arXiv Machine Learning By Vijay Kumar, Gautam Singh

Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems

Read the original on arXiv Machine Learning →

arXiv:2606. 16510v1 Announce Type: cross Abstract: This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

arXiv Machine Learning
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INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities

arXiv:2606. 18032v1 Announce Type: cross Abstract: We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN).

By Shayan Dodge (DESTeC, University of Pisa, Pisa, Italy), Alessandro Formisano (Department of Engineering, University of Campania Luigi Vanvitelli, Aversa, Italy), Sami Barmada (DESTeC, University of Pisa, Pisa, Italy)
arXiv Machine Learning
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arXiv:2607. 20378v1 Announce Type: new Abstract: Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability.

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