Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme
This work addresses the challenge of recovering underlying processes in particle evolution for applications in fields like physics or biology, representing an incremental advancement over existing JKO-based approaches.
The paper tackles the problem of learning population dynamics from evolutionary snapshots by introducing iJKOnet, which combines the JKO scheme with inverse optimization, and demonstrates improved performance over prior methods.
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.