Neural Parameter Regression for Explicit Representations of PDE Solution Operators

arXiv:2403.12764v1 Announce Type: new
Abstract: We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets (Lu et al., 2021) by employing Physics-Informed Neural Network (PINN, Raissi et al., 2019) techniques to regress Neural Network (NN) parameters. By parametrizing each solution based on specific initial conditions, it effectively approximates a mapping between function spaces. Our method enhances parameter efficiency by incorporating low-rank …

abstract arxiv cs.lg cs.na differential framework math.na network neural network novel operators physics physics-informed pinn regression solution type