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Lately, the approximation of operators for partial differential equations using deep learning has been extensively investigated. However, these deep learning approaches have limitations in terms of accuracy. In this work, we present a multi-level approach to accurately approximate linear operators using physics-informed Green operator networks. This method allows for the iterative reduction of the approximation errors through a sequence of operators, each targeting errors of increasing complexity at progressively smaller scales. Numerical examples for the one-dimensional Poisson problem will be presented to demonstrate the effectivenessof the proposed multi-level approach. | Lately, the approximation of operators for partial differential equations using deep learning has been extensively investigated. However, these deep learning approaches have limitations in terms of accuracy. In this work, we present a multi-level approach to accurately approximate linear operators using physics-informed Green operator networks. This method allows for the iterative reduction of the approximation errors through a sequence of operators, each targeting errors of increasing complexity at progressively smaller scales. Numerical examples for the one-dimensional Poisson problem will be presented to demonstrate the effectivenessof the proposed multi-level approach. | ||
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| + | <pdf>Media:Draft_Sanchez Pinedo_111518280130.pdf</pdf> | ||
Latest revision as of 13:44, 1 July 2024
Abstract
Lately, the approximation of operators for partial differential equations using deep learning has been extensively investigated. However, these deep learning approaches have limitations in terms of accuracy. In this work, we present a multi-level approach to accurately approximate linear operators using physics-informed Green operator networks. This method allows for the iterative reduction of the approximation errors through a sequence of operators, each targeting errors of increasing complexity at progressively smaller scales. Numerical examples for the one-dimensional Poisson problem will be presented to demonstrate the effectivenessof the proposed multi-level approach.
Full Paper
Document information
Published on 01/07/24
Accepted on 01/07/24
Submitted on 01/07/24
Volume Data Science, Machine Learning and Artificial Intelligence, 2024
DOI: 10.23967/wccm.2024.130
Licence: CC BY-NC-SA license
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