从头算广义朗之万方程
Ab Initio Generalized Langevin Equation
AI总结：
本文提出从头算广义朗之万方程AIGLE，结合机器学习与量子力学模拟，在涨落-耗散约束下构建力场、记忆核和噪声，高效模拟铁电畴壁和粗粒化电偶极子等慢集体变量动力学，计算效率比分子动力学高几个数量级。
摘要：
我们引入一种基于机器学习的方法，称为从头算广义朗之万方程（AIGLE），用于模拟材料和分子中慢集体变量的动力学。在该方案中，参数是从基于从头算量子力学模型的原子模拟中学习得到的。在Mori-Zwanzig形式体系下，并在涨落-耗散定理的约束下，构建力场、记忆核和噪声发生器。结合深度势能分子动力学和电子密度泛函理论，该方法为多种情形下的多尺度建模开辟了道路。在此，我们通过研究晶体钛酸铅中的两个介观过程来展示这一能力，即平面铁电畴壁的场驱动动力学，以及粗粒化电偶极子扩展晶格的动力学。在第一种情形中，AIGLE将从头算模拟的适用范围扩展到分子动力学无法触及的噪声驱动运动区域。在第二种情形中，AIGLE通过对记忆核采用局域近似并仅保留短程噪声关联来处理大量集体变量。该方案在计算效率上比分子动力学高几个数量级，并在低频下模拟微观动力学，能够准确重现主导的远红外吸收频率。
英文摘要：
We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig formalism, under the constraint of the fluctuation-dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multi-scale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of collective variables by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude, and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency.
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