Zhang Yichi, Apley Daniel W, Chen Wei
Mechanical Engineering, Northwestern University, Evanston, IL, US.
Industrial Engineering and Management Science, Northwestern University, Evanston, IL, US.
Sci Rep. 2020 Mar 18;10(1):4924. doi: 10.1038/s41598-020-60652-9.
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.
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，然后将数值变量拟合为标准高斯过程（GP）模型作为替代模型。这种方法在理论上具有局限性，并且无法捕捉定性水平之间的复杂相关性。我们在本文中提出了一种用于混合变量GP建模的新型潜变量（LV）方法与用于材料设计的BO框架的集成。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，这具有很强的物理依据。它提供了定性因素的灵活参数化和表示，并且与现有方法相比显示出卓越的建模精度。我们通过数值示例和材料设计示例测试来证明我们的方法。所选的材料设计示例代表了两种不同的场景，一种是关于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，另一种是关于材料组成的组合搜索以实现最佳混合有机-无机钙钛矿（HOIP）设计。结果发现，在所有测试示例中，映射的LVs提供了直观的可视化，并对定性因素的性质和影响有深入的了解。尽管以材料设计为例，但所提出的方法是通用的，可用于其他涉及基于物理的昂贵模拟的混合变量设计优化问题。
