# Multi-Agent System Identification with Nonlinear Sheaf Diffusion

arXiv: https://arxiv.org/abs/2605.11204 · HTML: https://mlsanity.com/paper/2605.11204/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 14 of 14)

- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Sheaf Neural Networks](https://mlsanity.com/paper/2012.06333/) (2020)
- [Nonparametric inference of interaction laws in systems of agents from trajectory data](https://mlsanity.com/paper/1812.06003/) (2018)
- [Learning Mean-Field Equations from Particle Data Using WSINDy](https://mlsanity.com/paper/2110.07756/) (2021)
- [Learning interaction kernels in heterogeneous systems of agents from multiple trajectories](https://mlsanity.com/paper/1910.04832/) (2019)
- [Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back](https://mlsanity.com/paper/2303.11323/) (2023)
- [Physics Informed Topology Learning in Networks of Linear Dynamical Systems](https://mlsanity.com/paper/1809.10535/) (2018)
- [Network Inference from Consensus Dynamics with Unknown Parameters](https://mlsanity.com/paper/1908.01393/) (2019)
- [Distributed Multi-agent Coordination over Cellular Sheaves](https://mlsanity.com/paper/2504.02049/) (2025)
- [Learning the Structure of Connection Graphs](https://mlsanity.com/paper/2510.11245/) (2025)
- [Heterogeneous Multi-Agent Multi-Target Tracking using Cellular Sheaves](https://mlsanity.com/paper/2512.24886/) (2025)
- [Network Inference from Consensus Dynamics](https://mlsanity.com/paper/1708.05329/) (2017)
- [Asynchronous Nonlinear Sheaf Diffusion for Multi-Agent Coordination](https://mlsanity.com/paper/2510.00270/) (2025)
- [Learning Consistent Causal Abstraction Networks](https://mlsanity.com/paper/2602.02623/) (2026)

## Abstract (arXiv)

Local interaction laws governing multi-agent systems can be difficult to recover from trajectory data, even when the dynamics are observed faithfully. In systems governed by a nonlinear sheaf Laplacian -- a generalization of the graph Laplacian accommodating heterogeneous state spaces and asymmetric communication channels -- the coordination law is encoded by edge potential functions whose gradients produce the inter-agent forces. Because trajectory observations record node-state evolution, they expose only the aggregate effect of the edge forces at each node: distinct interaction laws that agree at the node level are indistinguishable from trajectory data alone. We show that the fundamental obstruction to recovery is topological, measured by sheaf cohomology, and that unique recovery from an unconstrained function class is possible if and only if this cohomology vanishes. When the obstruction is nontrivial, we show that recovery within a finite-dimensional parameterized class is possible precisely when a data-dependent information matrix is positive definite. Experiments validate the theory and illustrate that accurate trajectory reproduction need not certify recovery of the underlying interaction law.