Mapping microstructure to shock-induced temperature fields using deep learning

Shockwaves traveling through materials trigger chemical and physical processes critical in planetary science, microparticle impact, materials synthesis, and detonation initiation. Energy localization into hotspots, arising from interactions between shockwaves and microstructural features (e.g., pore collapse, interfacial friction, cracks, localized plasticity), greatly accelerates thermally activated processes. Predicting hotspot formation is challenging due to strongly coupled mechanisms operating under extreme temperature, pressure, and strain rates, and across disparate time and length scales. Continuum models that resolve microstructure usually approximate sub-scale mechanisms (e.g., plasticity, pore collapse) and often treat hotspots statistically. Atomistic molecular dynamics (MD) can explicitly capture hotspot mechanisms but cannot reach mesoscale microstructural dimensions at reasonable cost. While MD studies have illuminated mechanisms and relative potency of hotspot formation processes, quantitative predictive models for hotspot temperature and size across mechanisms and complex geometries remain lacking. Comparisons between MD temperature fields and multi-physics continuum models show progress but also highlight intrinsic limitations and the need for nanometer-scale resolution with high computational cost. Deep learning has shown promise in modeling mesoscale thermo-mechanical shock response with accuracy comparable to physics-based simulations but at far lower cost. This work investigates whether deep learning can map complex initial microstructures to shock-induced, post-shock temperature fields obtained from explicit MD, using relatively few high-cost simulations for training. Inspired by field-to-field mapping approaches, the initial atomistic structure is reduced to scalar fields and the post-shock temperature to a single field. A U-Net-type 3D CNN (MISTnet) is trained on a dozen independent simulations to predict 3D temperature fields, including hotspot location and distribution, for unseen microstructures, achieving accuracy comparable or superior to physics-based and ML surrogates at a fraction of the computational cost.

Continuum-level shock models that incorporate microstructure typically approximate key hotspot mechanisms such as localized plasticity and pore collapse, often treating hotspots statistically. Atomistic MD has been extensively used to study hotspot formation mechanisms (porosity collapse, shear, friction, localized plasticity), yielding mechanistic insight but limited in scale and cost. Recent comparisons of MD-derived temperature fields with multi-physics continuum models demonstrate advances but also the necessity for nanometer-scale resolution, increasing computational expense. Deep learning has been used to model mesoscale thermo-mechanical responses under shock and other field-to-field mappings with strong performance. U-Net architectures have been effective for field predictions and image segmentation in materials science. Prior ML efforts (e.g., physics-aware recurrent CNNs) have modeled energy localization but with higher errors compared to the present work and often under different loading conditions. The gap remains in efficiently mapping complex microstructures directly to shock-induced temperature hotspot fields derived from explicit atomistic simulations.

Data generation via atomistic MD: The study built 11 independent polymer-bonded explosive (PBX) composite systems composed of RDX grains (spherical or facetted; oriented or randomly oriented) embedded in a polystyrene (PS) binder at two weight fractions (approximately 14.7% and 9.5% PS). Systems were constructed using the PBXgen builder. Four large systems (L1–L4) contained ~30 million atoms with cell dimensions ~84 nm × 18 nm × 220–239 nm; seven small systems (S1–S7) contained ~10 million atoms with dimensions ~60–64 nm × ~18 nm × ~98–110 nm. Particle diameters followed a bimodal distribution with maxima at ~8 and ~17 nm (scaled from experiments). Force fields: PS modeled with Dreiding; RDX with Smith–Bharadwaj potential (with modifications). Long-range electrostatics used PPPM. Simulations were performed in LAMMPS. Chemistry was neglected; focus was on hotspot formation immediately post-shock where reactions are minimal. Shock loading: A convergent shock approach generated two shocks at the z-boundaries propagating toward the center. To maximize data, systems were replicated along the shock direction so that shocks propagate in opposite directions on identical microstructures. Particle velocity was 2.5 km/s, yielding shock velocity ~6.7 km/s.

Field construction: Output field: The local post-shock temperature field was computed from the center-of-mass temperatures of RDX molecules and PS monomers, mapped onto voxels at ~1 ps after the shock front passage. Input fields (from the initial microstructure) were three scalar descriptors: (i) total mass density, (ii) RDX density, and (iii) product of RDX and PS densities to highlight interfaces. For small systems, fields were binned on a 32 × 16 × 32 grid with voxel sizes ~1.9 nm × 1.1 nm × 2.8 nm; for large systems, a 44 × 16 × 80 grid with similar voxel sizes was used. Due to shock compression, the output voxel length along the shock direction corresponded to ~1.7 nm. Temperature fields were assembled slice-by-slice following the shock front to minimize effects of thermal diffusion. Equations used: ρ_total = (N_RDX M_RDX + N_PS M_PS)/V_voxel; ρ_RDX = N_RDX M_RDX/V_voxel; ρ_PS = N_PS M_PS/V_voxel; interface descriptor Δ_interface = ρ_RDX ρ_PS; temperature T = sum of molecular temperatures divided by number of molecules in the voxel.

Dataset preparation and splitting: A total of 92 datasets were created: 28 from the seven small systems (two shocks per simulation and mirror augmentation), and 64 from the four large systems (two shocks per simulation; each shock region divided into four subdomains matching small-cell size; plus mirror augmentation). Datasets from the large systems may partially overlap. To prevent data leakage, all datasets derived from a given simulation (including subdomains and mirrored data) were grouped and assigned together to training, validation, or test sets. Splits were ~70% train, ~17% validation, ~13% test. Gaussian smoothing with a characteristic length equal to a voxel (~2 nm) was applied for certain evaluations to address MD stochasticity.

