# Learning Swarm Interaction Dynamics from Density Evolution

arXiv: https://arxiv.org/abs/2112.02675 · HTML: https://mlsanity.com/paper/2112.02675/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 44 references that are in the map.
- First posted on arXiv 5 Dec 2021.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Nonparametric inference of interaction laws in systems of agents from trajectory data](https://mlsanity.com/paper/1812.06003/) (2018)
- [Mean-Field Optimal Control](https://mlsanity.com/paper/1306.5913/) (2013)
- [Density control of large-scale particles swarm through PDE-constrained optimization](https://mlsanity.com/paper/2104.06373/) (2021)
- [Nonlocal flocking dynamics: Learning the fractional order of PDEs from particle simulations](https://mlsanity.com/paper/1810.11596/) (2018)
- [Semi-linear Poisson-mediated Flocking in a Cucker-Smale Model](https://mlsanity.com/paper/2102.08772/) (2021)

## Built on by (most cited first, 2 of 2)

- [Swarm Analytics: Designing Information Markers to Characterise Swarm Systems in Shepherding Contexts](https://mlsanity.com/paper/2208.12386/) (2022)
- [A Data-Adaptive Prior for Bayesian Learning of Kernels in Operators](https://mlsanity.com/paper/2212.14163/) (2022)

## Abstract (arXiv)

We consider the problem of understanding the coordinated movements of biological or artificial swarms. In this regard, we propose a learning scheme to estimate the coordination laws of the interacting agents from observations of the swarm's density over time. We describe the dynamics of the swarm based on pairwise interactions according to a Cucker-Smale flocking model, and express the swarm's density evolution as the solution to a system of mean-field hydrodynamic equations. We propose a new family of parametric functions to model the pairwise interactions, which allows for the mean-field macroscopic system of integro-differential equations to be efficiently solved as an augmented system of PDEs. Finally, we incorporate the augmented system in an iterative optimization scheme to learn the dynamics of the interacting agents from observations of the swarm's density evolution over time. The results of this work can offer an alternative approach to study how animal flocks coordinate, create new control schemes for large networked systems, and serve as a central part of defense mechanisms against adversarial drone attacks.