Semantic-Guided Manifold Search for Physical Inverse Design

Physical inverse design (e.g., spatial coil design) aims to identify geometric configurations satisfying target physical responses. We consider settings with expensive black-box simulations and no access to simulator gradients. As a practically important representative task, spatial coil design optimizes 3D conductive paths for induction heating and magnetic-field generation, and faces challenging high-dimensional geometric search under limited simulation budgets. Vanilla Bayesian optimization does not by itself specify how domain-relevant local deformations should be constructed from simulation feedback. We present Semantic-Guided Manifold Search (SemGMS), a closed-loop simulation-driven optimization framework. Rather than relying on large-language models to directly generate geometries, SemGMS distills current simulation feedback and historical trials into structured semantic actions. Its core module, the Geometry Grounding Translator (GGT), converts each semantic action into topology-preserving, bounded local deformation families for graph-represented geometries. A surrogate-guided executor performs Bayesian search strictly within these low-dimensional deformation families. Joint geometric feasibility is checked before each simulation. We validate SemGMS on SimCoil-Bench, a unified benchmark for spatial-coil inverse design encompassing welding-loss, magnetic-field, and hybrid multi-objective scenarios. Across five-seed evaluations, SemGMS achieves the lowest mean spatial uniformity errors among the compared methods on all three tasks while maintaining competitive response magnitude.