Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables
Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables
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DOI：
10.1038/s41598-020-60652-9
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发表时间：
2020-03-18
影响因子：
4.6
通讯作者：
Chen, Wei
中科院分区：
文献类型：
--
作者：
Zhang, Yichi;Apley, Daniel W.;Chen, Wei
尽管贝叶斯优化（BO）已被用于加速计算材料工程中的材料设计，但现有工作仅限于具有定量变量的问题。然而，材料系统的实际设计涉及代表材料成分、微观结构形态和加工条件的定性和定量设计变量。对于混合变量问题，现有的贝叶斯优化（BO）方法首先通过虚拟变量表示定性因素，然后将具有数值变量的标准高斯过程（GP）模型作为代理模型进行拟合。这种方法在理论上具有局限性，无法捕捉定性水平之间的复杂相关性。在本文中，我们提出将一种用于混合变量GP建模的新型潜在变量（LV）方法与用于材料设计的BO框架相结合。LVGP是一种根本不同的方法，它将定性设计变量映射到GP中的潜在数值LV，这具有很强的物理合理性。它为定性因素提供了灵活的参数化和表示，并且与现有方法相比显示出更高的建模精度。我们通过数值示例和材料设计示例的测试来展示我们的方法。所选的材料设计示例代表了两种不同的情况，一种是同时进行材料选择和微观结构优化以优化准随机太阳能电池的光吸收，另一种是对材料成分进行组合搜索以实现最佳的杂化有机 - 无机钙钛矿（HOIP）设计。研究发现，在所有测试示例中，映射的LV为定性因素的性质和影响提供了直观的可视化和重要的见解。尽管以材料设计为例，但所提出的方法是通用的，可用于其他涉及昂贵的基于物理的模拟的混合变量设计优化问题。
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 latentvariable (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 quasirandom 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.