DiffGLE: Differentiable Coarse-Grained Dynamics using Generalized Langevin Equation

Abstract: Capturing the correct dynamics at the Coarse-Grained (CG) scale remains a central challenge in the advancement of systematic CG models for soft matter simulations. The Generalized Langevin Equation (GLE), rooted in the Mori-Zwanzig formalism, provides a robust framework for incorporating friction and stochastic forces into CG models, that are lost due to the reduction in degrees of freedom. Leveraging recent advancements in Automatic Differentiation (AD) and reformulating the non-Markovian GLE using a colored noise ansatz, we present a top-down approach for accurately parameterizing the non-Markovian GLE for different coarse-grained fluids that accurately reproduces the velocity-autocorrelation function of the original All-Atom (AA) model. We demonstrate our approach on two different fluids namely, SPC/E water and carbon dioxide which have distinct structure and dynamical characteristics. Importantly, by being end-to-end differentiable, this approach offers a simplified and efficient solution to achieving accurate CG dynamics, effectively bypassing the complexities inherent in most bottom-up methods.