Estimation of material parameters based on precipitate shape: efficient identification of low-error region with Gaussian process modeling

Abstract

Abstract In this study, an efficient method for estimating material parameters based on the experimental data of precipitate shape is proposed. First, a computational model that predicts the energetically favorable shape of precipitate when a d-dimensional material parameter (x) is given is developed. Second, the discrepancy (y) between the precipitate shape obtained through the experiment and that predicted using the computational model is calculated. Third, the Gaussian process (GP) is used to model the relation between x and y. Finally, for identifying the “low-error region (LER)” in the material parameter space where y is less than a threshold, we introduce an adaptive sampling strategy, wherein the estimated GP model suggests the subsequent candidate x to be sampled/calculated. To evaluate the effectiveness of the proposed method, we apply it to the estimation of interface energy and lattice mismatch between MgZn2 ($${{\rm{\beta }}}_{1}^{\text{'}}$$ β 1 ' ) and α-Mg phases in an Mg-based alloy. The result shows that the number of computational calculations of the precipitate shape required for the LER estimation is significantly decreased by using the proposed method.