Data-Free Weak-Form Staggered Neural Operators for Magneto-Mechanical Coupling in Finite-Strain Elastomers
This study addresses the high computational cost and reliance on labeled data in magneto-mechanical coupling simulations for magnetically active elastomers undergoing large deformations. To this end, a data-free physics-informed operator learning framework is proposed. The framework constrains neural operator training using finite element weak-form residuals and introduces a weak-form alternating optimization strategy to decouple the strongly coupled saddle-point problem while preserving physical correlations. Furthermore, a neural-initialized Newton solver is incorporated to accelerate convergence. Experimental results demonstrate that the proposed method accurately captures coupled responses across diverse parameterized scenarios, significantly reducing computational costs and enhancing generalization capability.