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In this work, we study the inverse problem of identifying complex flockingdynamics in a domain cluttered with obstacles. We get inspiration from animalflocks moving in complex ways with capabilities far beyond what current robotscan do. Owing to the difficulty of observing and recovering the trajectories ofthe agents, we focus on the dynamics of their probability densities, which aregoverned by partial differential equations (PDEs), namely compressible Eulerequations subject to non-local forces. We formulate the inverse problem oflearning interactions as a PDE-constrained optimization problem of minimizingthe squared Hellinger distance between the histogram of the flock and thedistribution associated to our PDEs. The numerical methods used to efficientlysolve the PDE-constrained optimization problem are described. Realisticflocking data are simulated using the Boids model of flocking agents, whichdiffers in nature from the reconstruction models used in our PDEs. Our analysisand simulated experiments show that the behavior of cohesive flocks can berecovered accurately with approximate PDE solutions.

Learning Agent Interactions from Density Evolution in 3D Regions With Obstacles