Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs

Ðinh Dũng; Van Kien Nguyen; Duong Thanh Pham

doi:10.1016/j.jco.2023.101779

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Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs

Ðinh Dũng Van Kien Nguyen Duong Thanh Pham

Year: 2023 Journal: Journal of Complexity Vol: 79 Pages: 101779-101779 Publisher: Elsevier BV

DOI: 10.1016/j.jco.2023.101779

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Keywords:

Mathematics Gaussian measure Measure (data warehouse) Probability measure Parametric statistics Applied mathematics Artificial neural network Affine transformation Hilbert space Gaussian Polynomial Separable space Multilinear map Pure mathematics Discrete mathematics Mathematical analysis Computer science Artificial intelligence

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Model Reduction and Neural Networks

Physical Sciences → Physics and Astronomy → Statistical and Nonlinear Physics

Neural Networks and Applications

Physical Sciences → Computer Science → Artificial Intelligence

Probabilistic and Robust Engineering Design

Social Sciences → Decision Sciences → Statistics, Probability and Uncertainty

Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs

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