Project A10 (New): Population control of multiple walker simulations via a birth/death process
Conventional Molecular Dynamics (MD) simulations are generally unable to access the long-timescale phenomena that are common in nature. This timescale problem comes from the fact that a typical free energy landscape consists of many metastable states separated by high free energy barriers. If the barriers are much higher than the thermal energy, the system is kinetically trapped in some metastable state and barrier crossings will be rare events on the time scales that we can simulate. One strategy to alleviate this time scale problem is to employ collective variable (CV) based enhanced sampling methods such as metadynamics. A common way to improve the performance of CV-based methods is to employ multiple walkers that share a bias potential and collaboratively sample the free energy landscape. In this way, one reduces the wall-clock time for convergence and makes better usage of modern parallel HPC resources. However, the multiple walkers’ usefulness can be severely diminished due to walkers becoming correlated with each other. Thus, there is a need to develop a population control scheme for walkers to improve performance. In this project, we propose to develop a population control scheme for multiple walker CV-based enhanced sampling based on a recently introduced birth/death accelerated Langevin sampling algorithm (Lu et al., arXiv preprint at arXiv:1905.09863 ). We will adapt this birth/death scheme to atomistic/molecular systems and integrate it into a CV-based multiple walker framework.
The birth/death algorithm in the paper by Lu et al. is based on a Fokker-Planck equation with an additional birth/death term. The advantage of the birth/death term is to allow for global moves of the probability density mass between metastable modes without having to go through regions of low probability (i.e., barriers). In practice, the algorithm is implemented by considering an ensemble of walkers. Between birth/death events, each walker independently follows Langevin dynamics in the given energy landscape. Then periodically, one kills or duplicates walkers according to their birth/death rate. The non-local birth/death moves can significantly improve the sampling of the energy landscape. However, this scheme has some shortfalls. It cannot describe higher-lying free energy regions as walkers there tend to be killed. Furthermore, one must make sure that the initial distribution of walkers covers all the metastable states as the scheme cannot explore and find new metastable states on its own if the free energy barriers are too high. In other words, the method is based on the exploitation of information. On the other hand, CV-based methods are based on exploration and can find
new metastable states on their own. Therefore, combining the birth/death scheme with multiple walker CV-based enhanced sampling can improve both methods' performance.
The development of this birth/death scheme will require overcoming several theoretical and practical challenges. This project will thus be performed in a tight collaboration between theoretical physics (Burkhard Dünweg and Omar Valsson) and mathematics (Lisa Hartung).
On the fluctuations of the extremal and cluster level sets of branching Brownian motion
Lisa Hartung, Oren Louidor, Tianqi Wu
Probability theory and related fields, early access (2026)
see publication
A random walk approach to broadcasting on random recursive trees
Ernst Althaus, Lisa Hartung, Rebecca Steiner
J. Theor. Probability 39, 65 (2026)
see publication
From 1 to infinity: The log-correction for the maximum of variable speed branching Brownian motio
Alexander Alban, Anton Bovier, Annabell Gros, Lisa Hartung
Electronic J. of Probability 30, 1-46 (2025)
see publication
Maxima of a random model of the Riemann zeta function over intervals of varying length
Louis-Pierre Arguin, Guillaume Dubach, Lisa Hartung
Annales de L'Institut Henri Poincaré - Probabilités et statistiques 60, 588-611 (2024)
see publication
Branching Brownian Motion with Self-Repulsion
Anton Bovier, Lisa Hartung
Annales Henri Poincaré 24, 931-956 (2023)
see publication
The speed of invasion in an advancing population
Anton Bovier, Lisa Hartung
J. Mathematical Biology 87, 56 (2023)
see publication
Enhanced Sampling Methods for Molecular Dynamics Simulations
Jérôme Hénin, Tony Lelièvre, Michael R. Shirts, Omar Valsson, and Lucie Delemotte
Living Journal of Computational Molecular Science, 4(1), 1583, (2023)
see publication
Sampling rare event energy landscapes via birth-death augmented dynamics
Benjamin Pampel, Simon Holbach, Lisa Hartung, and Omar Valsson
Phys. Rev. E 107, 024141 (2023)
see publication
Refined Large Deviation Principle for Branching Brownian Motion Conditioned to Have a Low Maximum
Yanjia Bai, Lisa Hartung
ALEA - Latin American Journal of Probability and Mathematical Statistics 19, 8590880 (2022)
see publication
Improving the Efficiency of Variationally Enhanced Sampling with Wavelet-Based Bias Potentials
Benjamin Pampel and Omar Valsson
Journal of Chemical Theory and Computation 18, 7, 4127–4141 (2022)
see publication
Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: Extremal process in the weakly correlated regime
Maximilian Fels, Lisa Hartung
ALEA - Latin American Journal of Probability and Mathematical Statistics 18, 1689-1718 (2021)
see publication
Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: Convergence of the maximum in the regime of weak correlations
Maximilian Fels, Lisa Hartung
ALEA - Latin American Journal of Probability and Mathematical Statistics 18, 18901-1930 (2021)
see publication