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{'}}) 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.
Highlights
In this study, an efficient method for estimating material parameters based on the experimental data of precipitate shape is proposed
Given that experimental data of precipitate shape are naturally uncertain, estimating the “low-error region (LER)” in the material parameter space seems to be crucial, where the discrepancy between the precipitate shape obtained through the experiment and that predicted using a computational model becomes small
Our method is based on the computational model for predicting the energetically favorable shape of precipitate with the given material parameters
Summary
An efficient method for estimating material parameters based on the experimental data of precipitate shape is proposed. Given that experimental data of precipitate shape are naturally uncertain, estimating the “low-error region (LER)” in the material parameter space seems to be crucial, where the discrepancy between the precipitate shape obtained through the experiment and that predicted using a computational model becomes small. When the d-dimensional material parameter (x ∈ d) is given, we can calculate the discrepancy (y) between the precipitate shape obtained through the experiment and that predicted using the computational model. Unlike classical deterministic regression models, GP represents an unknown target function value as a random variable of a Gaussian distribution, which enables us to quantify uncertainty of the current prediction We utilized this uncertainty evaluation to define probabilistic estimation of LER for each uncalculated candidate x. The result showed that the proposed method can provide an efficient estimation of material parameters
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