Leveraging Gauge Freedom for Learning Non-Gradient Population Dynamics of Stochastic Systems
For researchers inferring population dynamics from stochastic systems, this work provides a more general method that overcomes the gradient-flow restriction, enabling accurate modeling of non-potential transport.
Existing population dynamics inference methods assume gradient flows, but the authors propose NGIF to infer non-gradient dynamics using a weak formulation of the continuity equation, achieving improved distributional accuracy and better capturing non-potential transport across low- and high-dimensional physics problems.
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. We propose Non-Gradient Inference Flows (NGIF), an algorithm to infer non-gradient population dynamics using a weak formulation of the continuity equation. This allows us to parameterize general vector fields and choose other selection criteria beyond minimal kinetic energy. We demonstrate on a variety of low- and high-dimensional physics problems that this more general approach improves distributional accuracy over gradient-restricted baselines and better captures non-potential transport.