SolidX: Learning Physical Interactions with Structured Bases for Multi-Solid Systems

Simulating contact-induced deformation in multi-solid systems is critical to many scientific and engineering applications, yet remains challenging for neural operators due to the complex and heterogeneous interactions among multiple physical bodies. Transformer-based neural operators have recently emerged as a powerful paradigm for physical modeling, typically compressing high-dimensional physical fields into a shared latent space to efficiently capture long-range physical dependencies. In multi-solid systems, however, such homogeneous latent representations tend to implicitly entangle distinct intra- and inter-solid couplings within the same set of latent tokens. Such entanglement can limit interaction-specific expressiveness, particularly in data-scarce scenarios. Inspired by structured decomposition principles in classical computational mechanics, we propose ***SolidX***, an interaction-structured neural operator that explicitly organizes latent physical bases around distinct interaction patterns in multi-solid systems. By assigning dedicated basis groups to heterogeneous physical interactions, SolidX captures complementary physical behaviors more effectively while retaining linear complexity. Extensive experiments across five multi-solid benchmarks demonstrate that SolidX consistently outperforms strong baselines in prediction accuracy, convergence efficiency, and sample efficiency. Our results indicate that interaction-structured representations provide an effective inductive bias for operator learning, particularly in data-scarce scenarios where high-fidelity data are usually expensive to obtain.