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

2021/08/01 by Ali Tavasoli, Tavasoli, Ali, Teague R. Henry +4
Computer Science · Decision Sciences · Engineering · Mathematics · Physics and Astronomy · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Social and Information Networks (cs.SI) #Systems and Control (eess.SY) #cs.AI #cs.LG #cs.SI #cs.SY #eess.SY #electronic engineering #information engineering #math.OC

paper · pdf · doi:10.48550/arxiv.2108.02005

arxiv created 2021/08/01 · openalex publication_date 2021/08/01 · arxiv updated 2021/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Spectral Properties of Dynamical Systems, Model Reduction and Decompositions
• Spectral analysis of nonlinear flows
• Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
• Extended dynamic mode decomposition with dictionary learning: a data-driven adaptive spectral decomposition of the Koopman operator
• Variational Approach for Learning Markov Processes from Time Series Data
• Modern Koopman Theory for Dynamical Systems
• Physics-informed machine learning

Related

• Unraveling Low-Dimensional Network Dynamics: A Fusion of Sparse Identification and Proper Orthogonal Decomposition
• Modeling epidemics on adaptively evolving networks: a data-mining perspective
• A machine learning approach to predicting dynamical observables from network structure
• Koopman operator based identification of nonlinear networks
• Inference, Prediction, and Control of Networked Epidemics