Neural Parameter Regression for Explicit Representations of PDE Solution Operators
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 matrices, thereby boosting computational efficiency and scalability. The framework shows remarkable adaptability to new initial and boundary conditions, allowing for rapid fine-tuning and inference, even in cases of out-of-distribution examples.
Cite
@article{arxiv.2403.12764,
title = {Neural Parameter Regression for Explicit Representations of PDE Solution Operators},
author = {Konrad Mundinger and Max Zimmer and Sebastian Pokutta},
journal= {arXiv preprint arXiv:2403.12764},
year = {2024}
}
Comments
ICLR24 Workshop AI4Differential Equations In Science, 15 pages, 4 figures, 2 tables, 1 algorithm