Skip to content
DraconiticResearch
Search Sources API
194,161 studies31 sourcesUpdated 7 min ago
PreprintarXiv licencearXiv

Underdamped Stochastic Optimal Transport with Landauer boundary conditions: machine learning and analytical solution

  • Julia Sanders
  • Dario Lucente
  • Marco Baldovin
  • Paolo Muratore-Ginanneschi
Open at sourcePDFDOICite

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.

Related

  1. Analytical and Numerical Analysis of Multidimensional Diffusion Processes in L2 Space Under Third-Kind Boundary Conditions
    Zafar Duman Abbasov, Ghadah Albeladi, Mohamed Gamal +1
    AxiomsPeer-reviewedCC BY5 citedGeneral mathematicsOpenAlex
  2. Analytical solutions of one class of Volterra quadratic stochastic operators of a two-sex population with continuous time
    Rasulov Xaydar Raupovich
    arXivPreprintCC BY-SA 4.0Full textDynamical systemsarXiv
  3. Analytical and Numerical Analysis of Time-Delayed NDF Control for Nonlinear Rotating Pendulums with Stiffness Modulation Under Simultaneous Resonance Conditions
    Khalid Alluhydan, M. N. Abd EL-Salam
    MathematicsPeer-reviewedCC BY 4.0General mathematicsCrossref
  4. Necessary and sufficient conditions for optimal control of coupled forward-backward stochastic control systems driven by G-Brownian motion
    Xiaojuan Li, Mingshang Hu
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  5. Stochastic Porous Media Equations With Nonhomogeneous Dirichlet Boundary Conditions
    Dan Goreac, Ioana Ciotir, Juan Li +1
    arXivPreprintCC BY-NC-SA 4.0Full textProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{sanders2026underdamped,
  title = {{Underdamped Stochastic Optimal Transport with Landauer boundary conditions: machine learning and analytical solution}},
  author = {Julia Sanders and Dario Lucente and Marco Baldovin and Paolo Muratore-Ginanneschi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41599},
  eprint = {2610.41599},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41599},
}
RIS
TY  - UNPB
TI  - Underdamped Stochastic Optimal Transport with Landauer boundary conditions: machine learning and analytical solution
AU  - Julia Sanders
AU  - Dario Lucente
AU  - Marco Baldovin
AU  - Paolo Muratore-Ginanneschi
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41599
UR  - https://arxiv.org/abs/2610.41599
AB  - 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.
ER  -