Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

TL;DR

This paper presents a method for discovering nonlinear partial differential equations from data using physics-informed neural networks, applicable to various physical systems and data arrangements.

Contribution

It introduces two classes of algorithms for PDE discovery based on data distribution, advancing the application of physics-informed neural networks in data-driven scientific discovery.

Findings

Effective in identifying PDEs for conservation laws

Successfully applied to fluid flow and wave propagation

Demonstrates robustness across diverse physics benchmarks

Abstract

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second part of our two-part treatise, we focus on the problem of data-driven discovery of partial differential equations. Depending on whether the available data is scattered in space-time or arranged in fixed temporal snapshots, we introduce two main classes of algorithms, namely continuous time and discrete time models. The effectiveness of our approach is demonstrated using a wide range of benchmark problems in mathematical physics, including conservation laws, incompressible fluid flow, and the propagation of nonlinear shallow-water waves.