提出新方法统一粗粒化模型的热力学与动力学，避免重复模拟。
Consistent Projection of Langevin Dynamics: Preserving Thermodynamics and Kinetics in Coarse-Grained Models
- 基于投影法推导出通用粗粒化动力学公式。
- 准确复现全空间模型的热力学与过渡时间尺度。
- 结合热力学插值，跨状态生成无需重算。
粗粒化是高效建模多尺度系统（如生物分子构象动力学）的重要手段。本文提出一种基于投影的通用阻尼朗之万动力学粗粒化框架。遵循齐万茨格投影方法，推导出粗粒化动力学的闭式表达式。此外，展示如何利用生成型动态模态分解（gEDMD）方法——该方法源自库普曼算子理论——来建模粗粒化动力学并评估其动力学特性，如转变时间尺度。最后，将该方法与热力学插值（TI）结合，这是一种在热力学状态间转换样本的生成方法，使该方法无需重复数值模拟即可扩展至不同热力学状态。通过二维模型系统验证，所提方法能准确捕捉全空间模型的热力学与动力学性质。
原文摘要 · Abstract (English)
Coarse graining (CG) is an important task for efficient modeling and simulation of complex multi-scale systems, such as the conformational dynamics of biomolecules. This work presents a projection-based coarse-graining formalism for general underdamped Langevin dynamics. Following the Zwanzig projection approach, we derive a closed-form expression for the coarse grained dynamics. In addition, we show how the generator Extended Dynamic Mode Decomposition (gEDMD) method, which was developed in the context of Koopman operator methods, can be used to model the CG dynamics and evaluate its kinetic properties, such as transition timescales. Finally, we combine our approach with thermodynamic interpolation (TI), a generative approach to transform samples between thermodynamic conditions, to extend the scope of the approach across thermodynamic states without repeated numerical simulations. Using a two-dimensional model system, we demonstrate that the proposed method allows to accurately capture the thermodynamic and kinetic properties of the full-space model.
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