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

• URL: http://arxiv.org/abs/2605.24651v1
• Date: Sat, 23 May 2026 16:35:08 GMT
• Title: WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains
• Abstract summary: WINO is a data-free framework that combines the efficiency of neural operators with the geometric flexibility of the $varphi$-FEM method.<n> WINO achieves high accuracy below 0.04 across all benchmarks, while reducing total computational time by 50--80% compared with purely data-driven methods.
• Score: 3.8397427914728426
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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. 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 that WINO achieves high accuracy below 0.04 across all benchmarks, while reducing total computational time by 50--80\% compared with purely data-driven methods.

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