Data-driven spatiotemporal modeling for structural dynamics on irregular domains by stochastic dependency neural estimation

Numerical simulations for spatiotemporal processes involving material, geometrical and contact nonlinearities might be computationally prohibitive for many-evaluation applications. Considering the strong nonlinearity of dynamic processes, the prediction of high-dimensional spatiotemporal responses remains challenging for most surrogate-based models. To address such issues, a Stochastic Dependency Neural Estimator (SDNE) is proposed to construct the mapping from the input parameter domain to the high-dimensional spatiotemporal response domain, revealing the underlying relationship between the high-dimensional regression estimation and manifold distribution hypothesis. Moreover, Graph Neural Networks (GNN) and Temporal Convolutional Neural Networks (TCN) are integrated to capture nonlinear features from irregular geometries and time series simultaneously. Two high-speed impact cases involving large deformation and highly nonlinear transients are investigated to validate the proposed method. The proposed SDNE achieves highly accurate prediction compared with Finite Element (FE) evaluations. To further validate the practical application of the proposed method, multi-objective crashworthiness optimizations are performed with the proposed SDNE. The results show that the proposed SDNE provides reliable predictions for spatiotemporal dynamics