Neural eikonal solver: improving accuracy of physics-informed neural networks for solving eikonal equation in case of caustics

DOI10.1016/J.JCP.2022.111789OpenAlexW4309776501MaRDI QIDQ2112483

Georgy Loginov, Serafim Grubas, Anton A. Duchkov

Publication date: 11 January 2023

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

Full work available at URL: https://arxiv.org/abs/2205.07989

zbMATH Keywords

seismiceikonal equationcausticsphysics-informed neural networktraveltimes

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Related Items (1)

NES

Uses Software

• TensorFlow
• Keras
• DiffSharp
• Adam
• DeepXDE
• DGM
• HypoSVI
• EikoNet
• PINNeik
• PINNtomo

Cites Work

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• Fast sweeping method for the factored eikonal equation
• Multilayer feedforward networks are universal approximators
• DGM: a deep learning algorithm for solving partial differential equations
• On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton-Jacobi partial differential equations
• Gradient-enhanced physics-informed neural networks for forward and inverse PDE 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
• An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications
• Fast Marching Methods
• A fast sweeping method for Eikonal equations
• Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
• DeepXDE: A Deep Learning Library for Solving Differential Equations
• Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
• PINNtomo

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