When the Simulator Is Wrong: Misspecified Dynamics Priors for Multi-Agent Forecasting in Robotic Active Matter

Mechanistic models of active matter are hand-crafted and low-dimensional, so they inevitably omit factors of the system they describe. We ask what such an imperfect simulator is worth when coupled to a data-driven predictor, using real trajectories of 45 bristle-bot robots sharing one arena. We fit a self-propulsion model with speed relaxation, anisotropic drag, and a confining potential by robust regression, then use its rollout as the initializer mean of the Leapfrog Diffusion Model (LED) in place of a learned one. The simulator is misspecified by construction. Fitted on collision-free windows and carrying no interaction term, it omits the many-body coupling that dominates a dense swarm. It is nonetheless a better mean than a learned one at every horizon (1s $\mathrm{minADE}$ $3.88\to3.48$\,px, 4s $16.34\to14.64$\,px), and, contrary to what we expected, it does not measurably widen the sample cloud. Average-sample error is unchanged within the precision we can resolve (4s $\mathrm{meanADE}$ $45.10$ vs $45.15$\,px) and average velocity error improves. The dispersion that remains is governed by the winner-take-all objective rather than by the missing physics. Supervising all samples with $\mathrm{minADE}+\lambda\,\mathrm{meanADE}$ cuts 4s $\mathrm{meanADE}$ to $41.08$\,px with the simulator untouched, trading against best-of-$K$ accuracy (4s $\mathrm{minADE}$ $14.64\to15.06$\,px). An incomplete mechanistic rollout can be a strong prior on the mean while leaving calibration of the spread a learning problem.