Girsanov reweighting for simulations of underdamped Langevin dynamics

Prof. Bettina G. Keller (Free University of Berlin)

Friday: May 22nd, 2026, 10:30 h

Abstract: Girsanov reweighting provides a rigorous framework for recovering unbiased kinetic and dynamical information from biased stochastic dynamics. More generally, it enables the reconstruction of path-dependent observables by reweighting trajectories generated under modified dynamics back to a desired target ensemble. One particularly important area of application is enhanced sampling in molecular dynamics, where external biases are introduced to accelerate rare events and explore long-time-scale processes that are otherwise inaccessible to conventional simulations.

While Girsanov reweighting is well established for overdamped Langevin dynamics, its application to underdamped dynamics is more subtle. In this setting, the validity of the reweighting procedure depends on the specific numerical Langevin integrator that is used. I will discuss a general approach to derive path probability ratios for Langevin integrators and show how properties such as absolute continuity determine whether rigorous reweighting is possible. In particular, I will present results for symmetric splitting integrators and discuss their implications for recovering unbiased kinetics from biased simulations.

I will then briefly discuss recent developments that translate these theoretical advances into practical simulation workflows, including implementations of Girsanov reweighting in OpenMM and Deeptime, as well as the π-Girsanov framework for constructing Markov state models from non-equilibrium and multiensemble biased simulations. These developments open new directions for Girsanov-based enhanced sampling, including kinetic optimization and iterative neural-network-driven sampling strategies.

References:
- B.G. Keller, P.G. Bolhuis. Annu. Rev. Phys. Chem. (2024) 75, 137-162.  https://doi.org/10.1146/annurev-physchem-083122-124538

- L. Donati, Luca, B.G. Keller. J. Chem. Phys. (2018) 149, 072335.  https://doi.org/10.1063/1.5027728

- S. Kieninger, S.Ghysbrecht, B.G. Keller. arXiv preprint  (2023) arXiv:2303.14696.   https://doi.org/10.48550/arXiv.2303.14696

- J.-L. Schäfer, B.G. Keller, J. Phys. Chem. B (2024) 128, 6014-6027.   https://doi.org/10.1021/acs.jpcb.4c01702

- M. Zhang, Y. Wang, B.G. Keller, H. Wu. arXiv preprint (2026) arXiv:2603.21890.   https://doi.org/10.48550/arXiv.2603.21890