Atomistic or ab initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models. Existing coarse-graining approaches define an effective interaction potential to match defined properties of high-resolution models or experimental data. In this paper, we reformulate coarse-graining as a supervised machine learning problem. We use statistical learning theory to decompose the coarse-graining error and cross-validation to select and compare the performance of different models. We introduce CGnets, a deep learning approach, that learns coarse-grained free energy functions and can be trained by a force-matching scheme. CGnets maintain all physically relevant invariances and allow one to incorporate prior physics knowledge to avoid sampling of unphysical structures. We show that CGnets can capture all-atom explicit-solvent free energy surfaces with models using only a few coarse-grained beads and no solvent, while classical coarse-graining methods fail to capture crucial features of the free energy surface. Thus, CGnets are able to capture multibody terms that emerge from the dimensionality reduction.

This work was supported by the National Science Foundation (CHE-1265929, CHE-1738990, and PHY-1427654), the Welch Foundation (C-1570), the MATH+ excellence cluster (AA1-6, EF1-2), the Deutsche Forschungsgemeinschaft (SFB 1114/C03, SFB 958/A04, TRR 186/A12), the European Commission (ERC CoG 772230 “ScaleCell”), the Einstein Foundation Berlin (Einstein Visiting Fellowship to C.C.), and the Alexander von Humboldt foundation (Postdoctoral fellowship to S.O.). Simulations have been performed on the computer clusters of the Center for Research Computing at Rice University, supported in part by the Big-Data Private-Cloud Research Cyberinfrastructure MRI-award (NSF Grant CNS-1338099), and on the clusters of the Department of Mathematics and Computer Science at Freie Universität, Berlin. G.D.F. acknowledges support from MINECO (Unidad de Excelencia María de Maeztu MDM-2014-0370 and BIO2017-82628-P) and FEDER. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement 675451 (CompBioMed Project). We thank the GPUGRID donors for their compute time.