ImpactFormer: A Space–Time Factorized Neural Operator for Heterogeneous Finite-Element Simulations

Learning a single surrogate across finite-element simulation datasets is challenging because their geometries, meshes, design parameterizations, and time grids differ. We study this problem for vehicle crash, one of the most demanding structural simulations, and introduce ImpactFormer, a neural operator trained jointly across crash datasets to map undeformed geometry and design parameters to complete spatiotemporal displacement fields. Each simulation is encoded by anchor tokens sampled from its structural mesh and a variable-length set of named parameter tokens, processed by a shared attention backbone with dataset-specific feature-wise modulation, so that datasets with different meshes and parameterizations share one conditional model. A space–time factorized head predicts simulation- and node-specific spatial coefficients of a single learned temporal basis shared across nodes, simulations, and datasets, so that one temporal representation serves datasets with different durations and frame counts and reconstructs complete trajectories in a single forward pass. We train a 19.2M-parameter model on 4,641 full-vehicle frontal crash simulations from five datasets: the CarCrashNet Neon, Yaris, and Silverado design-of-experiments tracks, the geometry-morphing SHIFT-Crash dataset, and Yaris-yield, a yield-strength dataset generated for this work. These datasets span approximately 350k to over 1M nodes, 12 to 40 predicted time frames, and three to six design parameters. Under a fixed evaluation protocol, ImpactFormer outperforms all state-of-the-art neural solvers on Neon, Yaris, Silverado and SHIFT-Crash: it reduces RMSE by up to 12.1% relative to the strongest of them, CrashSolver, and by 23% to 49% on average relative to AB-UPT, FIGConvUNet, Transolver, GeoTransolver and GAOT. It remains the most accurate neural solver on the complete meshes of up to 1.07M nodes, where it is up to 15% more accurate than CrashSolver retrained at full resolution. Pretrained only on sedans, ImpactFormer also adapts to a completely unseen pickup truck from a handful of simulations. Sixteen simulations of the truck reduce its error by 88%, and with four simulations its error is less than half that of the same network trained from scratch. Combined with a classical reduced-order model, ImpactFormer reduces error by up to 29% relative to CrashSolver on fixed meshes.