Top-Down approach to dynamical coarse-graining using Differentiable Generalized Langevin Equation

The accurate representation of dynamics at the coarse-grained (CG) level is a persistent challenge in developing CG models for soft matter systems. To address this, we present an effective top-down approach for parameterizing the Generalized Langevin Equation (GLE), a robust framework rooted in the Mori-Zwanzig formalism. By reformulating the non-Markovian GLE with a colored noise ansatz, our method compensates for the loss of friction and stochastic forces, which typically arise due to reduced degrees of freedom during coarse-graining. Leveraging recent advancements in Automatic Differentiation, we achieve an end-to-end differentiable solution that reproduces the dynamics of the original all-atom model. We demonstrate the effectiveness of our approach by applying it to two fluids with distinct structural and dynamical behaviors - SPC/E Water and Carbon dioxide. Importantly, this method provides a simple and efficient route for achieving accurate CG dynamics.