Uncovering Dynamical Equations for Coarse-Graining

The enormous amount of molecular dynamics data available calls for an ever-growing need for extracting macroscopic features while discarding less relevant information; coarse-graining (CG) is a viable strategy to accomplish that. CG consists in lumping degrees of freedom into effective “beads”. Such low resolution description requires both the coordinates of the new “beads” and their effective interactions. If a suitable CG model is found, interpreting and simulating the low resolution dynamics is easier than the original system. However, current CG models are usually based on the user’s physico - chemical intuition which does not guarantee that the correct low resolution description is recovered. Therefore, data-driven CG models are highly desirable: trajectory data contains the information in which we are interested, we just need to uncover it. We take a first step towards postulating CG equations of motion, as we test a data-based technique which approximates the system potential energy function as a sparse linear combination of user-defined functions. A sparse minimization problem is formulated on Brownian dynamics trajectory data, and solved using cross validation. Preliminary results on a 1D toy model show that our protocol systematically targets an optimally sparse linear combination, which accurately approximates the system energy function.