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Variationally mimetic operator networks (Q6185143)

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scientific article; zbMATH DE number 7796642

Language	Label	Description	Also known as
English	Variationally mimetic operator networks	scientific article; zbMATH DE number 7796642

Statements

scholarly article

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Variationally mimetic operator networks (English)

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Michael R. A. Abdelmalik

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Thomas J. R. Hughes

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Assad A. Oberai

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Computer Methods in Applied Mechanics and Engineering

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publication date

29 January 2024

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full work available at URL

https://arxiv.org/abs/2209.12871

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zbMATH Keywords

variational formulation

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deep neural operator

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deep operator network

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error analysis

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MaRDI profile type

MaRDI publication profile

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

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B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

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Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

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Parallel physics-informed neural networks via domain decomposition

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Scientific machine learning through physics-informed neural networks: where we are and what's next

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A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials

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Scalable uncertainty quantification for deep operator networks using randomized priors

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DeepM\&Mnet for hypersonics: predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators

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DeepM\&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks

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MIONet: Learning Multiple-Input Operators via Tensor Product

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Error estimates for DeepONets: a deep learning framework in infinite dimensions

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Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients

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A Bayesian level set method for geometric inverse problems

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Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)

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Imposing Dirichlet boundary conditions with Nitsche's method and spline-based finite elements

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Weak imposition of Dirichlet boundary conditions in fluid mechanics

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Identifiers

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10.1016/j.cma.2023.116536

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:6185143

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