Applications of physics informed neural operators

Abstract

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.

15 pages, 12 figures

References in corpus (14)

• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Fourier Neural Operator for Parametric Partial Differential Equations
• Enhancing Gravitational-Wave Science with Machine Learning
• Enabling real-time multi-messenger astrophysics discoveries with deep learning
• Accelerated, Scalable and Reproducible AI-driven Gravitational Wave Detection
• Accelerating parameter inference with graphics processing units
• Convergence of Artificial Intelligence and High Performance Computing on NSF-supported Cyberinfrastructure
• A brief overview of black hole-neutron star mergers
• Binary Neutron Star Merger Simulations with a Calibrated Turbulence Model
• FAIR principles for AI models with a practical application for accelerated high energy diffraction microscopy
• Inference-optimized AI and high performance computing for gravitational wave detection at scale
• Artificial neural network subgrid models of 2-D compressible magnetohydrodynamic turbulence
• Interpretable AI forecasting for numerical relativity waveforms of quasi-circular, spinning, non-precessing binary black hole mergers
• Advances in Machine and Deep Learning for Modeling and Real-time Detection of Multi-Messenger Sources

Cited by in corpus (8)

• FAIR for AI: An interdisciplinary and international community building perspective
• Plasma Surrogate Modelling using Fourier Neural Operators
• Applications of machine learning in gravitational wave research with current interferometric detectors
• Magnetohydrodynamics with Physics Informed Neural Operators
• A Spectral-based Physics-informed Finite Operator Learning for Prediction of Mechanical Behavior of Microstructures
• Rheo-SINDy: Finding a Constitutive Model from Rheological Data for Complex Fluids Using Sparse Identification for Nonlinear Dynamics
• Artificial-intelligence-based surrogate solution of dissipative quantum dynamics: physics-informed reconstruction of the universal propagator
• Resolving Turbulent Magnetohydrodynamics: A Hybrid Operator-Diffusion Framework