A deep learning surrogate optimizes polycrystalline copper microstructures under competing strength requirements, raising spall strength by up to about 29% with prediction errors below 3%

A 3D U-Net surrogate learns the mapping from polycrystalline microstructures to full-field velocity histories from plate-impact simulations, retaining spatial and temporal resolution so it supports both rapid spall-strength evaluation and mechanistic interpretation of wave interactions and failure. Unlike prior surrogates that use reduced microstructural representations to target a limited set of scalar properties, this work retains the full-field response, letting the surrogate serve both performance prediction and mechanistic interpretation. On an independent test set of 1140 microstructure realizations not used for training or tuning, absolute relative error in spall strength stays below 8%; for the optimal designs, ensemble-averaged spall strength over 100 realizations shows relative errors of about 3.0% (Case A1) and 1.2% (Case B) against CPFE.

Coupling the surrogate with stochastic microstructure generation and derivative-free Nelder–Mead optimization solves two design problems: constrained maximization of spall strength under a yield strength constraint, and target-matching inverse design of both spall and yield strengths. The framework explicitly accounts for the stochastic variability of the microstructure ensemble associated with each design vector through Monte Carlo averaging over realizations, rather than optimizing a single deterministic microstructure. Across the constrained optimization cases, optimal designs achieve up to about a 29% increase in spall strength while satisfying the prescribed yield strength constraint; 17 optimization runs were performed, each with about 100 objective evaluations and 100 stochastic realizations per evaluation.

A distribution-consistent reliability region (DCRR) based on maximum mean discrepancy (MMD) quantifies distributional shift between candidate microstructures and the training distribution, serving as a surrogate reliability monitor during optimization. MMD is computed in the learned feature space of an intermediate 3D U-Net encoder layer (enc3.conv_block.conv2) rather than in the raw five-dimensional descriptor space, because Euclidean proximity in descriptor space does not necessarily reflect similarity in higher-order morphological features relevant to predictions. The threshold is calibrated on the held-out test set as the largest MMD value for which all test designs satisfying it have spall-strength prediction errors below the prescribed tolerance; test designs within the training range satisfy the threshold, and MMD grows as descriptors depart from central training ranges. The authors state that the DCRR is not a probabilistic uncertainty bound and does not enforce strict out-of-distribution rejection; designs outside it are flagged for prioritized CPFE validation.

The optimization results reveal a competition between spall and yield strength: under a relaxed yield constraint, spall enhancement comes through morphological changes at the expense of yield strength, whereas a stricter constraint requires coordinated variation of multiple descriptors for concurrent strengthening. Subspace analyses that fix selected design variables show that varying a single variable alone cannot drive significant improvement, and the full-space optimum cannot be approximated by a subset of dominant variables; inverse design converges consistently for feasible targets but yields multiple local optima for infeasible targets. The Case A1 optimum corresponds to relatively large, elongated grains; Case B, with a stricter constraint and infeasible initialization, converges to finer, elongated grains and requires simultaneous strengthening of both properties; Case C1 converges from five distinct initial simplices to a tightly clustered region, while Case C2 with an infeasible target and expanded bounds yields initial-simplex-dependent solutions that partition into two clusters.

The framework targets settings where stochastic microstructures must be designed under competing quasi-static and dynamic performance requirements; the demonstration is polycrystalline copper under plate-impact loading, with all geometric, loading, and material parameters held fixed across microstructures so that variations in spall response arise from grain morphology. For researchers and engineers who want large-scale microstructural screening without giving up mechanistic insight, the framework offers a reusable pattern: replace repeated high-fidelity simulations with a full-field surrogate and use the DCRR to flag candidates for prioritized CPFE validation. The authors note that future extensions could integrate high-throughput dynamic experiments with the computational framework, letting predictive models guide experiments toward promising regions of the materials design space.

The DCRR is an empirically calibrated reliability indicator; the authors state it is not a probabilistic uncertainty bound and does not enforce strict out-of-distribution rejection, so its threshold is recalibrated with the surrogate and test set. The demonstration is limited to polycrystalline copper under plate-impact loading, and yield strength is estimated from mean grain size via the Hall–Petch relation, which depends only on mean grain size and is therefore invariant across stochastic realizations of a fixed design vector. In inverse design, infeasible targets lead to initial-simplex-dependent solutions with multiple local optima, indicating non-uniqueness of the inverse mapping when performance requirements cannot be jointly met. In addition, several equations, table values, and figure captions appear as placeholders in the loaded text, so reproducing specific parameters such as design-variable bounds, penalty parameters, and weighting values would require consulting the original figures and tables.