WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains

[2605.24651] WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains Skip to main content Search Submit Donate Log in Mathematics > Numerical Analysis arXiv:2605.24651 (math) [Submitted on 23 May 2026 ( v1 ), last revised 27 Aug 2026 (this version, v3)] Title: WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains Authors: Bokai Zhu , Yizheng Wang , Qinghui Zhang , Timon Rabczuk View PDF HTML (experimental) Abstract: We propose a Weak-form Physics-Informed Neural Operator (WINO), a data-free framework that combines the efficiency of neural operators with the geometric flexibility of the $\varphi$-finite element method ($\varphi$-FEM). $\varphi$-FEM is an unfitted method that accommodates geometric variations without body-fitted meshes, where the domain geometry is represented by the level-set function $\varphi$. To impose the boundary conditions, Dirichlet problems adopt the $\varphi$-FEM lifting so only the homogeneous displacement contribution is learned, whereas traction-driven Neumann problems additionally predict the auxiliary fields necessary for the unfitted weak formulation. Parameters are trained by minimizing squared weak-form residuals aligned with $\varphi$-FEM together with squared penalties on the cut-cell auxiliary equations, which removes the need for large paired datasets of converged reference solutions. When labeled reference data are available, an optional data-augmented variant (WINO+data) can further combine this physics-informed loss with a supervised term. After training, WINO outputs can seed the nonlinear $\varphi$-FEM solvers as neural operator warm starts (NOWS), which reduce iteration counts relative to traditional cold-started solvers. Numerical benchmarks show substantial accuracy of WINO together with total training times of about 15%-70% of those of supervised $\varphi$-FEM-FNO across all cases, without requiring reference-solution generation. Subjects: Numerical Analysis (math.NA) ; Machine Learning (cs.LG) Cite as: arXiv:2605.24651 [math.NA] (or arXiv:2605.24651v3 [math.NA] for this version) https://doi.org/10.48550/arXiv.2605.24651 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Bokai Zhu [ view email ] [v1] Sat, 23 May 2026 16:35:08 UTC (36,970 KB) [v2] Sun, 19 Jul 2026 08:45:06 UTC (21,098 KB) [v3] Thu, 27 Aug 2026 19:23:14 UTC (21,149 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2026-05 Change to browse by: cs cs.LG cs.NA math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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