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，由于精确积分所需的时间步长较小，大规模系统在长时间尺度上的精确模拟计算成本高昂。本文提出一种推理过程，将复杂系统映射至简化表示空间，并建模时间上的大步长跳跃。为此，我们提出时间滞后信息瓶颈（T-IB），这是一种基于信息论原理的目标函数，旨在捕获相关时间特征的同时丢弃高频信息，从而简化模拟任务并最小化推理误差。实验表明，T-IB能够学习信息最优表示，在选定时间滞后下精确建模原始过程的统计特性与动力学性质，其性能优于现有时间滞后降维方法。