Main supervisor: Simon Olsson | Associate Professor, Data Science and AI, Computer Science and Engineering Abstract: Iterative transfer operator (ITO) models have recently emerged as a promising surrogate framework for accelerating molecular dynamics (MD) simulations by directly learning finite-time transition densities of Langevin dynamics. In contrast to Boltzmann generators and equilibrium emulators, which require expensive long-timescale MD trajectories to approximate equilibrium statistics, ITO models can exploit transition information from entire trajectories and therefore offer substantially improved data efficiency. Despite these advantages, current ITO approaches exhibit important limitations. First, they struggle to accurately capture dynamics across extreme time scales: very short timescales close to the MD integration step size, as well as asymptotically long timescales corresponding to the equilibrium Boltzmann distribution. Second, existing methods rely almost exclusively on sampled trajectory data while largely ignoring force information, even though forces are readily available during MD simulation and directly encode local properties of the underlying energy landscape. This project investigates whether force information can be used to constrain ITO models in both the short-time and infinite-time limits. At short timescales, the Langevin transition density is strongly determined by local drift and diffusion terms, suggesting that force information could provide additional supervision where trajectory-based learning becomes inefficient. At long timescales, the transition operator should converge toward the invariant Boltzmann distribution, implying consistency conditions that are currently not enforced in existing ITO formulations. The proposed work will explore how these limiting behaviors can be incorporated directly into ITO models. In particular, recent diffusion-model training approaches that learn equilibrium distributions directly from force fields without requiring equilibrated MD trajectories may provide a mechanism for regularizing the long-time behavior of ITO models while preserving their ability to learn finite-time dynamics from trajectory data. The overall goal is to develop transfer operator models that remain accurate across all time scales while reducing dependence on expensive and scarce long MD simulations.