Langevin SDEs have unique transient dynamics

• URL: http://arxiv.org/abs/2505.21770v1
• Date: Tue, 27 May 2025 21:06:04 GMT
• Title: Langevin SDEs have unique transient dynamics
• Authors: Vincent Guan, Joseph Janssen, Nicolas Lanzetti, Antonio Terpin, Geoffrey Schiebinger, Elina Robeva,
• Abstract summary: We prove that the drift and diffusion terms of a Langevin SDE are jointly identifiable from temporal marginal distributions.<n>This complete characterization of structural identifiability removes the long-standing assumption that the diffusion must be known to identify the drift.
• Score: 3.5558885788605337
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The overdamped Langevin stochastic differential equation (SDE) is a classical physical model used for chemical, genetic, and hydrological dynamics. In this work, we prove that the drift and diffusion terms of a Langevin SDE are jointly identifiable from temporal marginal distributions if and only if the process is observed out of equilibrium. This complete characterization of structural identifiability removes the long-standing assumption that the diffusion must be known to identify the drift. We then complement our theory with experiments in the finite sample setting and study the practical identifiability of the drift and diffusion, in order to propose heuristics for optimal data collection.

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