Neural network architecture (MISTnet): A 3D U-Net architecture with encoder–decoder structure and skip connections. Encoder miniblocks: two 3×3×3 3D convolutions with ReLU activations, batch normalization before pooling, followed by 2×2×2 max pooling (stride 2). Decoder miniblocks: 3×3×3 transposed convolution for upsampling merged with the corresponding encoder feature map via skip connection, followed by two 3×3×3 convolutions with ReLU. Periodic padding was applied along directions transverse to shock to mimic periodic boundary conditions. Final layer: 1×1×1 convolution producing a single-channel temperature field. Input tensor dimensions: 32×16×32×3 (spatial × channels) for small systems.

Training: Optimizer Adam. Custom loss based on mean squared error with a weighting factor of 5 for voxels with target temperature >1800 K to emphasize hotspots. Learning rate schedule from 0.0005 to 0.0001 after 500 epochs. Early stopping based on validation loss: stop if no improvement >0.0005 for 200 epochs and restore best weights. Validation set was used only for early stopping. Sensitivity studies examined the number and nature of input descriptors (single and paired descriptors, and an additional descriptor P_total P_RDX) and the amount of training data.

Evaluation: Accuracy assessed via voxel-level parity plots (after Gaussian smoothing), cumulative volume vs. temperature distributions, hotspot metrics (average hotspot temperature and volume with thresholds at 1600–2000 K), and hotspot-by-hotspot clustering and matching between MD and MISTnet predictions. Computational efficiency relative to MD was noted.

• MISTnet accurately predicts 3D shock-induced temperature fields from initial microstructure alone, capturing location, size, and intensity of hotspots for unseen microstructures.
• The model reproduces hotspots arising from porosity collapse and interfacial processes (e.g., friction, acoustic mismatch), and it learns subtle effects such as higher temperatures from voids elongated along the shock direction compared to transverse elongation.
• Quantitative accuracy: For the test set, RMSE of the temperature field ≈ 97.62 K; hotspot average temperature error ΔT_hotspot ≈ 58.38 K; hotspot volume error ΔV_hotspot ≈ 224.16 nm³. Across all sets, normalized errors are ~2.3% in hotspot temperature and ~15% in hotspot volume.
• Parity of smoothed voxel temperatures and cumulative volume vs. temperature distributions show very good agreement between MISTnet and MD; highest temperatures tend to be mildly underestimated but correspond to small volumes.
• Hotspot-by-hotspot analysis shows strong spatial correspondence; largest hotspot size is slightly underestimated (~10%), and peak temperatures are slightly low.
• Compared to prior ML models (e.g., PARC), ΔT_hotspot errors are about seven times smaller (noting different shock conditions).
• Input descriptor study: even single-field inputs capture main features, but the three-descriptor combination (total density, RDX density, and interface density product) gives the best performance on unseen microstructures.
• Generalization tests to pure RDX single crystals with large cylindrical pores (not seen in training) show accurate hotspot shapes and correct trends with pore size and orientation, though temperatures are overestimated.
• Computational efficiency: once trained, MISTnet inference is ~10^8 times less costly than full MD simulations.

The study demonstrates that complex, coupled, sub-grid mechanisms governing shock-induced energy localization can be effectively bypassed at inference time by mapping initial microstructure fields directly to post-shock temperature fields using a deep 3D U-Net. This addresses the core challenge of predicting hotspot formation in heterogeneous composites without explicitly resolving all physics in continuum models or incurring the cost of large-scale MD. The strong agreement with MD at voxel, distributional, and individual hotspot levels indicates that the chosen microstructure descriptors encapsulate key physics such as porosity and interfacial effects. The model’s ability to learn orientation dependence of voids highlights that the CNN captures nontrivial structure–response relationships. Slight underprediction of extreme temperatures and minor underestimation of largest hotspot sizes suggest conservative behavior in high-temperature tails. The drastic computational savings enable rapid evaluation across microstructures, making MISTnet suitable as a surrogate to supply temperature fields to continuum solvers after shock passage, potentially improving predictions of thermally activated processes (phase transitions, reactions) and reducing empiricism in mesoscale models.

This work introduces MISTnet, a 3D U-Net-based deep learning model that maps initial microstructure fields to post-shock temperature fields in heterogeneous composites, trained on explicit multi-million-atom MD simulations. Using three microstructural descriptors (total density, constituent density, and an interface indicator), MISTnet accurately predicts hotspot locations, sizes, and temperatures for unseen microstructures at a fraction (~10^8× lower) of MD computational cost. The model captures subtle microstructure–hotspot relationships, such as pore orientation effects, and outperforms prior ML surrogates in hotspot temperature errors. Potential future directions include: (i) extending to parametric models (e.g., conditional U-Nets) that incorporate loading parameters like particle velocity; (ii) predicting additional fields (local stress and strain); (iii) integrating physics-based constraints (continuum mechanics, equations of state) in training; (iv) training with experimentally derived or real microstructural data; and (v) expanding applicability across resolutions by consistent multi-resolution training protocols.

• Chemical reactions were neglected; focus was on hotspot formation ~1 ps after shock front passage where chemistry is minimal. Force fields and classical MD dynamics introduce modeling approximations.
• Model trained and validated at a single particle velocity (2.5 km/s); applicability to other shock strengths requires retraining or a parametric/conditional model.
• Input/output discretization (voxel size and grid resolution) is fixed; due to size-dependent localization mechanisms, the model is not directly applicable to differently discretized fields without retraining at that resolution.
• Dataset size is limited (92 datasets from 11 simulations) with partial overlaps in large-system subdomains; although augmentation and careful splitting mitigate leakage, generalizability beyond studied compositions/architectures may be constrained.
• MISTnet tends to underestimate the highest temperatures and slightly underestimates the size of the largest hotspots (~10%).