Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme

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 iJKOnet, an approach that combines the JKO framework with inverse optimization techniques to learn population dynamics. Our method relies on a conventional 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.

Alexander Korotin

Researcher

My research interests include generative modeling, diffusion models, unpaired learning, optimal transport and Schrodinger bridges.