Probabilistic Microstructure-Aware Inverse Process Design with Uncertainty Quantification

The design of new materials can be significantly accelerated by the use of physics-based models that allow prediction of specific microstructures to achieve improved properties. But once a prediction has been made, the question becomes how to make that microstructure. This is an inverse problem, in which physics-based models of microstructure development are rapidly iterated as part of an optimization scheme to predict the required process parameters. Several groups have demonstrated such microstructure-aware inverse process design in various contexts, but few if any of these include an explicit accounting for uncertainty in the predictions. From the point of view of the designer, however, awareness of uncertainty is critical because it can determine whether or not the proposed process is practical, and is essential for assessing the likely variation in microstructure (and hence properties) resulting from process variation.

Here, we demonstrate an approach to probabilistic, microstructure-aware inverse process design that accounts for epistemic uncertainty. Our model problem is isothermal annealing of metals to achieve a specified grain size distribution. Using phase-field techniques to model grain growth, we employ Markov Chain Monte Carlo sampling combined with Bayesian optimization to account for uncertainty. The phase field models are parameterized and validated by comparison with experiments on pure copper, which allows us to determine the probability distributions of the model parameters (activation energy, grain boundary energy, and grain boundary mobility). We also demonstrate a surrogate model, trained on the phase field results, enabling us to reduce the overall computational cost by implementing a multi-fidelity modeling framework. This framework allows us to determine the optimum process parameters to achieve the microstructural design goal while quantitatively assessing the uncertainty in the predicted grain size distribution.