Neural Persistence Dynamics
Keywords: Persistent Homology, Multi-Time Attention, Latent ODE, Collective Behavior, Physical Sciences
TL;DR: We consider the problem of learning the dynamics in the topology of time-evolving point clouds, observed in systems that exhibit collective behavior such as swarms of birds, insects, or fish.
Abstract: 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. We implement this idea based on a latent ODE learned from vectorized (static) persistence diagrams and show that a combination of recent stability results for persistent homology justifies this modeling choice. Various (ablation) experiments not only demonstrate the relevance of each model component but provide compelling empirical evidence that our proposed model -- _Neural Persistence Dynamics_ -- substantially outperforms the state-of-the-art across a diverse set of parameter regression tasks.
Supplementary Material: zip
Primary Area: Machine learning for physical sciences (for example: climate, physics)
Submission Number: 19386
Loading