Koopman operator based identification of nonlinear networks

TL;DR

This paper introduces a Koopman operator-based method for identifying nonlinear network dynamics, capable of determining network structure and local node behaviors efficiently, especially in large sparse networks.

Contribution

The paper presents a novel two-step Koopman-based approach for complete network identification, including neighbor detection and local dynamics estimation, with reduced data requirements under sparsity.

Findings

Effective identification of network structure demonstrated on examples

Requires less data than traditional methods for sparse networks

Accurately estimates local dynamics and interactions

Abstract

In this work, we develop a method to identify continuous-time nonlinear networked dynamics via the Koopman operator framework. The proposed technique consists of two steps: the first step identifies the neighbors of each node, and the second step identifies the local dynamics at each node from a predefined set of dictionary functions. The technique can be used to either identify the Boolean network of interactions (first step) or to solve the complete network identification problem that amounts to estimating the local node dynamics and the nature of the node interactions (first and second steps). Under a sparsity assumption, the data required to identify the complete network dynamics is significantly less than the total number of dictionary functions describing the dynamics. This makes the proposed approach attractive for identifying large dimensional networks with sparse interconnections. The accuracy and performance of the proposed identification technique are demonstrated with several examples.