PDE generalization of in-context operator networks: a study on 1D scalar nonlinear conservation laws

DOI10.1016/J.JCP.2024.113379MaRDI QIDQ6639294

Liu Yang, Stanley Osher

Publication date: 15 November 2024

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

zbMATH Keywords

conservation lawsmachine learningoperator learningin-context learning

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx)

Cites Work

• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
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• Weighted essentially non-oscillatory schemes
• Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• DGM: a deep learning algorithm for solving partial differential equations
• A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
• Model reduction and neural networks for parametric PDEs
• Mosaic flows: a transferable deep learning framework for solving PDEs on unseen domains
• Transfer learning based multi-fidelity physics informed deep neural network
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios
• Solving high-dimensional partial differential equations using deep learning
• Solving parametric PDE problems with artificial neural networks
• Reliable extrapolation of deep neural operators informed by physics or sparse observations

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