Applications of physics informed neural operators

Abstract

We present a critical analysis of physics-informed neural operators to solve partial differential equations that are ubiquitous in the study and modeling of physics phenomena using carefully curated datasets. Further, we provide a benchmarking suite which can be used to evaluate physics-informed neural operators in solving such problems. We first demonstrate that our methods reproduce the accuracy and performance of other neural operators published elsewhere in the literature to learn the 1D wave equation and the 1D Burgers equation. Thereafter, we apply our physics-informed neural operators to learn new types of equations, including the 2D Burgers equation in the scalar, inviscid and vector types. Finally, we show that our approach is also applicable to learn the physics of the 2D linear and nonlinear shallow water equations, which involve three coupled partial differential equations. We release our artificial intelligence surrogates and scientific software to produce initial data and boundary conditions to study a broad range of physically motivated scenarios. We provide the \href{https://github.com/shawnrosofsky/PINO_Applications/tree/main}{source code}, an interactive \href{https://shawnrosofsky.github.io/PINO_Applications/}{website} to visualize the predictions of our physics informed neural operators, and a tutorial for their use at the \href{https://www.dlhub.org}{Data and Learning Hub for Science}.

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