Python Scripts Index

Click on a script name to download it.

• deep_ritz/

  • stationary_pdes/

    • elliptic_pdes/

      • div_a_grad_u_1d_parametric.py: Solves a 1D elliptic PDE with Dirichlet BCs using the Deep Ritz method and PINNs.

      • div_a_grad_u_1d_parametric_weak_bc.py: Solves a 1D elliptic PDE with Dirichlet BCs using the Deep Ritz method and PINNs.

      • div_a_grad_u_2d_parametric.py: Solves a 2D elliptic PDE with Dirichlet BCs using the Deep Ritz method and PINNs.

      • div_a_grad_u_laplacian_2d_parametric.py: Solves a 2D Poisson PDE with Dirichlet BCs using the Deep Ritz method and PINNs.

      • laplacian_2d_disk_parametric.py: Solves a 2D Poisson PDE with Dirichlet BCs using the Deep Ritz method and PINNs.

      • laplacian_2d_square_parametric.py: Solves a 2D Poisson PDE with Dirichlet BCs using the Deep Ritz method and PINNs.

      • laplacian_2d_square_parametric_strong_bc.py: Solves a 2D Poisson PDE with Dirichlet BCs using the Deep Ritz method and PINNs.

• domain/

  • meshless_domain.py: Provides examples and visualization of several meshless domains.

• examples_jax/

  • fbpinns/

    • laplacian_1d_fbpinn.py: Solves a 1D Poisson PDE with Dirichlet boundary conditions using PINNs.

  • pinns/

    • stationary_pdes/

      • elliptic_pdes/

        • bi_material_electrostatic_2d.py: Solves the electrostatics equation in 2D on a bi-material domain using PINNs.

        • laplacian_2d_disk_parametric_dirichlet_neumann_disk.py: Solves a 2D Poisson PDE with Dirichlet and Neumann BCs using PINNs.

        • laplacian_2d_disk_parametric_dirichlet_neumann_square.py: Solves a 2D Poisson PDE with Dirichlet and Neumann BCs using PINNs.

        • laplacian_2d_square.py: Solves a 2D Poisson PDE with Dirichlet boundary conditions using PINNs.

        • laplacian_2d_square_mapped.py: Solves a 2D Poisson PDE with Dirichlet boundary conditions using PINNs.

      • elliptic_systems/

        • navier_stokes_2d_NS2d-C.py: Solves the 2d Navier Stokes Equations described in

        • navier_stokes_2d_NS2d-C_bis.py: Solves the 2d Navier Stokes Equations described in

        • navier_stokes_2d_NS2d-C_ter.py: Solves the 2d Navier Stokes Equations described in

    • time_dependent_pdes/

      • hyperbolic_systems/

        • linearized_euler.py: Solves the linearized Euler equations in 1D using a PINN.

        • linearized_euler_strong_bc.py: Solves the linearized Euler equations in 1D using a PINN.

      • parabolic_pdes/

        • heat_1d.py: Solves the heat equation in 1D using a PINN.

        • heat_1d_strong.py: Solves the heat equation in 1D using a PINN.

        • viscous_burgers_1d.py: Solves the viscous Burgers advection equation in 1D using a PINN.

        • viscous_burgers_1d_with_source.py: Solves the viscous Burgers advection equation in 1D using a PINN.

  • projection/

    • linearized_euler_exact_sol.py: Learns the exact solution of a linearized Euler equation in 1D.

    • transport_t1x1v.py: Learns the initial condition of a transport equation in 1D.

• flows/

  • pendulum_flow.py: Learns the flow of a pendulum ODE using different training strategies.

• geometry/

  • learning_rsdf_2d_bean.py: An example illustrating rsdf nn to learn a bean shape from a parametric curve.

  • learning_rsdf_3d_sphere.py: An example illustrating rsdf nn to learn a sphere from a file point.

  • learning_rsdf_3d_torus.py: An example illustrating rsdf nn to learn a torus from a parametric curve.

• pinns/

  • preconditioned_pinns/

    • bi_material_electrostatic_2d.py: Solves the electrostatics equation in 2D on a bi-material domain using PINNs.

    • grad_div_2d_weak_bc.py: Solves a grad-div system in 2D with Dirichlet boundary conditions using a PINN.

    • heat_1d.py: Solves the heat equation in 1D using a PINN.

    • heat_1d_strong_bc.py: Solves the heat equation in 1D using a PINN.

    • laplacian_2d_square.py: Solves a 2D Poisson PDE with Dirichlet boundary conditions using PINNs.

    • laplacian_2d_square_parametric_data_loss.py: Solves a 2D Poisson PDE with Dirichlet boundary conditions using PINNs.

    • laplacian_3d_cube.py: Solves a 3D Poisson PDE with Dirichlet boundary conditions using PINNs.

