Leveraging Gauge Freedom for Learning Non-Gradient Population Dynamics of Stochastic Systems

ArXi:2605.25107v1 Announce Type: cross Existing work on population dynamics inference often focuses on flows arising from vector fields that are the gradients of scalar potentials. Among all admissible flows that are compatible with the population dynamics, gradient flows are optimal in a specific sense: they minimize kinetic energy. The selection of fields based on different criteria corresponds to a gauge freedom when determining population dynamics, which we leverage in this work.