Combining physics with multi-fidelity computation for improved Bayesian active learning based exploration over lattice Hamiltonian system

Optimization of computationally expensive simulation models and microscope experiments through active learning methods has been growing over the last decade, with examples such as optimal parameter search of physics-based lattice models, to searches through spaces for optimal growth for material synthesis. To reduce the cost, an approximated computationally cheaper version (low-fidelity) of the model can be represented which capture the essence of the true expensive systems (high-fidelity). To combine both, a multi-fidelity Bayesian optimization (MFBO) can be considered, where the adaptive search provides joint decisions of where (in the parameter space) to sample and which (in the fidelity space) model to evaluate. However, a standard MFBO is only by the multi-fidelity data. Here, we present a structured MFBO (sMFBO), where the zero mean multi-fidelity gaussian process (MFGP) is augmented with a probabilistic (Bayesian) model of the system's known physical behavior, to minimize the error from low-fidelity data with prior knowledge injection and thus accelerate the learning. The proposed method is demonstrated on lattice Hamiltonian system with rapid exploration over spin-spin interaction parameter space, lattice sizes as fidelity spaces, and maximizing the heat capacity. We also discuss the workflows based on the gradual evolution of the acquisition function from data driven (MFBO) to local physics-driven (sMFBO) during the discovery process. The proposed approach aims to avoid learning unphysical behavior and invariant to low-fidelity approximations and can be universally suitable for rapid multi-fidelity-based exploration over expensive systems.