Multi-fidelity Bayesian machine learning for global optimization

Abstract

The computational optimization and exploration of materials is a challenging task, due to the high dimensionality of the search space and the high cost of accurate quantum mechanical calculations. To reduce the number of costly calculations, the Bayesian Optimization Structure Search (BOSS) has been developed. BOSS combines sample-efficient active learning with Gaussian process regression. This work introduces several multi-fidelity approaches that can reduce the number of costly, accurate calculations even further by incorporating information from inexpensive but less accurate calculations. Using the intrinsic model of coregionalization, BOSS samples data from multiple atomistic calculations based on quantum chemistry (Gaussian16, using CCSD(T)), density-functional theory (FHI-aims, using a PBE-exchange correlation functional) and force fields (AMBER18). Multi-fidelity BOSS samples both, lower and higher-fidelity calculations, while maintaining CCSD(T) accuracy for the global minimum inference. We tested our new multi-fidelity approaches on a 4D alanine conformer search. There, multi-fidelity BOSS has reduced the computational cost, measured in CPU hours, by up to 90%. We found that the efficiency of the approaches depends mostly on the correlation and the computational cost difference between the fidelities. These tests serve as a benchmark for the great potential that multi-fidelity learning can have to reduce the cost of expensive structure-search problems.