Finite-Propagation-Aware Multiresolution Neural Operators for Structural Dynamics

Learning structural-dynamics surrogate models requires reasoning over irregular meshes and sparse sensor measurements while respecting the finite wave-propagation time for loads to arrive at different spatial locations. Standard neural operators can capture long-range spatial interactions, yet unconstrained message passing can produce unphysical early responses that violate wave-causality constraints. We introduce FPMR-NO, a finite-propagation-aware multiresolution neural operator that combines causal load-history encoding, wave travel-time gates, and coarse-to-fine graph aggregation. The model propagates separate latent messages corresponding to primary/compressional waves (P-waves), secondary/shear waves (S-waves), and mixed wave modes across graph edges only once the source-to-edge wave arrival condition is satisfied. This multiresolution pooling shortens computational paths without introducing unphysical zero-time shortcuts. On the DeformingPlate stress task, FPMR-NO achieves the lowest mean normalized relative L2 error among the evaluated methods, with a 2.4% relative improvement over AMG and a 1.7% improvement over Transolver. On real ETH four-story impact tests, it reduces macro-channel normalized root mean squared error (NRMSE) to 0.86, a 14.1% error reduction relative to the strongest baseline. Controlled graph-wave experiments further show a 71.8% reduction in relative L2 error and a 13.3-fold reduction in pre-arrival energy against an ungated counterpart.