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  • Open Access

Data-driven geometric phase in biological locomotion

Pyae Hein Htet and Kenta Ishimoto*

  • *Contact author: kenta.ishimoto@math.kyoto-u.ac.jp
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Phys. Rev. Research 8, 043108 – Published 30 October, 2026

DOI: https://doi.org/10.1103/qlj7-1kvn

Abstract

Geometric phase quantifies net locomotion in dissipative media via gauge theory, but linking this theoretical quantity to noisy, sparse, and weakly periodic biological shape data is challenging. We develop a theory-guided, data-driven Koopman autoencoder to recover the limit cycle embedded in imperfect cyclic data and extract shape gaits and geometric phase from sperm and nematode data. We introduce a geometric phase sensitivity function that quantifies responses to shape perturbations and reveals mechanical information using only gauge-theoretic structure, without assuming mechanical laws.

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Phys. Rev. Research 8, 043108– Published 30 October, 2026
  • Received 23 June 2026
  • Accepted 2 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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