equation over a 2D square domain
- Helmholtz equation over a 2D square domain: Hyper-parameter optimization
- Helmholtz equation over a 2D square domain with a hole
- Helmholtz sound-hard scattering problem with absorbing boundary conditions
- Kovasznay flow

## Time-dependent PDEs

- Burgers equation
- Heat equation
- Heat equation with training points resampling
- Diffusion equation
- Diffusion equation with hard initial and boundary conditions
- Diffusion equation with training points resampling
- Diffusion-reaction equation
- Burgers equation with residual-based adaptive refinement
- Allen-Cahn equation
- Klein-Gordon equation