Predicting Active-Matter Dynamics through Local Displacement and Velocity-Distribution Alignment

From molecular motors and cytoskeletal filaments to cells and animal groups, active matter comprises nonequilibrium systems of active particles that consume local energy and self-organize, leading to a wide range of emergent dynamics. Characterizing these systems from first principles is difficult because many microscopic parameters are unobservable in experiments. Meanwhile, modern microscopy enables the collection of abundant videos of these systems, making data-driven modeling a natural alternative. Here, we construct, train, and evaluate an active-matter foundation model using 204 reconstituted microtubule--motor experiments in cell-free transcription--translation droplets, spanning stationary and nonstationary phases including filament condensation, contracting spheres, rotational flows, and active turbulence. Compared with conventional pixel-space objectives in video models, incorporating velocity-space supervision through local-displacement prediction and speed-distribution alignment substantially improves dynamical prediction. Over 20-step prediction rollouts, it reduces cumulative pixel-space mean-squared error by 20\% and speed-distribution KL divergence by more than 50\% relative to the same displacement model without velocity supervision. From a short history of frames, the model forecasts dynamics that match experimental phases and distinguishes stationary from nonstationary behavior. The learned latent space exhibits an emergent organization by dynamical phase, and the resulting phase map tracks systems through time-dependent phase transitions and reveals concentration-driven transitions for individual motor species. These results establish velocity-space prediction as a route toward dynamical models of nonequilibrium systems.