Coarse-graining via reparametrization avoids force-matching and back-mapping

Energy minimization problems are highly non-convex problems at the heart of physical sciences. These problems often suffer from slow convergence due to sharply falling potentials, leading to small gradients. To make them tractable, we often resort to coarse-graining (CG), a type of lossy compression. We introduce a new way to perform CG using reparametrization, which does not require the costly steps of force-matching and back-mapping required in traditional CG. We focus on improving the slow dynamics by using CG to projecting onto slow modes. We also propose a way to find robust slow modes for many physical potentials. Our method also does not require data, which is expensive in molecular systems and a bottleneck for applying machine learning methods to such systems. We test our method on molecular dynamics for folding of small proteins. We observe that our method either reaches deeper (more optimal) energies or runs in shorter time than the baseline non-CG simulations.