Constructing Collective Variables Using Invariant Learned Representations

On the time scales accessible to atomistic numerical modeling, chemical reactions are considered rare events. Therefore, the atomistic simulations are commonly biased along a low-dimensional representation of a chemical reaction in an atomic structure space, i.e., along the collective variables. However, suitable collective variables are often complicated to guess a priori. We propose a novel method of collective variable discovery based on dimensionality reduction of the atomic representation vectors. These linear-scaling and invariant representations can be either fixed (untrained) or learned by supervised training of the end-to-end machine learning potential. The learned representations are expected to reflect not only the structural but also the energetic features of the system that are transferable to all of the reactive transformation covered by the machine learning potential. We demonstrate our approach on four high-barrier reactions ranging from a simple gas-phase hydrogen jump reaction to complex reactions in periodic models of industrially relevant heterogeneous catalysts. High data efficiency, automatized feature extraction, favorable scaling, and retention of inherent invariances are all properties that are expected to enable fast and largely automatic construction of suitable collective variables even in highly complex reactive scenarios such as reactive/catalytic transformations at solid-liquid interfaces.