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

Active matter comprises nonequilibrium systems whose constituents consume local energy and self-organize into a wide range of emergent dynamics. Characterizing active-matter systems from first principles remains challenging because many microscopic kinetic parameters are unobservable in experiments. Data-driven modelling provides a natural alternative, but current approaches focus on limited dynamical regimes. Here, we construct, train, and evaluate an active-matter foundation model that learns the dynamics of evolving active-matter systems spanning stationary and nonstationary phases, including filament condensation, contracting spheres, rotational flows, and active turbulence. Motivated by kinetic theory, we introduce velocity-space prediction and compare it with video models that directly forecast pixels. We show that adding velocity-field supervision through local-displacement prediction and speed-distribution alignment improves long-term trajectory fidelity, reducing cumulative pixel mean-squared error by 20\% and speed-distribution KL divergence by more than 50\% over 20-step rollouts compared with the same model without velocity supervision. We further reveal that the model's latent space is organized by dynamical phase beyond frame appearance, tracking time- and motor-concentration-dependent phase evolution, although neither concentration nor time is provided as an explicit input. Our results establish velocity-space prediction as a route toward dynamical models of nonequilibrium active matter, and we anticipate that this principle can extend to other temporal models.