Machine learning coarse grained models for water.

An accurate and computationally efficient molecular level description of mesoscopic behavior of ice-water systems remains a major challenge. Here, we introduce a set of machine-learned coarse-grained (CG) models (ML-BOP, ML-BOP(dih), and ML-mW) that accurately describe the structure and thermodynamic anomalies of both water and ice at mesoscopic scales, all at two orders of magnitude cheaper computational cost than existing atomistic models. In a significant departure from conventional force-field fitting, we use a multilevel evolutionary strategy that trains CG models against not just energetics from first-principles and experiments but also temperature-dependent properties inferred from on-the-fly molecular dynamics (~ 10's of milliseconds of overall trajectories). Our ML BOP models predict both the correct experimental melting point of ice and the temperature of maximum density of liquid water that remained elusive to-date. Our ML workflow navigates efficiently through the high-dimensional parameter space to even improve upon existing high-quality CG models (e.g. mW model).