Nonlinear model reduction for operator learning

Hamidreza Eivazi, Stefan Wittek, Andreas Rausch
3/27/2024
cs.LGmath.NA

No official code found. Best implementation: HamidrezaEiv/KPCA-DeepONet (7 stars, MIT, last commit 2024-09-12).

Abstract

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model reduction and neural networks, proper orthogonal decomposition (POD)-DeepONet, has been able to outperform other architectures in terms of accuracy for several benchmark tests. We extend this idea towards nonlinear model order reduction by proposing an efficient framework that combines neural networks with kernel principal component analysis (KPCA) for operator learning. Our results demonstrate the superior performance of KPCA-DeepONet over POD-DeepONet.

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Code Implementations(1)

HamidrezaEiv/KPCA-DeepONetCommunity100%
MIT

Nonlinear model reduction for operator learning

71PythonDec 11, 20232 years agoMIT
deeponetkernel-methodsmodel-reductionoperator-learningpartial-differential-equations+1 more

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Cite this paper

@article{eivazi2024nonlinear,
  title  = {Nonlinear model reduction for operator learning},
  author = {Hamidreza Eivazi and Stefan Wittek and Andreas Rausch},
  year   = {2024},
  eprint = {2403.18735},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2403.18735v1}
}

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