Replacing Chemical Intuition by Machine Learning: a Mixed Design of Experiments - Reinforcement Learning Approach to the Construction of Training Sets for Model Hamiltonians

Model Hamiltonians based on the so-called cluster expansion (CE), which consist of a linear fit of parameters corresponding to geometric patterns, provide an efficient and rigorous means to quickly evaluate the energy of diverse arrangements of adsorbate mixtures on reactive surfaces as typically relevant for heterogeneous catalysis. However, establishing the model Hamiltonian is a tedious task, requiring the construction and optimization of many geometries. Today, most of these geometries are constructed by hand, based on chemical intuition or random choices. Hence, the quality of the training set is unlikely to be optimal and its construction is not reproducible. Herein, we propose a reformulation of the construction of the training set as a strategy-based game, aiming at an efficient exploration of the relevant patterns constituting the model Hamiltonian. Based on this reformulation, we exploit a typical active learning solution for machine-learning such a strategy game: an upper confidence tree (UCT) based framework. However, in contrast to standard games, evaluating the true score is computationally expensive, as it requires a costly geometry optimization. Hence, we augment the UCT with a pre-exploration step inspired by the variance-based Design of Experiments (DoE) methods. This novel mixed UCT+DoE framework allows to automatically construct a well adapted training set, minimizing computational cost and user-intervention. As a proof of principle, we apply our UCT+DoE approach on the CO oxidation reaction on Pd(111), for which a relevant model Hamiltonian has been established previously. The results demonstrate the effectiveness of the custom built UCT and its significant benefits on a DoE-based approach.