    • linear_order2.py: Solves a 2D linear second-order PDE using PINNs.

    • linear_order2_laplacian.py: Solves a 2D Poisson PDE with Dirichlet boundary conditions using PINNs.

    • linearized_euler.py: Solves the linearized Euler equations in 1D using a PINN.

    • linearized_euler_data_loss.py: Solves the linearized Euler equations in 1D using a PINN.

    • navier_stokes_2d.py: Solves the Navier-Stokes equations in 2D using a PINN.

  • stationary_pdes/

    • elliptic_pdes/

      • bi_material_electrostatic_2d.py: Solves the electrostatics equation in 2D on a bi-material domain using PINNs.

      • div_a_grad_u_2d.py: Solves a 2D diffusion equation with Dirichlet BC.

      • homogeneous_helmholtz_2d.py: Solves the 2D Helmholtz PDE with homogeneous Dirichlet BCs using PINNs.

      • inhomogeneous_helmholtz_2d.py: Solves the 2D inhomogeneous Helmholtz PDE with homogeneous Dirichlet BCs using PINNs.

      • laplacian_2d_disk_parametric.py: Solves a 2D Poisson PDE with Dirichlet BCs and two parameters.

      • laplacian_2d_disk_parametric_dirichlet_neumann.py: Solves a 2D Poisson PDE with Dirichlet BCs using PINNs.

      • laplacian_2d_disk_parametric_pre_sampled_points.py: Solves a 2D Poisson PDE with Dirichlet BCs and two parameters.

      • laplacian_2d_disk_parametric_sobol.py: Solves a 2D Poisson PDE with Dirichlet BCs and two parameters.

      • laplacian_2d_multiscale.py: Solves a 2D multiscale Poisson PDE using PINNs.

      • laplacian_2d_square.py: Solves a 2D Poisson PDE with Dirichlet boundary conditions using PINNs.

      • laplacian_2d_square_parametric.py: Solves a 2D Poisson PDE with Dirichlet boundary conditions using PINNs.

      • laplacian_2d_square_parametric_data_loss.py: Solves a 2D Poisson PDE with Dirichlet boundary conditions using PINNs.

      • laplacian_2d_square_resnet.py: Solves a 2D Poisson PDE with Dirichlet boundary conditions using PINNs.

      • reaction_diffusion_2d_square_parametric.py: Solves a 2D Reaction-Diffusion PDE with Dirichlet boundary conditions.

    • elliptic_systems/

      • results/

      • grad_div_2d_strong_bc.py: Solves a grad-div system in 2D with Dirichlet boundary conditions using a PINN.

      • grad_div_2d_weak_bc.py: Solves a grad-div system in 2D with Dirichlet boundary conditions using a PINN.

      • grad_div_2d_weak_bc_pre_sampled_points.py: Solves a grad-div system in 2D with Dirichlet boundary conditions using a PINN.

      • navier_stokes_2d_cylinder.py: Solves the Navier-Stokes equations in 2D using a PINN.

      • navier_stokes_2d_NS2d-C.py: Solves the 2d Navier Stokes Equations described in

      • navier_stokes_2d_square.py: (No docstring found)

      • schrodinger_2d.py: Solves a time-independent Schrödinger equation in 2D.

  • time_dependent_pdes/

    • hyperbolic_pdes/

      • advection_1d_parametric_strong_bc.py: Solves the scalar linear advection equation in 1D using a PINN.

      • advection_1d_parametric_weak_bc.py: Solves the scalar linear advection equation in 1D using a PINN.

    • hyperbolic_systems/

      • linearized_euler.py: Solves the linearized Euler equations in 1D using a PINN.

      • linearized_euler_data_loss.py: Solves the linearized Euler equations in 1D using a PINN.

      • linearized_euler_strong_bc.py: Solves the linearized Euler equations in 1D using a PINN.

    • parabolic_pdes/

      • fisher_kpp_2d_neumann.py: Solves a 2D reaction-diffusion equation.

      • heat_1d.py: Solves the heat equation in 1D using a PINN.

      • heat_1d_strong_pre_processing.py: Solves a 1D heat equation with pre-processing.

      • heat_nd_strong_pre_processing.py: Solves a 1D heat equation with pre-processing.

      • reaction_diffusion_2d_neumann.py: Solves a 2D reaction-diffusion equation.

      • viscous_burgers_1d.py: Solves the viscous Burgers advection equation in 1D using a PINN.

      • viscous_burgers_1d_2.py: Solves the viscous Burgers advection equation in 1D using a PINN.

    • parabolic_systems/

      • results/

      • navier_stokes_2d.py: Solves the Navier-Stokes equations in 2D using a PINN.

      • navier_stokes_2d_strong_bc.py: Solves the Navier-Stokes equations in 2D using a PINN.

