Wei Chen ", Akshay Iyer'

¹ Department of Mechanical Engineering, Northwestern University, Evanston, Illinois, USA

EXTENDED ABSTRACT: Material design often involves qualitative and quantitative design variables, which requires systematic methods for the exploration of these mixed-variable design spaces. Existing machine learning (ML) models that can handle mixed variables as inputs require a large amount of data but do not provide uncertainty quantification that is crucial for sequential (adaptive) design of experiments. We have developed a novel Latent triable Gaussian Process (LVGP) based ML approach that involves a latent variable (LV) representation of qualitative inputs, and automatically discovers a categorical-to-numerical nonlinear map that transforms the underlying high dimensional physical attributes into the LV space. The nonlinear mapping also provides an inherent ordering and structure for the levels of the qualitative factor(s), which leads to substantial insight and interpretable ML. In addition, LVGP provides uncertainty quantification of prediction which is critical for adaptive sampling to sequentially choose samples based on current observations and the method also offers easy integration with Bayesian optimization (BO) or other reinforcement learning strategies for the purpose of design optimization. Although recent developments in mixed-variable Bayesian optimization have shown promise, high dimensional qualitative variables, i.e., with many levels, impose a large design cost as they typically require a larger dataset to quantify the effect of each level on the optimization objective. We develop a descriptor aided Bayesian optimization approach to address this challenge by leveraging domain knowledge about underlying physical descriptors. We show that physical descriptors can be intuitively embedded into the LVGP approach and used to selectively explore levels of qualitative variables in the Bayesian optimization framework. Using material design examples, we will show that our LVGP approach is robust to certain types of incomplete domain knowledge and significantly reduces the design cost for problems with high-dimensional qualitative variables.

Keywords: Material design, Latent Variable Gaussian Process, Mixed Variables, Descriptors, Bayesian optimization