ESPC-Transolver: An Equivalent-Surface Physics-Guided Coupling-Aware Transolver for 3D Multiple Scattering

Abstract

Cross-geometry generalization is particularly challenging because geometry-conditioned multiple-scattering surrogates must infer unseen objects' scattering properties from geometric features while accurately capturing complex, phase-sensitive interactions arising from repeated wave exchange. We introduce ESPC-Transolver, an equivalent-surface physics-guided, coupling-aware Transolver that separates local scattering-response representations from inter-object interaction modeling. For each sound-hard scatterer, canonical scattered-pressure responses are constructed under a shared set of spherical-wave excitations. A local Dirichlet-to-Neumann (DtN) map and modal scattering conversion express these responses on an enclosing sphere, providing physically consistent input channels across geometries. Shared object-local Transolver blocks encode these responses and incident-field traces, while relative-position-aware slice attention models inter-object coupling. Predicted interface pressure and normal flux recovered from the local operator define equivalent sources for reconstructing exterior near- and far-field scattering. We evaluate the method on three-dimensional acoustic multiple-scattering problems at a fixed frequency, comparing it with geometry-conditioned predictors and alternative neural network backbones. ESPC-Transolver achieves lower scattered-field prediction errors on held-out instances of familiar geometry families and generalizes effectively to previously unseen Peanut and Torus geometries. Exterior-field reconstructions reproduce multiple-scattering interference patterns, linking cross-geometry interface prediction to near-field pressure and far-field scattering recovery.