Multiphysics Post-Training: From Decoupled Modules to Coupled Equilibria

Multiphysics simulation is essential for systems governed by interacting physical processes, classically relying on partitioned analysis to couple interdisciplinary solvers through interface exchange. Neural simulation can inherit this modular architecture by assembling independently pretrained physical modules. However, directly assembling modules pretrained to learn isolated single physics introduces an objective mismatch, as they are never optimized for the target coupled equilibrium. To address this, we derive module-to-system error bounds, proving that coupled accuracy is governed by cross-interface operator coupling rather than module fidelity on isolated single physics alone. This motivates multiphysics post-training, a learning paradigm that adapts pretrained modules via a system-level loss on their joint predictions while keeping each module's inputs, outputs, and exchange structure unchanged. Under this paradigm, we provide two complementary implementations, Finite Unrolling (Unrolled-$K$) for low-latency inference and Equilibrium Post-Training (EquiPT), which achieves $\mathcal{O}(1)$ activation memory and high fidelity via an implicit adjoint. Across neutron–thermal, reaction–diffusion, and fluid–structure interaction benchmarks, EquiPT reduces system error by 48.7%–96.1% over frozen assembly. These gains stem from training at the coupled equilibrium rather than from coupled data alone, as EquiPT also reduces system error by 34.2%–74.1% relative to module-wise continued training on the same coupled data. Pretrained initialization further improves accuracy under the same post-training budget. Furthermore, post-training shifts the measured coupling spectral radii toward lower values, lowering the ceiling on interface error amplification along each eigenmode.