Towards Exact Molecular Dynamics Simulations With Invariant Machine-Learned Models

Molecular dynamics (MD) simulations constitute the cornerstone of contemporary atomistic modeling in chemistry, biology, and materials science. However, one of the widely recognized and increasingly pressing issues in MD simulations is the lack of accuracy of underlying classical interatomic potentials, which hinders truly predictive modeling of dynamics and function of (bio)molecular systems. Classical potentials often fail to faithfully capture key quantum effects in molecules and materials. In this thesis, we develop a combined machine learning (ML) and quantum mechanics approach that enables the direct reconstruction of flexible molecular force fields from high-level ab initio calculations. We approach this challenge by incorporating fundamental physical symmetries and conservation laws into ML techniques. Using conservation of energy -- a fundamental property of closed classical and quantum mechanical systems -- we 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 faithfully reproduces global force fields at quantum-chemical CCSD(T) level of accuracy and allows converged MD simulations with fully quantized electrons and nuclei. We present MD simulations, for flexible molecules with up to a few dozen atoms and provide insights into the dynamical behavior of these molecules. Our approach provides the key missing ingredient for achieving spectroscopic accuracy in molecular simulations