FastVPINNs Module Documentation

This section covers the documentation of the FastVPINNs modules. The package is divided into several subpackages, each of which is documented in its own section. The main module documentation is provided below.

FE - Finite Element routines for 2D domains
Geometry - Meshing and Geometry routines
Model - Dense Neural Network Model
Physics - Physics classes for the problem
Data - Data handling routines
Utils - Utility functions

FE

This section holds the documentation for the FE module of the FastVPINNs package. The module provides the necessary classes and functions to obtain the finite element test functions and quadrature points for the 2D domain within the FastVPINNs package. This section is broadly classified into

Finite Element Test Functions

Quadrature Functions

Finite Element Transformations

Finite Element Setup

Geometry

This section holds the documentation for the the geometry module of the FastVPINNs package. The module provides the necessary classes and functions to obtain the geometry information either from the external mesh file or from the internal mesh generation routines. This supports the generation of VTK and GMSH files for visualization purposes.

Model

This section holds the documentation for the the Model module of the FastVPINNs package. The module provides the necessary classes and functions to train a Variational physics informed neural network (VPINN) model for the given physics problem. The model contains only the information about the neural network architecture and the training process. The physics information is provided by the user in the form of a physics class. The model class is responsible for training the neural network and providing the necessary prediction functions.

Model Types

Physics

This section holds the documentation for the the Physics module of the FastVPINNs package. The module provides the necessary classes and functions to define the physics of the problem. The physics class contains the information about the governing equations and their loss calculation in the variational form.

Forward Problems

Inverse Problems (Constant Coefficient)

Inverse Problems (Spatially Varying Coefficient)

Convection-Diffusion-2D - Inverse Problem with Spatially Varying Coefficient

Data

This section holds the documentation for the the datahandler module of the FastVPINNs package. The module provides the necessary classes and functions to handle the data for the training of the VPINN model. The datahandler class is responsible for generating and assembling the tensors into required format for the training process.

Utils

This section holds the documentation for all the helper functions, which are responsible for plotting and console outputs.