A valuable step in the modeling of multiscale dynamical systems in fields
such as computational chemistry, biology, materials science and more, is the
representative sampling of the phase space over long timescales of interest;
this task is not, however, without challenges. For example, the long term
behavior of a system with many degrees of freedom often cannot be efficiently
computationally explored by direct dynamical simulation; such systems can often
become trapped in local free energy minima. In the study of physics-based
multi-time-scale dynamical systems, techniques have been developed for
enhancing sampling in order to accelerate exploration beyond free energy
barriers. On the other hand, in the field of Machine Learning, a generic goal
of generative models is to sample from a target density, after training on
empirical samples from this density. Score based generative models (SGMs) have
demonstrated state-of-the-art capabilities in generating plausible data from
target training distributions. Conditional implementations of such generative
models have been shown to exhibit significant parallels with long-established
-- and physics based -- solutions to enhanced sampling. These physics-based
methods can then be enhanced through coupling with the ML generative models,
complementing the strengths and mitigating the weaknesses of each technique. In
this work, we show that that SGMs can be used in such a coupling framework to
improve sampling in multiscale dynamical systems.

在多尺度动力学系统中，通过代表性采样长时间尺度的相空间是一项有价值的工作，但也面临挑战。我们展示了基于评分的生成模型可以在这种耦合框架中用于提高多尺度动力学系统的采样效果。

多尺度建模中的微宏一致性：基于评分模型的辅助采样快慢动力系统

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

This paper introduces coordinate-independent methods for analysing multiscale
dynamical systems using numerical techniques based on the transfer operator and
its adjoint. In particular, we present a method for testing whether an
arbitrary dynamical system exhibits multiscale behaviour and for estimating the
time-scale separation. For systems with such behaviour, we establish techniques
for analysing the fast dynamics in isolation, extracting slow variables for the
system, and accurately simulating these slow variables at a large time step. We
illustrate our method with numerical examples and show how the reduced slow
dynamics faithfully represents statistical features of the full dynamics which
are not coordinate dependent.

本文介绍了基于传递算子及其伴随数值技术的、用于分析多尺度动力学系统的坐标无关方法。我们提出了一种测试任意动力学系统是否具有多尺度行为并估计时间尺度分离的方法。对于具有这种行为的系统，我们建立了分析快速动态并提取系统慢变量、以及用大时间步长进行准确模拟这些慢变量的技术。我们通过数值例子说明了我们的方法，并展示了所减少的慢动态如何忠实地表现了不依赖于坐标的全动态的统计特性。