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- Dienstag, 27.10.2020, 15:00 Uhr (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Carsten Hartmann, Brandenburgische Technische Universität Cottbus-Senftenberg:
Convergence to equilibrium in underdamped Langevin dynamics: Fluctuation-dissipation relations, entropy production and optimal control
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Online Event
Abstrakt
We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin system at small noise (or low temperature) that is characterised by metastability and slow convergence to equilibrium. We follow an approach proposed by Pavon and co-workers [1] and consider a Langevin equation that is simulated at a high temperature, with the control playing the role of a friction that balances the additional noise so as to restore the original invariant measure at a lower temperature. We discuss different limits as the temperature ratio goes to infinity and prove convergence to a limit dynamics. It turns out that, depending on whether the lower (“target”) or the higher (“simulation”) temperature is fixed, the controlled dynamics converges either to the overdamped Langevin equation or to a deterministic gradient flow. This implies that (a) the ergodic limit and the large temperature separation limit do not commute in general, and that (b) it is not possible to accelerate the speed of convergence to the ergodic limit by making the temperature separation larger and larger. We discuss the implications of these observation from the perspective of stochastic optimisation algorithms and enhanced sampling schemes in molecular dynamics. This is joint work with Tobias Breiten, Lara Neureither and Upanshu Sharma [2]. [1] Y. Chen, T.T. Georgiou and M. Pavon. Fast cooling for a system of stochastic oscillators. J. Math. Phys. 56:113302, 2015. [2] T. Breiten, C. Hartmann, L. Neureither and U. Sharma. Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: a stochastic control approach. Preprint, 2020.
Weitere Informationen
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Veranstalter
WIAS Berlin
- Donnerstag, 29.10.2020, 16:00 Uhr (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Emil Cortes André, Technical University of Denmark:
An analysis of collective effects in nanolasers using minimally extended rate equations
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Online Event
Veranstalter
WIAS Berlin