Here is a gallery of tutorials and examples to get you started with ScimBa.

Tutorials

Each tutorial is a single Jupyter notebook that helps you get started with Scimba.

2D Laplacian Problems

Solve 2D Laplacian problems with Dirichlet boundary conditions.

Scimba basics I: approximation of the solution of a 2D Laplacian

Natural Gradients Preconditioners

Setup an equation for applying preconditioners.

Scimba basics II: Natural gradient preconditioners

Defining Domains

Learn how to define and work with computational domains.

Creating meshless domains

Defining Models

Learn how to define physical models and PDEs in Scimba for different problem types.

Defining a physical model

Projection of functions

Learn how to approximate a function given as an evaluation procedure with a network based approximation space.

Projection of a function on an approximation space.

Saving and loading PINNs

Save and load PINNs.

Saving and loading PINNs

Strong Boundary Conditions

Implementation of strong boundary conditions in 2D problems.

Strong boundary conditions

Mixed Boundary Conditions

Handling mixed boundary conditions.

Imposing mixed boundary conditions

Time Discrete Methods

Explore time discretization methods for temporal PDEs.

Using Time-Discrete Schemes

Scimba optimizers

Scimba optimizers how to.

Scimba Optimizers

PINN’s losses

How to define and tune losses and losses weights.

Losses in Scimba PINNs

Examples

Each example is a single Jupyter notebook.

1D viscous Burger equation

Solves the viscous Burgers advection equation in 1D using a PINN.

PINNs: viscous Burgers 1D

Inhomogeneous Helmholtz equation

Solves an inhomogeneous Helmholtz equation using a PINN and a MLP with multi-scale Fourier features.

PINNs: Inhomogeneous Helmholtz equation

Linearized Euler system

Solves the linearized Euler system using a PINN.

PINNs: linearized Euler 1D

Grad div system 2D

Solves a 2D grad div system with PINNs.

PINNs: grad-div system 2D

Div A grad u system 2D

Solves a 2D div A grad u system with the deep Ritz method.

Deep Ritz: div A grad u 2D

Navier Stokes system of equations

Solves a 2D Navier Stokes system with PINNs.

PINNs: Navier Stokes equation

2D laplacian disk

Solves a 2D laplacian on a disk with the deep Ritz method.

Deep Ritz: 2D laplacian on a disk

Pendulum flow

Learns the flow of a pendulum ODE with different training strategies.

Flows: pendulum

Kinetic Vlasov equation

Solves a kinetic Vlasov equation in 1D with neural Semi-Lagrangian approach.

Time discrete: kinetic Vlasov in 1D

Rotating transport equation

Solves a rotating transport equation in 2D with neural Galerkin approach.

Time discrete: rotating transport

2D heat equation

Solves a 2D heat equation with discrete pinns using implicit scheme.

Time discrete: heat equation

Transport equation in a cylinder

Solves a transport equation in a cylinder with neural Semi-Lagrangian approach.

Time discrete: transport in a cylinder

Advection of a 3D level-set function

Solves the advection of a 3D level-set function with neural Semi-Lagrangian approach.

Time discrete: advection of a 3D level-set function

Learning the Signed Distance Function of a shape

Learns the Signed Distance Function of a shape given as a file of points on its contour.

Learning the Signed Distance Function of a shape

A complete list of PyTorch script examples is available in the examples/examples_torch/ directory of the repository.

Scimba API documentation

Basic configuration

Please refer to the basic configuration page for an overview of scimba_torch global parameters.

Available Packages

scimba_torch.approximation_space	Defines the approximation space and its components.
scimba_torch.domain	Defines mesh-based and meshless domains.
scimba_torch.flows	Various numerical integrators for ODEs.
scimba_torch.integration	Integration methods for volumetric and surfacic domains.
scimba_torch.geometry	A module implementing tools for geometry learning.
scimba_torch.neural_nets	Defines neural networks.
scimba_torch.numerical_solvers	Defines numerical solvers.
scimba_torch.optimizers	Scimba optimizers and losses.
scimba_torch.physical_models	Defines physical models.
scimba_torch.plots	Plot utilities.
scimba_torch.utils	Utility functions and classes.