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New PINN Frameworks Tackle Complex Singularities and Perturbations

By PulseAugur Editorial · [3 sources] ·

Two new research papers introduce advanced Physics-Informed Neural Network (PINN) frameworks for solving complex mathematical problems. The first, INI-VPINN, implicitly handles Neumann boundary and interface conditions, achieving higher accuracy and faster convergence on multi-material domains with geometric singularities. The second, a Petrov-Galerkin VPINN, efficiently solves two-dimensional singularly perturbed problems by using neural networks for trial solutions and tensor-product hat functions as test functions, demonstrating high accuracy in capturing multiscale features. AI

IMPACT These new frameworks offer improved accuracy and efficiency for solving complex mathematical problems, potentially advancing scientific simulation and modeling.

RANK_REASON Two academic papers published on arXiv detailing new methods for physics-informed neural networks.

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 3 sources. How we write summaries →

New PINN Frameworks Tackle Complex Singularities and Perturbations

COVERAGE [3]

  1. arXiv cs.LG TIER_1 English(EN) · 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) ·

    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). INI-VPINN naturally incorporates Neumann boundary and interface conditions into the variational formulation. It removes the need for additional…

  2. arXiv cs.LG TIER_1 English(EN) · Sami Barmada ·

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

    We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN). INI-VPINN naturally incorporates Neumann boundary and interface conditions into the variational formulation. It removes the need for additional loss terms or multiple subdomain networks. This f…

  3. arXiv cs.LG TIER_1 English(EN) · Vijay Kumar, Gautam Singh ·

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

    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. The appro…

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