记忆条件扩散模型用于广义朗之万动力学
Memory-Conditioned Diffusion Model for Generalized Langevin Dynamics
- Oak Ridge National Laboratory（橡树岭国家实验室）
- University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对广义朗之万动力学的非马尔可夫特性，提出记忆条件扩散方法，利用递归指数滤波器库和核分数估计器学习随机流映射，实现长记忆保留与高效预测，并在等离子体刮削层模型中验证了非高斯间歇行为。
AI中文摘要：
广义朗之万方程描述了非马尔可夫动力学，其中解析变量的演化依赖于其过去的状态。我们提出了一种记忆条件扩散方法，用于从观测轨迹中学习这些动力学的随机流映射，而无需识别记忆核或重构未解析变量。一个紧凑的、递归更新的指数滤波器库使得流映射能够在多个时间尺度上保留预测历史，而无需依赖长观测窗口。下一步分布以当前观测和该记忆状态为条件，其存储和更新成本对于固定库大小而言与历史长度无关。预测标准指导记忆预算的分配，在向量基准中采用参考辅助选择，并且可选的线性投影进一步降低了条件维度。一种基于核的分数估计器生成条件样本，无需训练分数网络，这些样本用于训练神经流映射以进行自回归模拟。三个数值示例评估了在较小条件维度下的长记忆保留、耦合向量动力学中的预测压缩，以及非高斯条件分布和间歇事件。非高斯示例再现了等离子体刮削层随机模型中的条件不对称性和爆发统计。
英文摘要：
Generalized Langevin equations describe non-Markovian dynamics in which the evolution of resolved variables depends on their past. We propose a memory-conditioned diffusion method for learning stochastic flow maps of these dynamics from observed trajectories, without identifying a memory kernel or reconstructing unresolved variables. A compact, recursively updated bank of exponential filters enables the flow map to retain predictive history over multiple time scales without conditioning on long observation windows. The next-step distribution is conditioned on the current observation and this memory state, whose storage and update costs are independent of the history length for a fixed bank size. Predictive criteria guide the memory budget, with reference-assisted selection in the vector benchmark, and an optional linear projection further reduces the conditioning dimension. A kernel-based score estimator generates conditional samples without training a score network, and these samples are used to train a neural flow map for autoregressive simulation. Three numerical examples assess long-memory retention at small conditioning dimension, predictive compression in coupled vector dynamics, and non-Gaussian conditional distributions and intermittent events. The non-Gaussian example reproduces conditional asymmetry and burst statistics in a stochastic model of the plasma scrape-off layer.
