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The paper applies a machine-learning-based direct optimization method to find optimal control protocols for underdamped stochastic systems, including Landauer bit-erasure boundary conditions. It is primarily a stochastic thermodynamics and control problem, but the ML method is the core contribution. Readers should note that the results are benchmarked against a perturbative expansion in the overdamped limit, so the claimed validity of the learned solutions depends on that comparison.
Underdamped Stochastic Optimal Transport with Landauer boundary conditions: machine learning and analytical solution
arXiv:2610.41599v1 Announce Type: cross Abstract: Finding optimal transport protocols for underdamped stochastic processes is a difficult yet important problem in control theory. In this paper we develop a direct method, based on machine learning, to find the optimal solution of the problem in the presence of non-linear boundary conditions, including those modelling the Landauer bit-erasure problem. The dynamics is steered from a single-peak to a double-peak distribution in position space, by only acting on a controllable external potential. The problem is highly non-linear, and analytical solutions are not available in general. We benchmark our numerical results with a perturbative expansion, which is expected to hold in a suitable overdamped limit.
Abstract:Finding optimal transport protocols for underdamped stochastic processes is a difficult yet important problem in control theory. In this paper we develop a direct method, based on machine learning, to find the optimal solution of the problem in the presence of non-linear boundary conditions, including those modelling the Landauer bit-erasure problem. The dynamics is steered from a single-peak to a double-peak distribution in position space, by only acting on a controllable external potential. The problem is highly non-linear, and analytical solutions are not available in general. We benchmark our numerical results with a perturbative expansion, which is expected to hold in a suitable overdamped limit.
Main: 12 pages, 6 figures. Supplemental material: 11 pages
Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG); Optimization and Control (math.OC)
arXiv:2610.41599 [cond-mat.stat-mech]
(or arXiv:2610.41599v1 [cond-mat.stat-mech] for this version)
https://doi.org/10.48550/arXiv.2610.41599 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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