Approximation bounds for convolutional neural networks in operator learning

DOI10.1016/j.neunet.2023.01.029arXiv2207.01546OpenAlexW4318159342MaRDI QIDQ6403941

Paolo Zunino, Stefania Fresca, Andrea Manzoni, Nicola Rares Franco

Publication date: 4 July 2022

Full work available at URL: https://doi.org/10.1016/j.neunet.2023.01.029

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Numerical analysis (65-XX) Approximations and expansions (41-XX)

Cites Work

• Unnamed Item
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• A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs
• Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method
• POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition
• High-order approximation rates for shallow neural networks with cosine and \(\mathrm{ReLU}^k\) activation functions
• Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
• Universality of deep convolutional neural networks
• A Generalization of Hermite's Interpolation Formula
• Enhancing Accuracy of Deep Learning Algorithms by Training with Low-Discrepancy Sequences
• A deep learning approach to Reduced Order Modelling of parameter dependent partial differential equations
• Error estimates for DeepONets: a deep learning framework in infinite dimensions
• Equivalence of approximation by convolutional neural networks and fully-connected networks
• Reduced Basis Methods for Partial Differential Equations
• Approximation by superpositions of a sigmoidal function

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