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:2209.11395 , year=
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Autoencoders enable nonlinear dimensionality reduction for parametric ODEs, with analysis of exact representation properties and convergence of the reduced model to the original.
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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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Model reduction of parametric ordinary differential equations via autoencoders: representation properties and convergence analysis
Autoencoders enable nonlinear dimensionality reduction for parametric ODEs, with analysis of exact representation properties and convergence of the reduced model to the original.