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PreprintCC BY 4.0arXiv

Optimal Bias Potentials via Ergodic Optimal Control and Generator Learning

  • Lei Guo
  • Carsten Hartmann
  • Thomas Berger
  • Feliks Nüske
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Abstract

We investigate the computation of optimal bias potentials for accelerating transitions between metastable states and for computation of equilibrium properties in molecular dynamics simulations. We formulate optimal biasing as an ergodic optimal control problem (OCP), which can be recast as a linear eigenvalue problem for the infinitesimal generator of the unbiased dynamics. We demonstrate that data-driven learning methods for the generator enable reliable solution of the OCP, computation of biasing potentials, extraction of equilibrium properties, and acceleration of state transitions. We also explore the relation of the control problem to coarse grained representations and learning of coarse grained dynamics.

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Cite

BibTeXRIS
BibTeX
@misc{guo2026optimal,
  title = {{Optimal Bias Potentials via Ergodic Optimal Control and Generator Learning}},
  author = {Lei Guo and Carsten Hartmann and Thomas Berger and Feliks Nüske},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28010},
  eprint = {2609.28010},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28010},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Optimal Bias Potentials via Ergodic Optimal Control and Generator Learning
AU  - Lei Guo
AU  - Carsten Hartmann
AU  - Thomas Berger
AU  - Feliks Nüske
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28010
UR  - https://arxiv.org/abs/2609.28010
AB  - We investigate the computation of optimal bias potentials for accelerating transitions between metastable states and for computation of equilibrium properties in molecular dynamics simulations. We formulate optimal biasing as an ergodic optimal control problem (OCP), which can be recast as a linear eigenvalue problem for the infinitesimal generator of the unbiased dynamics. We demonstrate that data-driven learning methods for the generator enable reliable solution of the OCP, computation of biasing potentials, extraction of equilibrium properties, and acceleration of state transitions. We also explore the relation of the control problem to coarse grained representations and learning of coarse grained dynamics.
ER  -