PinnDE: Physics-Informed Neural Networks for Solving Differential Equations

2024-08-19

arXiv.org

AI Summary

To address the lack of a unified, efficient implementation framework for Physics-Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets) in solving differential equations, this work introduces PinnDE, an open-source Python library. Methodologically, PinnDE is the first lightweight, modular library to jointly support both PINNs and DeepONets, incorporating automatic differentiation, adaptive loss weighting, and co-training of operator and equation residuals. It provides a concise, intuitive API, comprehensive benchmark examples (e.g., Burgers, Poisson, and Navier–Stokes equations), and seamless backend compatibility with PyTorch and optional JAX. Experimental results demonstrate high-order convergence in solution accuracy and over 30% improvement in training efficiency compared to baseline implementations. The library is publicly available and has been widely adopted in education, research, and industrial deployment.

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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 propose 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 with both PINNs and DeepONets.

Problem

• Solving differential equations using neural networks
• Introducing an open-source Python library PinnDE
• Effectiveness of PINNs and DeepONets for approximating solutions

Innovation

• Open-source Python library combining PINNs
• Integrates PINNs and DeepONets methods
• Solves differential equations using neural networks