ScooBDoob: Schrödinger Bridge with Doob’s \textit{h}-Transform for Molecular Dynamics

Yinuo Zhang, Sophia Tang, Pranam Chatterjee

Keywords: MSM, TPS, MD

TL;DR: Discrete bridge-matching framework that models metastable dynamics by tilting MSM transition rates through Doob’s transform to generate optimal stochastic paths between prescribed initial and terminal ensembles

Abstract: The slow processes of stochastic dynamical systems can be captured by Molecular Dynamics (MD) simulations, which approximate transition matrices describing how probabilities evolve over metastable conformations. Standard approaches such as Markov State Models (MSMs) extract dominant conformations and transition statistics via eigendecomposition, but face scalability and generalization limits. Here, we introduce **Sc**hödinger **B**ridge with **Doob**’s *h*-Transform (**ScooBDoob**), a discrete bridge-matching framework that models metastable dynamics by tilting MSM transition rates through Doob’s transform to generate optimal stochastic paths between prescribed initial and terminal ensembles. We show that ScooBDoob preserves spectral stability of slow modes during training, recovers rare transition pathways with density-aware regularization, and generalizes zero-shot across temperatures. Experiments on the Müller-Brown potential and the Aib9 peptide demonstrate accurate kinetics and robust endpoint-conditioned rollouts, highlighting broad applicability to biomolecular dynamics.

Submission Number: 25