Learning Thermal Response Forces: A Method for Extending the Thermodynamic Transferability of Coarse-Grained Models via Machine-Learning.

Machine-learned (ML) coarse-grained (CG) models are a promising tool for significantly enhancing the efficiency of molecular simulations by systematically removing degrees of freedom while retaining fidelity to the underlying fine-grained model. The CG potential of mean force (PMF) is inherently dependent on thermodynamic conditions and, hence, a CG force-field (FF) which is trained at one thermodynamic state point is not necessarily accurate at another. We propose, in this work, a novel and data-efficient means of learning temperature dependence into ML CG force-fields via training on the thermal response forces of the PMF, driven by learning entropic effects. We demonstrate how incorporating these terms into ML CG FFs confers significantly improved transferability for CG water models and demonstrate how this transferability enables accurate structural correlations across a range of temperatures. Additionally, we demonstrate how the transferability of the CG models developed enables the construction of an empirical relationship between AA and CG dynamics for dynamical rescaling.