Simulation-Free Learning of Population Dynamics with Wasserstein Lagrangian Residuals

TL;DR

Double-Stitch is a simulation-free method for learning population dynamics in Wasserstein space by minimizing the residual of a Lagrangian equation derived from a Clebsch variational principle. It enables accurate modeling of both dissipative and conservative dynamics without iterative numerical solvers, achieving faster training than simulation-based approaches while matching or surpassing performance on synthetic, single-cell, and ocean vortex data.

Why It Matters

The method enables efficient and accurate modeling of complex evolving systems such as biological populations and fluid flows without relying on computationally expensive simulations, making it practical for real-world applications where data is sparse and dynamics are non-gradient-like.

Key Findings

• Double-Stitch learns population dynamics without simulations by penalizing the residual of a Lagrangian equation in Wasserstein space.
• The approach supports both dissipative and conservative dynamics, unlike Wasserstein gradient flows which are limited to the former.
• It trains 4 to 14 times faster than simulation-based Wasserstein Lagrangian Mechanics while achieving competitive or superior accuracy across multiple datasets.