ScooBDoob: Schrödinger Bridge with Doob’s h-Transform for Molecular Dynamics

Yinuo Zhang, Sophia Tang, Pranam Chatterjee

Keywords: Transition path sampling, Schrödinger bridge, Markov State Models, Doob’s h-transform, molecular dynamics

TL;DR: ScooBDoob models rare-event molecular transitions by learning Doob-transformed MSM bridges with density-aware regularization and spectral constraints.

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**hr**ö**dinger **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 demonstrate ScooBDoob’s ability to recover slow processes and generate feasible, target-conditioned trajectories on the Müller-Brown potential and the Aib9 peptide, which folds between two distinct macrostates.

Submission Number: 131