Collective variable discovery

Last month marked the culmination of a two major projects regarding collective variable discovery, a fundamental interdisciplinary problem in drug discovery, computational statistical physics, and stochastic processes. From a probabilistic perpsective, this problem asks: how can we map a stochastic process to low dimensions and still preserve its statistics? In two case study-style papers on the butane molecule and Lennard-Jones clusters we provide some answers by resorting to quantitive coarse graining theory and proposing algorithms that use some of my favourite tools from geometric data science.