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

TL;DR

This work tackles predicting multi-field shock dynamics in meso-structured media, where pore collapse and complex interfacial phenomena challenge traditional surrogates. The authors introduce MSTM, a hybrid CNN–LSTM autoregressive model that evolves seven coupled fields $(\rho, p, T, E, m, u_x, u_y)$ on a $60\times60$ grid using five-frame inputs to predict the next frame, trained on high-fidelity MARBL hydrocode data. Across porous and lattice configurations, MSTM achieves mean errors of $1.4\%$ and $3.2\%$ respectively and delivers greater than $10^3\times$ speedups, while reducing MSE and SSIM dissimilarity by about $94\%$ relative to seven single-field surrogates; the model generalizes across porosity, lattice angle, and loading, and maintains mass-averaged QoIs within ~5\%. These results establish MSTM as a practical, high-fidelity, multi-field surrogate that enables design optimization and uncertainty quantification for meso-structured materials in planetary defense and inertial fusion energy contexts.

Abstract

The ability to predict how shock waves traverse porous and architected materials is a key challenge in planetary defense and in the pursuit of inertial fusion energy. Yet capturing pore collapse, anomalous Hugoniot responses, and localized heating - phenomena that strongly influence 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 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 captures nonlinear shock-driven dynamics across porous and architected configurations, achieving mean errors of 1.4% and 3.2% respectively, all while delivering over three orders of magnitude in speedup. MSTM reduces mean-squared error and structural dissimilarity by 94% relative torelative to single-field spatio-temporal models. This advance transforms problems once considered intractable into tractable design studies, establishing a practical framework for optimizing meso-structured materials in planetary impact mitigation and inertial fusion energy.

Figures (12)

• Figure 1: Simulation setup designed to study shock wave propagation through meso-structured media. The simulation output was used as the training, validation and test data set for the deep learning models.
• Figure 2: MSTM schematic architecture. The model combines CNN and LSTM blocks to recursively predict the seven‑field evolution. The CNN layers extract spatial features at each time step, and the LSTM layers capture their temporal evolution.
• Figure 3: Formal description of the MSTM architecture. The model takes as input a batch of sequences with shape $(\text{batch},\text{T},7,60,60)$, processes each slice through two convolutional layers (3$\times$3 kernels and ReLU activations) and max pooling, feeds the resulting feature vectors into a four‑layer LSTM, and uses a fully connected layer to project the final hidden state to the next‑step field tensor $(1,7,60,60)$.
• Figure 4: Single‐step field prediction of the porous material MSTM model. The upper panel shows the model inputs: five consecutive time steps for each of the seven physical fields—materials on a $60\times60$ grid (shape $[5,7,60,60]$). Each field is visualized as a stack of five two‐dimensional snapshots; the arrows indicate how these temporal sequences feed into the model. The lower panel displays the model outputs: one predicted frame for each of the seven fields on the same $60\times60$ grid at the next time step (shape $[1,7,60,60]$).
• Figure 5: Autoregressive inference process of the MSTM model for a single field. In the first step, the network receives five consecutive ground‑truth frames $z_{t_0}\ldots z_{t_4}$ (purple outlines) to predict frame $\hat{z}_{t_5}$ (orange). For the next prediction, the input window advances by discarding $z_{t_0}$ and appending the most recent prediction, yielding $\{z_{t_1},\ldots,z_{t_4},\hat{z}_{t_5}\}$ to produce $\hat{z}_{t_6}$. This sliding‑window process continues, each new prediction replaces the oldest entry in the input sequence, until the final target frame $\hat{z}_{t_n}$ is generated.