An Approach to Rapid Exploration-Exploitation in N-Dimensional Functional Space of Material Properties using a Physics Driven Multi-Objective Bayesian optimization

For any specific application, optimal parameters choice is critical in finding the desired material properties. However, the complexity arises with high dimensional parameter space, and where the functional map between material parameter and response is unknown or expensive. The complexity furthermore increases, even where generative physical model of material behavior is known and reliable, when a trade-off between multiple functionalities is required to attain the desired material performance. In order to tackle these, we present Multi-objective Bayesian optimization (MOBO) workflow for the ferroelectric performance optimization based on the numerical solution of the Ginzburg-Landau equation with electrochemical or semiconducting boundary conditions. In MOBO, each unknown/expensive functional forms are represented with computationally cheap posterior Gaussian process models fitted from prior evaluations, and then select future evaluations through exploration/exploitation from maximizing an acquisition function, ultimately to identify the set of optimal solutions at different trade-offs between functionalities (Pareto frontier). Unlike exhaustive grid-based search, this approach uses adaptive sampling technique and attempt for minimal expensive evaluations to reach towards the goal. In this work, with the parameters for a prototype bulk antiferroelectric (PbZrO3), we first develop a physics-driven decision tree of target functions from the loop structures. Then, a physics-driven MOBO architecture is developed to build and explore Pareto-frontiers by optimizing user-chosen multiple target functions jointly. This approach allows for rapid initial materials and device parameter selection for a given application and can be further expanded towards the active experiment setting to reduce time and effort.