Nonlinear model reduction for operator learning
Hamidreza Eivazi Stefan Wittek Andreas Rausch
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.