Work

SetPINNs: Set-based Physics-informed Neural Networks

Year: 2024

Type: preprint

Abstract: Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal solutions. We introduce SetPINNs, a framework that effectively captures local dependencies. With a finite element-inspired sampling scheme, we partition the domain into sets to model local dependencies while simultaneously enforcing physical laws. We provide a rigorous theoretical analysis showing that SetPINNs yield unbiased, lower-variance estimates of residual energy and its gradients, ensuring improved domain coverage and reduced residual error. Extensive experiments on synthetic and real-world tasks show improved accuracy, efficiency, and robustness.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2409.20206

Authors: Nagda, Mayank, Ostheimer, Phil, Specht, Thomas, Rhein, Frank, Jirasek, Fabian, Mandt, Stephan, Kloft, Marius, Fellenz, Sophie

Institutions: Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau, Karlsruhe Institute of Technology, University of California, Irvine

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4403815103

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Cited by: 1

Related to: 10