Physics-informed neural networks for the shallow-water equations on the sphere

DOI10.1016/j.jcp.2022.111024OpenAlexW3140906137WikidataQ114163357 ScholiaQ114163357MaRDI QIDQ2133783

Alex Bihlo, Roman O. Popovych

Publication date: 5 May 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.00615

zbMATH Keywords

geophysical fluid dynamicsphysics-informed neural networksscientific machine learningshallow-water equations on the sphere

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)

Related Items (6)

Improved deep neural networks with domain decomposition in solving partial differential equations ⋮ A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions ⋮ Kolmogorov n-width and Lagrangian physics-informed neural networks: a causality-conforming manifold for convection-dominated PDEs ⋮ Adaptive transfer learning for PINN ⋮ Multi-level neural networks for accurate solutions of boundary-value problems ⋮ Operator approximation of the wave equation based on deep learning of Green's function

Uses Software

• chammp
• TensorFlow
• DiffSharp
• ImageNet
• Adam
• AlexNet
• PPINN
• XPINNs
• GPT-3
• PINNsNTK
• NSFnets

Cites Work

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• Atmospheric circulation dynamics and general circulation models
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• Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Large Sample Properties of Simulations Using Latin Hypercube Sampling
• Invariant Discretization Schemes for the Shallow-Water Equations
• Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
• Deep Learning: An Introduction for Applied Mathematicians
• Approximation by superpositions of a sigmoidal function

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