SKM 2023 – scientific programme

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SYFP: Symposium Physics of Fluctuating Paths

SYFP 1: Physics of Fluctuating Paths

SYFP 1.3: Invited Talk

Tuesday, March 28, 2023, 10:30–11:00, HSZ 01

Path reweighting for Langevin dynamics — •Bettina Keller — Freie Universität Berlin, Berlin, Germany

Transition processes in molecular dynamics are investigated by simulating the molecular dynamics as underdamped Langevin dynamics on a high-dimensional energy surface. The accuracy of the rate estimates depends critically on the number of transitions observed in the simulated trajectories. However, the relevant molecular timescales are often beyond the reach of molecular simulations - even when the simulation is conducted on a supercomputer. Slow molecular processes include formation of molecular complexes, transitions through membranes, or phase transitions in crystalline materials. By biasing the potential energy one can sample transitions of rare events, but the rate estimates are distorted. Path reweighting techniques [1, 2] unbias the rate estimates by explicitly calculating the path probability density in the original and biased potential, and thus enable us to characterize slow molecular processes. While the path probability density for overdamped Langevin dynamics is well-documented, little information is available on the path probability densities for underdamped Langevin dynamics [3]. This hampers the use of path reweighting in molecular simulations. I will focus on Langevin integrators constructed via the operator splitting technique, and derive their path probability density. An important intermediate result is the single-step transition probability which maps a point in state space to another point in state space. The image of this function determines whether the integrator can be used (efficiently) for path reweighting. I will demonstrate the results on model potentials and molecular examples.

[1] Luca Donati and Bettina G Keller. Girsanov reweighting for metadynamics simulations. The Journal of Chemical Physics, 149(7):072335, 2018.

[2] Luca Donati, Marcus Weber, and Bettina G Keller. A review of Girsanov reweighting and of square root approximation for building molecular Markov state models. Journal of Mathematical Physics, 63(12):123306, 2022.

[3] Stefanie Kieninger and Bettina G Keller. Path probability ratios for Langevin dynamics exact and approximate. The Journal of Chemical Physics, 154(9):094102, 2021.