Systems and methods for determining states of flow of objects in a scene. The methods and systems include measuring states of the flow at observed sample points of the scene, wherein the scene contains a set of sample points having subsets of observed and unobserved sample points. Store in a memory an operator specifying time-varying dynamics of training states of flow of the objects in the scene. Estimate, using the operator and the measured states at the subset of observed sample points, the states of the flow of the objects at the subset of unobserved sample points of the scene. Output the states of the flow at the set of unobserved sample points of the scene, so as to assist in a management of managing states of flow of objects in the scene.