Data-driven geometric phase in biological locomotion

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.