Structural Bayesian Optimization for Active Physical Learning: Applications in Ferroelectrics and Magnetic Systems

A typical modern-day scientific study includes learnings from both theoretical and experimental components. Even though such methods are different by the nature of their operations, both rely on explorations over parameter spaces. Classical Bayesian Optimization (BO) provides a smart way to explore broad parameter spaces, well suitable for solving data-driven scenarios where inclusion of physical knowledge is not necessarily important. To incorporate physical knowledge in the form of priors, we combine unstructured (non-parametric) and structured (semi-parametric and parametric) BO approaches in this work. This approach seeks to guide exploration of parameter space while refining physical laws to describe functional behavior over this space. It also uses combined aleatoric, estimated epistemic uncertainty to guide the exploration. This routine is demonstrated for modeling magnetization using Ising model, simulating excitation energies for two dimensional magnetic systems and energy wells for ferroelectrics. It is aimed to be extended towards performing automated experiment in the context of automated materials synthesis and microscopies.