Thermostats for sampling and optimization

Benedict Leimkuhler

School of Mathematics, University of Edinburgh

I will discuss the use of thermostat-like temperature controls for wide ranging applications in chemical simulation, statistical computation and machine learning.

Thermostats like Langevin and Nos\’{e}-Hoover have their origins in molecular dynamics simulation where they are used to control the thermodynamic state of the system to match a laboratory (or in vivo) setup; as such they are well used tools of materials science.   More recently they have been embraced by statisticians who increasingly use them for sampling tasks with respect to general statistical models. They even find uses in machine learning where they help to regulate models containing noisy gradients (as arise when ’subsampling’ is used).  In this talk I will discuss two topics in thermostatting:  (1) the discretization and parameterization of Langevin dynamics  for thermodynamic sampling and (2)  the use of Nos\’{e}-Hoover-like methods for efficient optimization of general objective functions.

[1] Contraction and convergence rates for discretized kinetic Langevin dynamics, Benedict Leimkuhler, Daniel Paulin, Peter A Whalley, 2023. https://arxiv.org/pdf/2302.10684

[2]  Friction-adaptive descent: a family of dynamics-based optimization methods, Katerina Karoni, Benedict Leimkuhler, Gabriel Stoltz, 2023.  https://arxiv.org/pdf/2306.06738