Failure-informed adaptive sampling for PINNs. II: Combining with re-sampling and subset simulation

DOI10.1007/s42967-023-00312-7MaRDI QIDQ6593776

Tao Tang, Tao Zhou, Liang Yan, Zhiwei Gao

Publication date: 27 August 2024

Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

failure probabilityadaptive samplingphysic-informed neural networks (PINNs)

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Inverse problems for PDEs (35R30) Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) (68T20)

Cites Work

• Weak adversarial networks for high-dimensional partial differential equations
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• DGM: a deep learning algorithm for solving partial differential equations
• Self-adaptive physics-informed neural networks
• When and why PINNs fail to train: a neural tangent kernel perspective
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
• Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
• DeepXDE: A Deep Learning Library for Solving Differential Equations
• Machine Learning and Computational Mathematics
• Respecting causality for training physics-informed neural networks
• Failure-Informed Adaptive Sampling for PINNs

Related Items (2)

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