A Model of Flocking Using Sheaves

Joseph Geisz
Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:313-337, 2026.

Abstract

Sheaves have been used recently to model information on networks, such as the spread of opinions in a social network. Dynamical systems on networks model the evolving states of nodes on graphs. Using these lenses of sheaf theory and network dynamics, we explore a model of flocking. We describe from this perspective what it means for birds to come to consensus on flight velocities, and a system of ordinary differential equations (ODEs) that describes this consensus process. Then we couple these consensus dynamics with flight dynamics to describe a model of flocking. We include numerous visualizations of examples in 2 dimensions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v321-geisz26a, title = {A Model of Flocking Using Sheaves}, author = {Geisz, Joseph}, booktitle = {Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025)}, pages = {313--337}, year = {2026}, editor = {Bernardez Gil, Guillermo and Black, Mitchell and Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Garcı́a-Rodondo, Ińes and Holtz, Chester and Kotak, Mit and Kvinge, Henry and Mishne, Gal and Papillon, Mathilde and Pouplin, Alison and Rainey, Katie and Rieck, Bastian and Telyatnikov, Lev and Yeats, Eric and Wang, Qingsong and Wang, Yusu and Wayland, Jeremy}, volume = {321}, series = {Proceedings of Machine Learning Research}, month = {01--02 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v321/main/assets/geisz26a/geisz26a.pdf}, url = {https://proceedings.mlr.press/v321/geisz26a.html}, abstract = {Sheaves have been used recently to model information on networks, such as the spread of opinions in a social network. Dynamical systems on networks model the evolving states of nodes on graphs. Using these lenses of sheaf theory and network dynamics, we explore a model of flocking. We describe from this perspective what it means for birds to come to consensus on flight velocities, and a system of ordinary differential equations (ODEs) that describes this consensus process. Then we couple these consensus dynamics with flight dynamics to describe a model of flocking. We include numerous visualizations of examples in 2 dimensions.} }
Endnote
%0 Conference Paper %T A Model of Flocking Using Sheaves %A Joseph Geisz %B Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025) %C Proceedings of Machine Learning Research %D 2026 %E Guillermo Bernardez Gil %E Mitchell Black %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Ińes Garcı́a-Rodondo %E Chester Holtz %E Mit Kotak %E Henry Kvinge %E Gal Mishne %E Mathilde Papillon %E Alison Pouplin %E Katie Rainey %E Bastian Rieck %E Lev Telyatnikov %E Eric Yeats %E Qingsong Wang %E Yusu Wang %E Jeremy Wayland %F pmlr-v321-geisz26a %I PMLR %P 313--337 %U https://proceedings.mlr.press/v321/geisz26a.html %V 321 %X Sheaves have been used recently to model information on networks, such as the spread of opinions in a social network. Dynamical systems on networks model the evolving states of nodes on graphs. Using these lenses of sheaf theory and network dynamics, we explore a model of flocking. We describe from this perspective what it means for birds to come to consensus on flight velocities, and a system of ordinary differential equations (ODEs) that describes this consensus process. Then we couple these consensus dynamics with flight dynamics to describe a model of flocking. We include numerous visualizations of examples in 2 dimensions.
APA
Geisz, J.. (2026). A Model of Flocking Using Sheaves. Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), in Proceedings of Machine Learning Research 321:313-337 Available from https://proceedings.mlr.press/v321/geisz26a.html.

Related Material