PinnDE: Physics-Informed Neural Networks for Solving Differential Equations

TL;DR

PinnDE is an open-source Python library that leverages physics-informed neural networks and deep operator networks to effectively solve differential equations, providing a practical tool for researchers and practitioners.

Contribution

The paper introduces PinnDE, a new software library that integrates PINNs and DeepONets for solving differential equations, with examples demonstrating its effectiveness.

Findings

PinnDE successfully approximates solutions of differential equations.

The library supports both PINNs and DeepONets approaches.

Worked examples validate PinnDE's accuracy and usability.

Abstract

In recent years the study of deep learning for solving differential equations has grown substantially. The use of physics-informed neural networks (PINNs) and deep operator networks (DeepONets) have emerged as two of the most useful approaches in approximating differential equation solutions using machine learning. Here, we introduce PinnDE, an open-source Python library for solving differential equations with both PINNs and DeepONets. We give a brief review of both PINNs and DeepONets, introduce PinnDE along with the structure and usage of the package, and present worked examples to show PinnDE's effectiveness in approximating solutions of systems of differential equations with both PINNs and DeepONets.