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

arXiv:2605.24651 · math.NA, cs.LG, cs.NA · Submitted 2026-05-23 · Read on arXiv

math.NA, cs.LG, cs.NA

Submitted: 2026-05-23

Updated: 2026-08-27

Code: https://github.com/bokai-zhu/WINO

Terminology

• Benchmark — 31× in this paper · explained in 2 episodes
• Accuracy — 25× in this paper · explained in 1 episode
• Loss Function — 17× in this paper · explained in 2 episodes
• Fidelity — 11× in this paper · explained in 2 episodes
• Fourier Neural Operator — 6× in this paper
• Robustness — 6× in this paper · explained in 5 episodes
• Adam — 5× in this paper · explained in 2 episodes
• DeepONet — 5× in this paper · explained in 2 episodes
• Weak-form Physics-Informed Neural Operator — 5× in this paper
• Activation Function — 2× in this paper · explained in 1 episode
• Core — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Aggregation — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Computational overhead — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Distribution Shift — 1× in this paper · explained in 5 episodes
• Generative AI — 1× in this paper · explained in 2 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Homogenization — 1× in this paper · explained in 2 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Latent Space — 1× in this paper · explained in 7 episodes

Sources

• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Fourier Neural Operator for Parametric Partial Differential Equations
• Finite Element Operator Network for Solving Elliptic-type parametric PDEs
• NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers
• Pretrain Finite Element Method: A Pretraining and Warm-start Framework for PDEs via Physics-Informed Neural Operators
• SOAP: Improving and Stabilizing Shampoo using Adam

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