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Vincent Guan

Visiteur de recherche indépendant - University of British Columbia
Superviseur⋅e principal⋅e
Kirill Neklyudov
Sujets de recherche
Causalité

Publications

A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots
Vincent Guan
Lazar Atanackovic
Kirill Neklyudov
The population dynamics of molecules, cells, and organisms are governed by a number of unknown forces. In the last decade, population dynami… (voir plus)cs have predominantly been modeled with Wasserstein gradient flows. However, since gradient flows minimize free energy, they fail to capture important dynamical properties, such as periodicity. In this work, we propose a change in perspective by considering dynamics that minimize a population-level action under a damped Wasserstein Lagrangian. By deriving the corresponding Hamiltonian equations of motion, we formalize Wasserstein Lagrangian Mechanics, a structured class of second-order dynamics that encompasses classical mechanics, quantum mechanics, and gradient flows. We then propose WLM as the first algorithm that learns these second-order dynamics from observed marginals, without specifying the Lagrangian. By directly learning the population mechanics, WLM can both forecast and interpolate unseen marginals, and outperforms existing gradient flow and flow matching methods across a wide range of dynamics, including vortex dynamics, embryonic development, and flocking.
2026-05-07
arXiv (prépublication)
doi.org
arxiv.org