Simulation-Free Learning of Population Dynamics with Wasserstein Lagrangian Residuals
This study addresses the inability of Wasserstein gradient flows to capture conservative dynamics and the prohibitive training costs of existing Lagrangian methods that rely on numerical simulations. To overcome these limitations, this work proposes Double-Stitch, a simulation-free framework. By leveraging the Clebsch variational principle, the method derives velocity-gradient-free equations of motion and achieves efficient learning of Lagrangian mechanics in Wasserstein space by penalizing equation residuals along learned trajectories. Theoretically, vanishing residuals guarantee that the equations of motion are satisfied, thereby entirely eliminating numerical solving steps during training. Experiments demonstrate that Double-Stitch matches or surpasses baseline performance on synthetic, single-cell, and ocean eddy datasets while accelerating training by 4 to 14 times.