Machine-learned topological transport of magnetic colloids
Abstract
By modulating the orientation of a uniform magnetic field it is possible to transport magnetic microparticles above magnetic patterns. In periodic patterns, driving control loops that wind around special orientations, which are dictated by the symmetry of the pattern, induce transport by one unit cell. The transport is topologically protected with trajectories controlled by the winding numbers of the control loop around the special orientations. In non-periodic patterns, the special orientations are position dependent, precluding a global characterization of the transport using a small set of winding numbers. We use here a reinforcement learning agent trained with Brownian dynamics simulation data that uses the local environment of the magnetic pattern to decide an action over the control loop. The agent autonomously discovers topological transport protocols directly from the particle response without prior characterization of the magnetic potential landscape. An agent trained solely on a complex non-periodic pattern directly generalizes to completely unseen periodic, quasicrystalline, and disordered substrates. Moreover, the agent dynamically adjusts the control loop to transport particles across lattice defects and to counterbalance external drift forces that would cause static topological loops to fail. By adding a pathfinding algorithm to the model, we additionally achieve simultaneous, independent transport of multiple identical colloids along different on demand trajectories. We demonstrate that the control loops can be directly transferred to an experimental setup to successfully drive magnetic microparticles across a non-uniform magnetic thin film.
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BibTeX
@misc{wohlrab2026machinelearned,
title = {{Machine-learned topological transport of magnetic colloids}},
author = {Sebastian Wohlrab and Aneena Rinu Perayil and Piotr Kuświk and Maciej Urbaniak and Feliks Stobiecki and Arne J. Vereijken and Arno Ehresmann and Thomas M. Fischer and Daniel de las Heras},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17344},
eprint = {2610.17344},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17344},
}
RIS
TY - UNPB
TI - Machine-learned topological transport of magnetic colloids
AU - Sebastian Wohlrab
AU - Aneena Rinu Perayil
AU - Piotr Kuświk
AU - Maciej Urbaniak
AU - Feliks Stobiecki
AU - Arne J. Vereijken
AU - Arno Ehresmann
AU - Thomas M. Fischer
AU - Daniel de las Heras
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17344
UR - https://arxiv.org/abs/2610.17344
AB - By modulating the orientation of a uniform magnetic field it is possible to transport magnetic microparticles above magnetic patterns. In periodic patterns, driving control loops that wind around special orientations, which are dictated by the symmetry of the pattern, induce transport by one unit cell. The transport is topologically protected with trajectories controlled by the winding numbers of the control loop around the special orientations. In non-periodic patterns, the special orientations are position dependent, precluding a global characterization of the transport using a small set of winding numbers. We use here a reinforcement learning agent trained with Brownian dynamics simulation data that uses the local environment of the magnetic pattern to decide an action over the control loop. The agent autonomously discovers topological transport protocols directly from the particle response without prior characterization of the magnetic potential landscape. An agent trained solely on a complex non-periodic pattern directly generalizes to completely unseen periodic, quasicrystalline, and disordered substrates. Moreover, the agent dynamically adjusts the control loop to transport particles across lattice defects and to counterbalance external drift forces that would cause static topological loops to fail. By adding a pathfinding algorithm to the model, we additionally achieve simultaneous, independent transport of multiple identical colloids along different on demand trajectories. We demonstrate that the control loops can be directly transferred to an experimental setup to successfully drive magnetic microparticles across a non-uniform magnetic thin film.
ER -