Nonlinear model reduction for operator learning

arXiv:2403.18735v1 Announce Type: new
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 …

abstract accuracy architecture architectures arxiv cs.lg cs.na deeponet extension function math.na networks neural networks nonlinear model pod spaces terms type