A Helmholtz equation solver using unsupervised learning: application to transcranial ultrasound

DOI10.1016/J.JCP.2021.110430OpenAlexW3097938572MaRDI QIDQ2131029

Ben T. Cox, Antonio Stanziola, Bradley E. Treeby, Simon R. Arridge

Publication date: 25 April 2022

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

Full work available at URL: https://arxiv.org/abs/2010.15761

zbMATH Keywords

Helmholtz equationunsupervised learningtranscranial ultrasoundlearned optimizerphysics-based loss function

Mathematics Subject Classification ID

Numerical linear algebra (65Fxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Elliptic equations and elliptic systems (35Jxx)

Related Items (2)

Finite element approximation of wave problems with correcting terms based on training artificial neural networks with fine solutions ⋮ NSNO: Neumann series neural operator for solving Helmholtz equations in inhomogeneous medium

Uses Software

• k-Wave
• PyTorch
• U-Net
• PyTorch Lightning
• ANODEs
• MgNet
• PDE-Net

Cites Work

• Unnamed Item
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• MgNet: a unified framework of multigrid and convolutional neural network
• A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
• Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
• Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation
• Shifted-Laplacian Preconditioners for Heterogeneous Helmholtz Problems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Solving ill-posed inverse problems using iterative deep neural networks
• Deep Convolutional Neural Network for Inverse Problems in Imaging
• A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems

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