Variational Physics-informed Neural Operator (VINO) for solving partial differential equations

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autorschaft

  • Mohammad Sadegh Eshaghi
  • Cosmin Anitescu
  • Manish Thombre
  • Yizheng Wang
  • Xiaoying Zhuang
  • Timon Rabczuk

Organisationseinheiten

Externe Organisationen

  • Bauhaus-Universität Weimar
  • Indian Institute of Technology Bombay (IITB)
  • Tsinghua University
  • Tongji University
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Aufsatznummer117785
FachzeitschriftComputer Methods in Applied Mechanics and Engineering
Jahrgang437
Frühes Online-Datum3 Feb. 2025
PublikationsstatusVeröffentlicht - 15 März 2025

Abstract

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or boundary conditions or different input configurations. This study proposes the Variational Physics-Informed Neural Operator (VINO), a deep learning method designed for solving PDEs by minimizing the energy formulation of PDEs. This framework can be trained without any labeled data, resulting in improved performance and accuracy compared to existing deep learning methods and conventional PDE solvers. By discretizing the domain into elements, the variational format allows VINO to overcome the key challenge in physics-informed neural operators, namely the efficient evaluation of the governing equations for computing the loss. Comparative results demonstrate VINO's superior performance, especially as the mesh resolution increases. As a result, this study suggests a better way to incorporate physical laws into neural operators, opening a new approach for modeling and simulating nonlinear and complex processes in science and engineering.

ASJC Scopus Sachgebiete

Zitieren

Variational Physics-informed Neural Operator (VINO) for solving partial differential equations. / Eshaghi, Mohammad Sadegh; Anitescu, Cosmin; Thombre, Manish et al.
in: Computer Methods in Applied Mechanics and Engineering, Jahrgang 437, 117785, 15.03.2025.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Eshaghi MS, Anitescu C, Thombre M, Wang Y, Zhuang X, Rabczuk T. Variational Physics-informed Neural Operator (VINO) for solving partial differential equations. Computer Methods in Applied Mechanics and Engineering. 2025 Mär 15;437:117785. Epub 2025 Feb 3. doi: 10.48550/arXiv.2411.06587, 10.1016/j.cma.2025.117785
Eshaghi, Mohammad Sadegh ; Anitescu, Cosmin ; Thombre, Manish et al. / Variational Physics-informed Neural Operator (VINO) for solving partial differential equations. in: Computer Methods in Applied Mechanics and Engineering. 2025 ; Jahrgang 437.
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AU - Wang, Yizheng

AU - Zhuang, Xiaoying

AU - Rabczuk, Timon

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