Spatio-temporal, multi-field deep learning of shock propagation in meso-structured media

Abstract: The ability to predict how shock waves traverse porous and architected materials is a decisive factor in planetary defense, national security, and the race to achieve inertial fusion energy. Yet capturing pore collapse, anomalous Hugoniot responses, and localized heating -- phenomena that can determine the success of asteroid deflection or fusion ignition -- has remained a major challenge despite recent advances in single-field and reduced representations. We introduce a multi-field spatio-temporal deep learning model (MSTM) that unifies seven coupled fields -- pressure, density, temperature, energy, material distribution, and two velocity components -- into a single autoregressive surrogate. Trained on high-fidelity hydrocode data, MSTM runs about a thousand times faster than direct simulation, achieving errors below 4\% in porous materials and below 10\% in lattice structures. Unlike prior single-field or operator-based surrogates, MSTM resolves sharp shock fronts while preserving integrated quantities such as mass-averaged pressure and temperature to within 5\%. This advance transforms problems once considered intractable into tractable design studies, establishing a practical framework for optimizing meso-structured materials in planetary impact mitigation, inertial fusion energy, and national security.