Parallel spatiotemporal order-reduced Gaussian process for dynamic full-field multi-physics prediction of hypervelocity collisions in real-time with limited data

Abstract

Data-driven evaluation of full-field variables over time poses considerable challenges and little explored. Therefore, we propose a novel dynamic parallel spatiotemporal order reduced Gaussian Process scheme (Dyna-PSTORGP) to accurately predict the full-field, time-sequenced multi-physics responses of hypervelocity collisions in real-time using limited data. In which, we first propose parallel and reduction in space and temporal dimensionalities and investigate the optimal temporal reconstruction method, establishing the spatial-temporal unified latent (feature) spaces that efficiently decouple the strong nonlinear and multi-physics dynamic responses. Next, we propose a hierarchical parallel multi-Gaussian Processes model, emulating the maps from initial input conditions to spatiotemporal order-reduced dynamic response. This hierarchical parallelism operates on two levels: an inner parallel modeling across each component of order-reduced spatial output within individual time steps, and an outer parallel modeling across the reduced time steps. This dual-layered structure not only enhances computational efficiency and enables accurate dynamic response predictions across spatiotemporal scales, effectively addressing the common issue of error accumulation in sequential prediction, but also ensures rapid training and prediction with confidence intervals. Moreover, we investigated different kernels and sensitivity to assess the effects of varying initial conditions in hypervelocity collisions, revealing the collision inclination angle exerts a greater influence on the damage response than both the direction angle and collision velocity. Numerical examples, including simulations on the Whipple shield and space station, validate the Dyna-PSTORGP model's capability for rapid parallel construction and training, completing in seconds (e.g., 12.8 s) with a limited dataset (e.g., 125 samples). The model achieves real-time, high-precision multi-physics predictions for complex nonlinear hypervelocity collisions (e.g., 1.9 s) and consistently maintains high accuracy (e.g., relative errors <5 %) across full-field, high-dimensional scenarios (e.g., 1,134,172 degrees of freedom).