Shawn G. Rosofsky

Shawn G. Rosofsky, Hani Al Majed, E. A. Huerta

We present an end-to-end framework to learn partial differential equations that brings together initial data production, selection of boundary conditions, and the use of physics-informed neural operators to solve partial differential equations that are ubiquitous in the study and modeling of physics phenomena. 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 source code, an interactive website to visualize the predictions of our physics informed neural operators, and a tutorial for their use at the Data and Learning Hub for Science.

Shawn G. Rosofsky, E. A. Huerta

The modeling of multi-scale and multi-physics complex systems typically involves the use of scientific software that can optimally leverage extreme scale computing. Despite major developments in recent years, these simulations continue to be computationally intensive and time consuming. Here we explore the use of AI to accelerate the modeling of complex systems at a fraction of the computational cost of classical methods, and present the first application of physics informed neural operators to model 2D incompressible magnetohydrodynamics simulations. Our AI models incorporate tensor Fourier neural operators as their backbone, which we implemented with the TensorLY package. Our results indicate that physics informed neural operators can accurately capture the physics of magnetohydrodynamics simulations that describe laminar flows with Reynolds numbers $Re\leq250$. We also explore the applicability of our AI surrogates for turbulent flows, and discuss a variety of methodologies that may be incorporated in future work to create AI models that provide a computationally efficient and high fidelity description of magnetohydrodynamics simulations for a broad range of Reynolds numbers. The scientific software developed in this project is released with this manuscript.