Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks

DOI10.1016/j.camwa.2021.11.001OpenAlexW3212711897WikidataQ114201508 ScholiaQ114201508MaRDI QIDQ825483

Matteo Salvador, Andrea Manzoni, Luca Dedè

Publication date: 17 December 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.17152

zbMATH Keywords

neural networksproper orthogonal decompositionreduced order modelingparametrized PDEskernel proper orthogonal decomposition

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Learning and adaptive systems in artificial intelligence (68T05) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical problems in dynamical systems (65P99)

Related Items (9)

Model order reduction method based on (r)POD-ANNs for parameterized time-dependent partial differential equations ⋮ A non-intrusive neural network model order reduction algorithm for parameterized parabolic PDEs ⋮ Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression ⋮ Conditional variational autoencoder with Gaussian process regression recognition for parametric models ⋮ Operator inference for non-intrusive model reduction with quadratic manifolds ⋮ A dynamic mode decomposition based reduced-order model for parameterized time-dependent partial differential equations ⋮ \textit{FastSVD-ML-ROM}: a reduced-order modeling framework based on machine learning for real-time applications ⋮ AI‐enhanced iterative solvers for accelerating the solution of large‐scale parametrized systems ⋮ Solving parametric partial differential equations with deep rectified quadratic unit neural networks

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