Physics Informed Neural Network Code for 2D Transient Problems (PINN-2DT) Compatible with Google Colab

TL;DR

This paper introduces an open-source, Google Colab-compatible Physics Informed Neural Network environment for simulating 2D transient PDE problems, supporting various boundary conditions, customizable architectures, and multiple physical applications.

Contribution

It provides a flexible, easy-to-use platform for 2D transient PDE simulations with extensive features and a library of example problems, enhancing accessibility and reproducibility.

Findings

Supports multiple boundary conditions including Neumann and Dirichlet.

Includes routines for visualization and convergence analysis.

Offers a library of diverse physical simulation examples.

Abstract

We present an open-source Physics Informed Neural Network environment for simulations of transient phenomena on two-dimensional rectangular domains, with the following features: (1) it is compatible with Google Colab which allows automatic execution on cloud environment; (2) it supports two dimensional time-dependent PDEs; (3) it provides simple interface for definition of the residual loss, boundary condition and initial loss, together with their weights; (4) it support Neumann and Dirichlet boundary conditions; (5) it allows for customizing the number of layers and neurons per layer, as well as for arbitrary activation function; (6) the learning rate and number of epochs are available as parameters; (7) it automatically differentiates PINN with respect to spatial and temporal variables; (8) it provides routines for plotting the convergence (with running average), initial conditions learnt, 2D and 3D snapshots from the simulation and movies (9) it includes a library of problems: (a) non-stationary heat transfer; (b) wave equation modeling a tsunami; (c) atmospheric simulations including thermal inversion; (d) tumor growth simulations.