SOME COMPARISONS OF NEURAL NETWORK ARCHITECTURES FOR SCIENTIFIC MACHINE LEARNING
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Authors
Sustaita, Javier J.
Subjects
scientific machine learning
physics-informed neural networks
operator learning
residual neural networks
DeepONet
Fourier neural operator
physics-informed neural networks
operator learning
residual neural networks
DeepONet
Fourier neural operator
Advisors
Austin, Anthony
Date of Issue
2023-12
Date
Publisher
Monterey, CA; Naval Postgraduate School
Language
Abstract
We compare several neural network architectures for approximating solutions to and solution operators for a handful of elementary 1D partial differential equations. Specifically, we examine whether residual layers offer any benefits over fully connected layers in the context of physics-informed machine learning, finding that the two perform similarly on the problems considered. We also compare the popular DeepONet and Fourier neural operator approaches to operator learning and observe that while the two attain comparable accuracies for linear problems, the latter yields more accurate models in the presence of a simple nonlinearity.
Type
Thesis
Description
Series/Report No
Department
Applied Mathematics (MA)
Organization
Identifiers
NPS Report Number
Sponsors
Office of Naval Research, Arlington, VA 22203
Funder
Format
Citation
Distribution Statement
Approved for public release. Distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.