Nonlinear model reduction for operator learning

Hamidreza Eivazi, Stefan Wittek, Andreas Rausch

Keywords: Operator learning, nonlinear model reduction, kernel methods

TL;DR: We introduce kernel-PCA DeepONet (KPCA-DeepONet) as an efficient framework to combine nonlinear model reduction with operator learning.

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.

Submission Number: 73