CoRaWS: Zero-Shot Neural Warm Starts across Topology Families for Nonlinear Magnetostatics

Neural network surrogates have attracted broad interest because they can support repeated physical simulations at low inference cost. However, if deployment on an unseen target topology family still requires collecting high-fidelity labels and training a model, the preparation cost may offset the gains at inference. Even when field prediction errors are low, the predicted solution may not satisfy the numerical solver's convergence criteria. Applications to unseen topology families therefore need to control data preparation costs while ensuring the accuracy of the final solution. For nonlinear magnetostatics, we propose complementary approaches to data construction and initial-guess prediction. We first develop EMTopoGen, a parametric topology generator combining primitive shapes, assembly relations, and continuous parameters. Using it, we construct EMTopoBench-54 with 54 topology families and 27,000 high-fidelity simulation samples. This benchmark supports the study of compositional generalization through training on source families and evaluation on unseen target families. We then develop CoRaWS, a neural warm-start method based on constitutive coordinate reparameterization and field-magnitude awareness. After training on source families, the method generates finite element initial guesses for unseen target topology families without target-family labels or fine-tuning, accelerating the solution process while maintaining high fidelity. Experiments on nonlinear magnetostatic problems show that CoRaWS offers advantages for FEM acceleration, indicating its potential for engineering simulation. Code will be released upon acceptance.