Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.

翻译：马尔可夫过程是描述各领域动态系统的常用数学模型。然而，由于精确积分需要极小的时间步长，在长时间尺度下精准模拟大规模系统的计算成本极为高昂。本文提出一种将复杂系统映射至简化表征空间、并实现时间大跨度建模的推理过程。为此，我们提出基于信息论原理的“时间延迟信息瓶颈”（Time-lagged Information Bottleneck，简称T-IB）目标函数，旨在捕获关键时序特征的同时，通过剔除高频信息来简化仿真任务并最小化推断误差。实验表明，T-IB能学习出信息最优表征，在选定时间延迟下精准复现原始过程的统计特性与动力学规律，其表现优于现有时间滞后降维方法。