sheaf-laplacian-coordination

Sheaf Laplacian coordination models agent interactions as a cellular sheaf over a graph, then applies Laplacian diffusion to drive consensus. Build a CellularSheaf with stalks for each agent, define restriction maps per edge, and run diffusion dynamics to reach distributed agreement across your network.

Harmonic extension infers globally consistent assignments for missing or partial observations in a network by solving a harmonic condition on the sheaf. Use it when you have partial data from sensors or agents and need to reconstruct missing values while respecting the network's structural constraints.

Yes, cohomology detection identifies obstructions to global agreement by analyzing the sheaf structure. These obstructions reveal fundamental limitations preventing all agents from reaching consensus, helping you diagnose why coordination fails.

Sheaf neural networks learn restriction maps and diffusion layers directly from data using Catlab.jl. Define stalks as vector-valued representations per agent, parameterize restriction maps as learnable functions per edge, and train end-to-end on coordination or inference tasks.

You need to represent your multi-agent system as a directed or undirected graph with vector-valued stalks per node and define or learn restriction maps per edge. Catlab.jl must be available for constructing the cellular sheaf and Laplacian operators.

Yes, sheaf Laplacian coordination is designed for swarm robotics and sensor networks where agents have partial observations. It handles vector-valued state representations and distributed consensus across heterogeneous network topologies.