English

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

Computational Engineering, Finance, and Science 2024-02-21 v2 Machine Learning Mathematical Software Numerical Analysis Numerical Analysis

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.

Keywords

Cite

@article{arxiv.2310.03755,
  title  = {Physics Informed Neural Network Code for 2D Transient Problems (PINN-2DT) Compatible with Google Colab},
  author = {Paweł Maczuga and Maciej Sikora and Maciej Skoczeń and Przemysław Rożnawski and Filip Tłuszcz and Marcin Szubert and Marcin Łoś and Witold Dzwinel and Keshav Pingali and Maciej Paszyński},
  journal= {arXiv preprint arXiv:2310.03755},
  year   = {2024}
}

Comments

21 pages, 13 figures

R2 v1 2026-06-28T12:41:51.663Z