Adaptive Discovery and Mixed-Variable Bayesian Optimization of Next Generation Synthesizable Microelectronic Materials

Chen Wei

Northwestern University

Design of new materials is characterized by several challenges such as high-dimensionality of the atomic structure-composition variable space, formidable cost of directly using high-fidelity simulations for design optimization, dispersity in literature-reported similar materials and synthesis methods, complex physical mechanisms, and mixed qualitative and quantitative design variables that lead to a disjointed design space. Even though machine learning (ML) techniques have been employed to expedite materials innovation, existing methods treat ML and design optimization as two separate processes, failing to resolve the fundamental challenges associated with high dimensionality and mixed-variable complexity.

We have developed a ML enhanced mixed-variable material design optimization framework to efficiently extract useful information from existing data in literature and physics-based simulations to guide the autonomous search for optimal materials. Our proposed framework is composed of three computational modules: (1) a natural language processing (NLP) based virtual screening and concept exploration module, (2) a density functional theory (DFT)-based high-fidelity evaluation model, and (3) a novel latent-variable Gaussian process (LVGP) ML model for mixed-variable problems with uncertainty quantification, which seamlessly integrates with Bayesian Optimization (BO) and achieves superb efficiency through embedded physics-based dimension reduction. 

We will present our approach using the testbed of functional materials exhibiting metal-insulation transitions (MITs), a class of quantum materials that can revolutionize microelectronics science to provide energy saving solutions. With the information extracted from the literature, we build a classification model that estimates the probability of a material exhibiting MIT. We then use DFT to evaluate the materials proposed by the classifier to be potential MITs, augment the training dataset and train the model iteratively, thus updating the model in an active learning fashion to acquire an effective MIT/non-MIT classifier.  Using the conditional variational autoencoder (CVAE) method, we construct a generative model that can suggest synthesis recipes for a new compound. The feasibilities of these generated recipes are verified with DFT calculations.

The adaptive discovery process of our framework is driven by a novel LVGP model which is capable of fitting and predicting material properties from the composition design space, where some design variables, e.g., choices of elements on various sites, are categorical instead of numerical. This is achieved via mapping the categorical variables to a latent space, and tune the latent space organization based on observations using the maximum likelihood estimation (MLE).  The LVGP approach provides a principled Bayesian statistical representation of design responses and uncertainty, which is a critical component in the sequential sampling of Bayesian Optimization. Guided by an acquisition function that takes into account exploration of high uncertainty space and exploitation of high performance space, we perform multi-criteria Bayesian Optimization to search for MITs that possesses both high bandgap and stability. Through an adaptive learning process, the computational cost for locating the optimal configuration is significantly reduced. In addition, our LVGP approach provides interpretable ML through insights gained from the distances of different material design concepts in the latent space. 

So far, through our ML models and computational evaluations, we have discovered several potential MIT materials that have not previously been reported, for which experimental syntheses of these materials by our collaborators are in process. Besides, we have constructed a database of MITs that is open to the public. By investigating the feature importance, we gained physical insights and identified new important descriptors that may help future studies. We anticipate the framework can be extended beyond MITs and accelerate the design of novel materials.