On the training and generalization of deep operator networks

DOI10.1137/23M1598751zbMATH Open1543.6833MaRDI QIDQ6573171

Sanghyun Lee, Yeonjong Shin

Publication date: 16 July 2024

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

divide-and-conquerdeep operator networksgeneralization error analysissequential training method

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10)

Cites Work

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• Correction to: ``On the stability and accuracy of least squares approximations
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• The deal.II library, version 9.2
• SVD perspectives for augmenting DeepONet flexibility and interpretability
• Spectral Methods for Time-Dependent Problems
• MIONet: Learning Multiple-Input Operators via Tensor Product
• Error estimates for DeepONets: a deep learning framework in infinite dimensions
• Active Neuron Least Squares: A Training Method for Multivariate Rectified Neural Networks
• Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance
• On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
• Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations
• Convergence rate of DeepONets for learning operators arising from advection-diffusion equations

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