Work

FE-PINNs: Finite-element-based physics-informed neural networks for surrogate modeling

Year: 2026

Type: article

Abstract: We present a method whereby the finite element (FE) method is used to train physics-informed neural networks that are suitable for surrogate modeling. The method is based on a new class of mesh-based neural network operators called stenciled operators, which leverage the inverse isoparametric map of the FE method. In contrast with graph-based methods, stenciled operators can incorporate non-local information over arbitrary spatial domains with computational costs that are length-scale invariant. Using stenciled convolutional operations as an exemplar, we demonstrate the performance of the method in several training and testing scenarios with linear-elastic boundary-value problems of varying geometries. The resulting neural networks show reasonable accuracy when tested on unseen geometries that are similar to those used for training. Furthermore, when the number of training geometries is increased, the testing errors systematically decrease, demonstrating that the neural networks learn how to generalize as the training set becomes larger. Further extending the method to allow for variable boundary conditions, properties, and body forces will lead to a general-purpose surrogate modeling framework that can leverage existing FE codes for training.

Source: APL Machine Learning

DOI: 10.1063/5.0299671

Authors: Pranav Sunil, Ryan B. Sills

Institution: Rutgers, The State University of New Jersey

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Army Research Office

Awards: G1432373144, G3039063760, G7452299184, CAREER: Using Physics-Based Machine Learning to Reconcile the Crack Tip with the Plastic Zone during Fracture of Metals