A purely data-driven framework for prediction, optimization, and control of networked processes: application to networked SIS epidemic model
This provides a method for controlling complex networked processes like epidemics, though it appears incremental as it builds on existing operator-theoretic approaches.
The authors tackled the problem of identifying and controlling stochastic nonlinear dynamics in large-scale networks without prior knowledge of network structure, using a data-driven framework based on Koopman operator techniques. They achieved this by converting nonlinear programming into a convex optimization with fewer variables, enabling effective model predictive control.
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.