Work

Meshfree Variational-Physics-Informed Neural Networks (MF-VPINN): An Adaptive Training Strategy

Year: 2024

Type: article

Abstract: In this paper, we introduce a Meshfree Variational-Physics-Informed Neural Network. It is a Variational-Physics-Informed Neural Network that does not require the generation of the triangulation of the entire domain and that can be trained with an adaptive set of test functions. In order to generate the test space, we exploit an a posteriori error indicator and add test functions only where the error is higher. Four training strategies are proposed and compared. Numerical results show that the accuracy is higher than the one of a Variational-Physics-Informed Neural Network trained with the same number of test functions but defined on a quasi-uniform mesh.

Source: Algorithms

DOI: 10.3390/a17090415

Authors: Stefano Berrone, Moreno Pintore

Institutions: Politecnico di Torino, Institut national de recherche en sciences et technologies du numérique, Sorbonne Université, Laboratoire Jacques-Louis Lions

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,819

Funder: Politecnico di Torino