A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems

DOI10.1137/19M1310050zbMath1455.35246arXiv1909.11759OpenAlexW3093990252MaRDI QIDQ5132016

Lizuo Liu, Xiaoguang Li, Wei Cai

Publication date: 9 November 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.11759

zbMATH Keywords

neural networkHelmholtz equationsphase shifthigh frequency waves

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) PDEs in connection with optics and electromagnetic theory (35Q60) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Waves and radiation in optics and electromagnetic theory (78A40) Numerical methods for partial differential equations, boundary value problems (65N99)

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Uses Software

• Adam

Cites Work

• Unnamed Item
• Least-squares finite element method for fluid dynamics
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• BCR-net: A neural network based on the nonstandard wavelet form
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Learning dominant wave directions for plane wave methods for high-frequency Helmholtz equations
• A wideband fast multipole method for the Helmholtz equation in three dimensions
• Ten Lectures on Wavelets
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• Finite Element Methods of Least-Squares Type
• Accuracy Properties of the Wave‐Ray Multigrid Algorithm for Helmholtz Equations
• A fast multipole method for Maxwell equations stable at all frequencies

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