[2506.01502] Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme

Computer Science > Machine Learning arXiv:2506.01502 (cs) [Submitted on 2 Jun 2025 (v1), last revised 2 Mar 2026 (this version, v3)] Title:Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme Authors:Mikhail Persiianov, Jiawei Chen, Petr Mokrov, Alexander Tyurin, Evgeny Burnaev, Alexander Korotin View a PDF of the paper titled Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme, by Mikhail Persiianov and 4 other authors View PDF HTML (experimental) Abstract:Learning population dynamics involves recovering the underlying process that governs particle evolution, given evolutionary snapshots of samples at discrete time points. Recent methods frame this as an energy minimization problem in probability space and leverage the celebrated JKO scheme for efficient time discretization. In this work, we introduce $\texttt{iJKOnet}$, an approach that combines the JKO framework with inverse optimization techniques to learn population dynamics. Our method relies on a conventional $\textit{end-to-end}$ adversarial training procedure and does not require restrictive architectural choices, e.g., input-convex neural networks. We establish theoretical guarantees for our methodology and demonstrate improved performance over prior JKO-based methods. The code of $\texttt{iJKOnet}$ is available at this https URL. Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) Cite as: arXiv:2506.01502 [cs.LG]   (or arXiv:2506.0...