An abstract framework for neural flows with composition and separation structures is proven to universally approximate any operator, recovering ResNet and plain architectures via discretization.
arXiv preprint arXiv:2508.20650 , year=
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McMg is a phase-space multi-channel multigrid preconditioner that maps residuals to corrections while retaining unresolved wave information in extra channels, showing fewer iterations and lower runtime than classical and neural baselines on high-wavenumber 3D Helmholtz problems.
citing papers explorer
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Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations
An abstract framework for neural flows with composition and separation structures is proven to universally approximate any operator, recovering ResNet and plain architectures via discretization.
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McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation
McMg is a phase-space multi-channel multigrid preconditioner that maps residuals to corrections while retaining unresolved wave information in extra channels, showing fewer iterations and lower runtime than classical and neural baselines on high-wavenumber 3D Helmholtz problems.