A purely data-driven framework for prediction, optimization, and control of networked processes: application to networked SIS epidemic model

TL;DR

This paper introduces a data-driven framework using Koopman operator theory to identify and control stochastic nonlinear dynamics in large-scale networks without prior structural knowledge, enabling efficient model predictive control.

Contribution

It develops a novel operator-theoretic approach that leverages two-step snapshot data to identify dynamics and control large networked systems through convex optimization.

Findings

Successfully identifies underlying network dynamics from data

Enables control of complex network processes via convex optimization

Applies to large-scale networked epidemic models

Abstract

Networks are landmarks of many complex phenomena where interweaving interactions between different agents transform simple local rule-sets into nonlinear emergent behaviors. While some recent studies unveil associations between the network structure and the underlying dynamical process, identifying stochastic nonlinear dynamical processes continues to be an outstanding problem. Here we develop a simple data-driven framework based on operator-theoretic techniques to identify and control stochastic nonlinear dynamics taking place over large-scale networks. The proposed approach requires no prior knowledge of the network structure and identifies the underlying dynamics solely using a collection of two-step snapshots of the states. This data-driven system identification is achieved by using the Koopman operator to find a low dimensional representation of the dynamical patterns that evolve linearly. Further, we use the global linear Koopman model to solve critical control problems by applying to model predictive control (MPC)--typically, a challenging proposition when applied to large networks. We show that our proposed approach tackles this by converting the original nonlinear programming into a more tractable optimization problem that is both convex and with far fewer variables.