Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: A stochastic control approach

@article{Breiten2021StochasticGD,
  title={Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: A stochastic control approach},
  author={Tobias Breiten and Carsten Hartmann and Lara Neureither and Upanshu Sharma},
  journal={Journal of Mathematical Physics},
  year={2021}
}
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), for which the dynamics can easily get trapped inside metastable subsets of the phase space. We follow [Chen et al., J. Math. Phys. 56, 113302, 2015] and consider a Langevin equation that is simulated at a high… 

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