Neural Persistence Dynamics

We consider the problem of learning the dynamics in the topology of time-evolving point clouds, the prevalent spatiotemporal model for systems exhibiting collective behavior, such as swarms of insects and birds or particles in physics. In such systems, patterns emerge from (local) interactions among self-propelled entities. While several well-understood governing equations for motion and interaction exist, they are notoriously difficult to fit to data, as most prior work requires knowledge about individual motion trajectories, i.e., a requirement that is challenging to satisfy with an increasing number of entities. To evade such confounding factors, we investigate collective behavior from a topological perspective, but instead of summarizing entire observation sequences (as done previously), we propose learning a latent dynamical model from topological features per time point. The latter is then used to formulate a downstream regression task to predict the parametrization of some a priori specified governing equation.