Inferring effective forces for Langevin dynamics using Gaussian processes

Effective forces -- derived from experimental or {\it in silico} molecular dynamics time traces -- are critical in developing reduced and computationally efficient descriptions of otherwise complex dynamical problems. Thus, designing methods to learn effective forces efficiently from time series data is important. Of equal importance is the fact that methods should be suitable in inferring forces for undersampled regions of the phase space where data are limited. Ideally, a method should {\it a priori} be minimally committal as to the shape of the effective force profile, exploit every data point without reducing data quality through any form of binning or pre-processing, and provide full credible intervals (error bars) about the prediction. So far no method satisfies all three criteria. Here we propose a generalization of the Gaussian process (GP), a key tool in Bayesian nonparametric inference and machine learning, to achieve this for the first time.