• plots/

  • grad_shafranov_with_hole.py: Solves the Grad-Shafranov equation in 2D on a tokamak-like geometry using PINNs.

  • kinetic_vlasov_1d_1v.py: Solves the Vlasov equation in 1Dx1V using the neural semi-Lagrangian method.

  • laplacian_2d_square_mapping.py: Solves a 2D Poisson PDE with Dirichlet boundary conditions using PINNs.

  • projection_1d.py: Approximation and plot of a 1D parametric function using a neural network.

  • projection_1d_params.py: Approximation and plot of a 1D parametric function using a neural network.

  • projection_transport_t1x1v.py: Approximation and plot of a 2D time-dependent function using a neural network.

  • projection_transport_t1x1v_segment.py: Approximation and plot of a 2D time-dependent function using a neural network.

  • projection_transport_t2x2v.py: Approximation and plot of a 3D time-dependent function using a neural network.

  • time_discrete_heat_1d.py: Solves the heat equation in 1D using a discrete PINN.

• projection/

  • custom_space.py: (No docstring found)

  • kernel_space_1d_projection.py: Projection of a 1D function using kernel-based approximation spaces.

  • kernel_space_projection.py: Projection of a 2D function using kernel-based approximation spaces.

  • linearized_euler_ic.py: Learns the initial condition of a linearized Euler equation in 1D.

  • preconditioned_projection.py: Approximation of a function using several optimization strategies.

  • preconditioned_projection_heat_1d.py: Projection of a 1D time-dependent function using preconditioned methods.

  • projection_spectral.py: Learns an oscillatory function using a neural network or a spectral approximation.

  • separable_natural_gradient_projection.py: Learns a low- (or high-) rank function using a spectral approximation.

  • separable_natural_gradient_projection_spectral.py: Learns a low- (or high-) rank function using a neural network.

• time_discrete/

  • advection_1d.py: Solves a 1D advection equation using two time-sequential schemes.

  • advection_1d_dirichlet.py: Solves a 1D advection equation with a parametric Dirichlet boundary condition.

  • advection_1d_non_autonomous.py: Solves a 1D advection equation with a time-dependent velocity.

  • advection_1d_parametric.py: Solves a 1D parametric advection equation using two time-sequential schemes.

  • advection_1d_periodic.py: Solves a 1D advection equation in a periodic domain using a discrete PINN.

  • advection_2d_dirichlet.py: Solves a 2D advection equation with a parametric Dirichlet boundary condition.

  • advection_2d_disk_neural_sl.py: Solves the advection of a 2D parametric bump function on a disk.

  • advection_2d_disk_parametric_discrete_pinn.py: Solves the advection of a 2D bump function on a disk with a discrete PINN.

  • advection_2d_filamenting.py: Approximates a filamenting 2D function.

  • advection_2d_vlasov.py: Solves the Vlasov equation on a periodic square.

  • advection_3d_parametric_cylinder.py: Solves the advection of a 3D parametric bump function in a cylinder.

  • advection_diffusion_nd.py: Solves an advection-diffusion equation in dimension 1 to 8.

  • advection_diffusion_nd_gaussian.py: Solves an advection-diffusion equation in dimension 1 to 8.

  • allen_cahn_1d_parametric.py: Solves a 1D Allen-Cahn equation with periodic boundary conditions.

  • fisher_kpp_2d_neumann.py: Solves a 2D reaction-diffusion equation.

  • heat_1d.py: Solves a 1D heat equation using a discrete PINN.

  • heat_2d.py: Solves a 2D heat equation using neural Galerkin.

  • heat_2d_implicit_discrete_pinns.py: Solves a 2D heat equation using an explicit or implicit discrete PINNs.

  • kinetic_1d_1v_vlasov.py: Solves the Vlasov equation on a periodic square.

  • kinetic_2d_2v_radiative_transfer.py: Solves the radiative transfer equation with a discrete PINN.

  • level_set_2d.py: Solves the advection of a 2D level-set function.

  • level_set_3d.py: Solves the advection of a 3D level-set function.

  • level_set_3d_parametric.py: Solves the advection of a parametric 3D level-set function.

  • postprocess_advection_3d_parametric_cylinder.py: Postprocess the results of the 3D cylindrical transport problem.

  • postprocess_level_set_2d.py: Postprocess the results of the 2D level-set transport problem.

  • postprocess_level_set_3d.py: Postprocess the results of the 3D level-set transport problem.

  • postprocess_level_set_3d_parametric.py: Postprocess the results of the 3D parametric level-set transport problem.

  • reaction_diffusion_2d_neumann.py: Solves a 2D reaction-diffusion equation.

  • reaction_diffusion_2d_neumann_weak_bc.py: Solves a 2D reaction-diffusion equation.