A Likelihood Approach for Inference of Population Heterogeneity in Particle Ensembles with Second-Order Langevin Dynamics

Condensed Matter > Soft Condensed Matter [Submitted on 13 Nov 2024 (v1), last revised 1 Jun 2026 (this version, v2)] Title:A Likelihood Approach for Inference of Population Heterogeneity in Particle Ensembles with Second-Order Langevin Dynamics View PDF HTML (experimental)Abstract:The inherent complexity of biological agents often leads to motility behavior that appears to have random components. Robust stochastic inference methods are therefore required to understand and predict the motion patterns from time-discrete trajectory data provided by experiments. In many cases, second-order Langevin models are needed to adequately capture the motility. Additionally, population heterogeneity needs to be taken into account when analyzing data from several individual organisms. In this work, we describe a maximum likelihood approach to infer dynamical, stochastic models and, simultaneously, estimate the heterogeneity in a population of motile active particles from discretely sampled, stochastic trajectories. To this end, we propose a method to approximate the likelihood for non-linear second-order Langevin models. We show that this maximum likelihood ansatz outperforms alternative approaches, especially for short trajectories. Additionally, we demonstrate how a measure of uncertainty for the heterogeneity estimate can be derived. We thereby pave the way for the systematic, data-driven inference of dynamical models for actively driven entities based on trajectory data, deciphering temporal fluctuations and inter-particle variability. Submission history From: Jan Albrecht [view email][v1] Wed, 13 Nov 2024 15:27:02 UTC (823 KB) [v2] Mon, 1 Jun 2026 16:18:18 UTC (558 KB) Current browse context: cond-mat.soft Change to browse by: References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) IArxiv Recommender (What is IArxiv?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.