Abstract
Although Bayesian Optimization (BO) has been employed for accelerating materials design in computational materials engineering, existing works are restricted to problems with quantitative variables. However, real designs of materials systems involve both qualitative and quantitative design variables representing material compositions, microstructure morphology, and processing conditions. For mixed-variable problems, existing Bayesian Optimization (BO) approaches represent qualitative factors by dummy variables first and then fit a standard Gaussian process (GP) model with numerical variables as the surrogate model. This approach is restrictive theoretically and fails to capture complex correlations between qualitative levels. We present in this paper the integration of a novel latent-variable (LV) approach for mixed-variable GP modeling with the BO framework for materials design. LVGP is a fundamentally different approach that maps qualitative design variables to underlying numerical LV in GP, which has strong physical justification. It provides flexible parameterization and representation of qualitative factors and shows superior modeling accuracy compared to the existing methods. We demonstrate our approach through testing with numerical examples and materials design examples. The chosen materials design examples represent two different scenarios, one on concurrent materials selection and microstructure optimization for optimizing the light absorption of a quasi-random solar cell, and another on combinatorial search of material constitutes for optimal Hybrid Organic-Inorganic Perovskite (HOIP) design. It is found that in all test examples the mapped LVs provide intuitive visualization and substantial insight into the nature and effects of the qualitative factors. Though materials designs are used as examples, the method presented is generic and can be utilized for other mixed variable design optimization problems that involve expensive physics-based simulations.
Highlights
In contrast to the traditional trial-and-error based experiment approach to materials design, computational materials design methods have emerged as an efficient and effective alternative in the past decade, building upon the advancement of simulation techniques such as finite element analysis (FEA) and density functional theory (DFT) that can accurately model and predict material properties at different length scales[8,9]
The proposed framework is built upon a novel latent variable Gaussian process (GP) (LVGP) modeling approach that we recently developed for creating response surfaces with both qualitative and quantitative inputs[27]
Noting that the underlying physical variables may be extremely high-dimensional, the LVGP mapping serves as a low-dimensional LV surrogate for the high-dimensional physical variables that captures their collective effect on the response
Summary
In contrast to the traditional trial-and-error based experiment approach to materials design, computational materials design methods have emerged as an efficient and effective alternative in the past decade, building upon the advancement of simulation techniques such as finite element analysis (FEA) and density functional theory (DFT) that can accurately model and predict material properties at different length scales[8,9]. Gaussian process (GP) models, a.k.a., kriging models have become the most popular method for modeling simulation response surfaces[21,22,23] and are widely employed in BO frameworks, because of its flexibility to capture complex nonlinear response surface as well as to quantify uncertainties in prediction These standard GP models are only applicable for quantitative inputs (i.e., quantitative design variables). In addition to outstanding predictive performance, this LV mapping provides an inherent ordering and structure for the levels of the qualitative factor(s), such as the type of material constituents and processing types, which can provide substantial insights into their influence on the material properties/performance In this manner the LVGP approach can model a large number of qualitative levels with a relatively small number of parameters, which improves the prediction while maintaining low computational costs. In contrast to the existing methods for handling qualitative factors[24,25,26,30], LVGP is compatible with any standard GP correlation functions for quantitative inputs, including nonseparable correlation functions such as power exponential, Matèrn and lifted Brownian
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