Identifying the dynamics of interacting objects with applications to scene understanding and video temporal manipulation.

There is an ongoing effort in the machine learning community to enable machines to understand the world symbolically, facilitating human interaction with learned representations of complex scenes. A pre-requisite to achieving this is the ability to identify the dynamics of interacting objects from time traces of relevant features. In this paper, we introduce GrODID (GRaph-based Object-Centric Dynamic Mode Decomposition), a framework based on graph neural networks that enables Dynamic Mode Decomposition for systems involving interacting objects. The main idea is to model individual, potentially non-linear dynamics using a Koopman operator and identify its corresponding Dynamic Mode Decomposition using deep AutoEncoders, while the interactions amongst systems are captured by a graph, modeled by a Graph Neural Net (GNN). The potential of this approach is illustrated with several applications arising in the context of video analytics: video forward and backwards prediction, video manipulation and achieving temporal super-resolution.