Accurate Molecular Dynamics Enabled by Efficient Physically-Constrained Machine Learning Approaches

We develop a combined machine learning (ML) and quantum mechanics approach that enables data-efficient reconstruction of flexible molecular force fields from high-level ab initio calculations, through the consideration of fundamental physical constraints. We discuss how such constraints are recovered and incorporated into ML models. Specifically, we use conservation of energy - a fundamental property of closed classical and quantum mechanical systems -- to derive an efficient gradient-domain machine learning (GDML) model. The challenge of constructing conservative force fields is accomplished by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. We proceed with the development of a multi-partite matching algorithm that enables a fully automated recovery of physically relevant point-group and fluxional symmetries from the training dataset into a symmetric variant of our model. The developed symmetric GDML (sGDML) approach is able to faithfully reproduce global force fields at the accuracy high-level ab initio methods, thus enabling sample intensive tasks like molecular dynamics simulations at that level of accuracy.