  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.
