非平衡系统粗粗谷物建模 (Data-driven Coarse-grained Modeling of Non-equilibrium Systems)

Modeling a high-dimensional Hamiltonian system in reduced dimensions with respect to coarse-grained (CG) variables can greatly reduce computational cost and enable efficient bottom-up prediction of main features of the system for many applications. However, it usually experiences significantly altered dynamics due to loss of degrees of freedom upon coarse-graining. To establish CG models that can faithfully preserve dynamics, previous efforts mainly focused on equilibrium systems. In contrast, various soft matter systems are known out of equilibrium. Therefore, the present work concerns non-equilibrium systems and enables accurate and efficient CG modeling that preserves non-equilibrium dynamics and is generally applicable to any non-equilibrium process and any observable of interest. To this end, the dynamic equation of a CG variable is built in the form of the non-stationary generalized Langevin equation (nsGLE) to account for the dependence of non-equilibrium processes on the initial conditions, where the two-time memory kernel is determined from the data of the two-time auto-correlation function of the non-equilibrium trajectory-averaged observable of interest. By embedding the non-stationary non-Markovian process in an extended stochastic framework, an explicit form of the non-stationary random noise in the nsGLE is introduced, and the cost is significantly reduced for solving the nsGLE to predict the non-equilibrium dynamics of the CG variable. To prove and exploit the equivalence of the nsGLE and extended dynamics, the memory kernel is parameterized in a two-time exponential expansion. A data-driven hybrid optimization process is proposed for the parameterization, a non-convex and high-dimensional optimization problem.

翻译：模拟高维汉密尔顿系统时,在低维度方面模拟粗度(CG)变量,可以大大降低计算成本,并能对系统许多应用程序的主要特征进行有效的自下而上预测。然而,由于粗度加宽时失去自由度,它通常会经历显著的动态变化。为了建立能够忠实保存动态的CG模型,以前的努力主要侧重于平衡系统。相比之下,各种软质系统在平衡方面是众所周知的。因此,目前的工作涉及非平衡系统,并能够准确和高效的CG模型,以保存非平衡的动态,并且一般适用于任何非平衡过程的自下而上地预测系统的主要特征。为此,CGGG变量的动态方程式以非静止通用的兰氏方程式(nsGLEE)的形式建构成,以说明非平衡进程对初始条件的依赖性。两种时间的内存值均匀值都来自双时间的自动对齐度(nal-coloral-al-lation)数据,在非平衡-Gal-ral-ral-ral-ral-lial-lial-lial-lial-lieval-lal-lieval-lal-lal-lieval-lal-lal-laisl化过程中,在不透明-de-laisl-laislation-lax-laisl-lais-laislislislisl)进程中,在不持续一个不透明-c-laislislislislislisld-c-laisl化为一种长期的快速、透明化的快速、透明-c-c-c-c-c-c-c-c-c-c-lax-lax-c-c-c-c-c-c-c-c-c-c-l-l-l-l-l-l-l-l-cal-c-l-ld-ld-c-l-l-lal-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l流-l-l-l-l流-l-l-l