RiemannONets: interpretable neural operators for Riemann problems

DOI10.1016/j.cma.2024.116996zbMATH Open1539.65139MaRDI QIDQ6550161

Vivek Oommen, Ameya D. Jagtap, Ahmad Peyvan, George Em. Karniadakis

Publication date: 4 June 2024

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

zbMATH Keywords

Riemann problemscompressible flowsdata-driven basisneural operator networks

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Basic methods in fluid mechanics (76M99) Software, source code, etc. for problems pertaining to numerical analysis (65-04)

Cites Work

• B-DeepONet: an enhanced Bayesian deeponet for solving noisy parametric PDEs using accelerated replica exchange SGLD
• DeepM\&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks
• DeepM\&Mnet for hypersonics: predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators
• A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data
• Physics-informed neural networks for inverse problems in supersonic flows
• Physics-informed neural networks for high-speed flows
• Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
• 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
• A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials
• Scalable uncertainty quantification for deep operator networks using randomized priors
• SVD perspectives for augmenting DeepONet flexibility and interpretability
• Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
• High-order methods for hypersonic flows with strong shocks and real chemistry
• Learning stiff chemical kinetics using extended deep neural operators

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