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

TL;DR

This paper introduces physics-informed neural networks that incorporate physical laws into their training to solve nonlinear partial differential equations, enabling data-efficient and physics-consistent solutions.

Contribution

It presents a novel class of neural networks that encode physical laws as priors, facilitating solution inference and discovery of PDEs in a data-efficient manner.

Findings

Networks can infer solutions to PDEs accurately.

Models serve as differentiable physics-informed surrogate models.

Two classes of algorithms for different data scenarios are developed.

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 two part treatise, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct classes of algorithms, namely continuous time and discrete time models. The resulting neural networks form a new class of data-efficient universal function approximators that naturally encode any underlying physical laws as prior information. In this first part, we demonstrate how these networks can be used to infer solutions to partial differential equations, and obtain physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters.