Fitting Hamiltonian Parameters with Bayesian Optimization of Numerical Simulations

Tuning simulation models to accurately reproduce experimental observations is a challenging but vital task for predicting material properties and informing further experiments. The search for a set of suitable Hamiltonian parameters should ideally minimize the number of dispatched simulations and be fully automated to maximize throughput. We describe a framework that utilizes Bayesian optimization[1], which fits surrogate models predicting the expected difference between target observables and results of numerical simulations, to intelligently explore and optimize in parameter space. The optimization scheme is robust in application and can function without relying on any gradient information. We apply this methodology to Monte Carlo simulations of a coarse-grained binary alloy model to successfully recover a reference interspecies coupling calculated from first principles methods[2]. The Hamiltonian fitting procedure is then demonstrated for experimental data and dynamical simulations of continuous spin models for magnetic materials.

[1] H. J. Kushner. J. Basic Eng. 86, (1964); J. Močkus. J. Glob. Optim. 4, (1975); D. Jones, M. Schonlau, W. Welch. J. Glob. Optim. 13, (1998).

[2] S. Curtarolo et al., Comp. Mat. Sci. 58 218 (2012).