∆-Learning for Coarse-Grained Potentials

Coarse-grained molecular dynamics (CGMD) simulations address lengthscales and timescales that are critical to many chemical and material applications. Nevertheless, contemporary CGMD modeling is relatively bespoke and there are no black-box CGMD methodologies available that could play a comparable role in discovery applications that density functional theory plays for electronic structure. This gap might be filled by machine learning (ML) based CGMD potentials that simplify model development, but these methods are still in their early stages and have yet to demonstrate a significant advantage over existing physics-based CGMD methods. Here we explore the potential of $\Delta$-learning models to leverage the advantages of these two approaches. This is implemented by using ML-based potentials to learn the difference between the target CGMD variable and the predictions of physics-based potentials. The $\Delta$-models are benchmarked against the baseline models in reproducing on-target and off-target atomistic properties as a function of CG resolution, mapping operator, and system topology. The $\Delta$-models outperform the reference ML-only CGMD models in nearly all scenarios. In several cases, the ML-only models also manage to minimize training error while still producing qualitatively incorrect dynamics, which is corrected by the $\Delta$-models. Given their negligible added cost, $\Delta$-models provide essentially free gains over their ML-only counterparts. Nevertheless, an unexpected finding is that neither the $\Delta$-learning models nor ML-only models significantly outperform the elementary pair-wise models in reproducing atomistic properties. This fundamental failure is attributed to the relatively large irreducible force errors associated with coarse-graining that produces little benefit from using more complex potentials.