Zero-Shot Compositional Generalization in Neural PDE Solvers via Conservative Material-Guided Routing

Neural PDE solvers have shown strong generalization across new geometries and parameter regimes, but a distinct question remains less explored: if a model has seen different physical constituents separately during training, can it correctly combine that knowledge when those familiar constituents appear together for the first time? In this setting, the individual constituents are not new; what is new is their composition. We study this problem as zero-shot compositional generalization in heterogeneous PDEs. For latent-state transformer PDE solvers, providing material information as input features alone does not necessarily ensure that this information is used appropriately when forming latent physical states. To address this, we introduce Material-Interface Guided Transolver with Conservative Compositional Routing (CCR-MIG), which allows constituent information not only to be represented as input, but also to influence latent-state formation. Rather than perturbing the learned routing logits, CCR-MIG composes constituent-specific routing distributions with the original data-driven routing through a bounded convex mixture, and a conflict-aware gate reduces this intervention where constituent influences overlap. We evaluate the method on heterogeneous linear elasticity and steady thermal conduction. Across six seeded training runs, CCR-MIG reduces the mean relative error of the original Transolver from 0.08456 to 0.05818 in elasticity and from 0.03775 to 0.02323 in thermal conduction. Compared with a feature-matched baseline that receives the same constituent information but leaves latent-state formation unchanged, CCR-MIG further reduces error by 23.4% and 18.9%, respectively. Effect sizes favor CCR-MIG in all four primary comparisons, though six paired runs do not support a conclusive significance claim.