Demos of Forward Problems

Here are some demos of solving forward problems of PDEs.

ODEs

• A simple ODE system
• Lotka-Volterra equation
• Second order ODE

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
• 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

• Beltrami flow
• Wave propagation with spatio-temporal multi-scale Fourier feature architecture
• Schrodinger equation

Integro-differential equations

• Integro-differential equation
• Volterra IDE

Fractional PDEs

• Fractional Poisson equation in 1D
• Fractional Poisson equation in 2D
• Fractional Poisson equation in 3D
• Fractional diffusion equation