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A valuable step in the modeling of multiscale dynamical systems in fieldssuch as computational chemistry, biology, materials science and more, is therepresentative sampling of the phase space over long timescales of interest;this task is not, however, without challenges. For example, the long termbehavior of a system with many degrees of freedom often cannot be efficientlycomputationally explored by direct dynamical simulation; such systems can oftenbecome trapped in local free energy minima. In the study of physics-basedmulti-time-scale dynamical systems, techniques have been developed forenhancing sampling in order to accelerate exploration beyond free energybarriers. On the other hand, in the field of Machine Learning, a generic goalof generative models is to sample from a target density, after training onempirical samples from this density. Score based generative models (SGMs) havedemonstrated state-of-the-art capabilities in generating plausible data fromtarget training distributions. Conditional implementations of such generativemodels have been shown to exhibit significant parallels with long-established-- and physics based -- solutions to enhanced sampling. These physics-basedmethods can then be enhanced through coupling with the ML generative models,complementing the strengths and mitigating the weaknesses of each technique. Inthis work, we show that that SGMs can be used in such a coupling framework toimprove sampling in multiscale dynamical systems.

Micro-Macro Consistency in Multiscale Modeling: Score-Based Model Assisted Sampling of Fast/Slow Dynamical Systems