用流匹配方法精准模拟非马尔可夫粒子系统的短时动态。
Capturing non-Markovian dynamics in non-equilibrium stochastic systems using flow matching
- 通过流匹配直接建模粒子模拟中的通量分布，融入非马尔可夫与非高斯效应。
- 在短时间尺度上准确捕捉系统行为，统计矩预测优于传统马尔可夫模型。
- 适合研究低密度、非平衡粒子系统中复杂动力学的科研人员。
具有粗粒度随机偏微分方程（SPDE）表示的随机粒子系统水动力模型，如正则化德恩-卡瓦萨基（DK）方程，在短时系统动态（受非马尔可夫效应主导）及低粒子密度区域（分布高度非高斯）中无法准确描述真实行为。本文提出一种生成式流匹配方法，直接基于粒子模拟的通量分布进行建模，显式包含非马尔可夫与非高斯特性。以非相互作用布朗粒子系统的克兰默首达时间问题为例，验证表明该方法能准确捕捉短时行为，并在数量密度的统计矩预测上显著优于马尔可夫基准模型——正则化DK方程。
原文摘要 · Abstract (English)
Hydrodynamic models of stochastic particle systems represented by coarse-grained stochastic partial differential equations (SPDE), such as the regularized Dean-Kawasaki (DK) equation, do not accurately capture the short-time system dynamics that is dominated by non-Markovian effects, and low particle density regimes where the distributions are highly non-Gaussian. We develop a generative flow matching method that directly models the probability distribution of fluxes from particle simulations that explicitly incorporates non-Markovian and non-Gaussian effects. As a demonstration, we use this method to simulate the Kramers first passage time problem for a system of non-interacting Brownian particles. We show the model accurately captures the short-time behavior and provides better predictions of the statistical moments of the number density when compared against the solution of the Markovian baseline, regularized DK equation.
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