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

arXiv: https://arxiv.org/abs/2108.02005 · HTML: https://mlsanity.com/paper/2108.02005/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 86 references that are in the map.
- First posted on arXiv 1 Aug 2021.

## Builds on (most cited first, 26 of 26)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [Data-driven discovery of Koopman eigenfunctions for control](https://mlsanity.com/paper/1707.01146/) (2017)
- [Generalizing Koopman Theory to allow for inputs and control](https://mlsanity.com/paper/1602.07647/) (2016)
- [Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability](https://mlsanity.com/paper/1906.03663/) (2019)
- [Variational approach for learning Markov processes from time series data](https://mlsanity.com/paper/1707.04659/) (2017)
- [Optimal construction of Koopman eigenfunctions for prediction and control](https://mlsanity.com/paper/1810.08733/) (2018)
- [Active Learning of Dynamics for Data-Driven Control Using Koopman Operators](https://mlsanity.com/paper/1906.05194/) (2019)
- [Koopman operator-based model reduction for switched-system control of PDEs](https://mlsanity.com/paper/1710.06759/) (2017)
- [Koopman-based lifting techniques for nonlinear systems identification](https://mlsanity.com/paper/1709.02003/) (2017)
- [Analysis and Control of Epidemics: A survey of spreading processes on complex networks](https://mlsanity.com/paper/1505.00768/) (2015)
- [Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables](https://mlsanity.com/paper/1808.10551/) (2018)
- [Optimal resource allocation for competitive spreading processes on bilayer networks](https://mlsanity.com/paper/1512.05299/) (2015)
- [Optimal Resource Allocation for Network Protection Against Spreading Processes](https://mlsanity.com/paper/1309.6270/) (2013)
- [Power grid transient stabilization using Koopman model predictive control](https://mlsanity.com/paper/1803.10744/) (2018)
- [An Optimal Control Formulation of Pulse-Based Control Using Koopman Operator](https://mlsanity.com/paper/1707.08462/) (2017)
- [Model Reduction Methods for Complex Network Systems](https://mlsanity.com/paper/2012.02268/) (2020)
- [Optimal Patching in Clustered Malware Epidemics](https://mlsanity.com/paper/1403.1639/) (2014)
- [Robust Economic Model Predictive Control of Continuous-time Epidemic Processes](https://mlsanity.com/paper/1707.00742/) (2017)
- [Campaigning in Heterogeneous Social Networks: Optimal Control of SI Information Epidemics](https://mlsanity.com/paper/1512.07966/) (2015)
- [GEMFsim: A Stochastic Simulator for the Generalized Epidemic Modeling Framework](https://mlsanity.com/paper/1604.02175/) (2016)
- [Koopman Mode Decomposition of Oscillatory Temperature Field inside a Room](https://mlsanity.com/paper/2008.12149/) (2020)

## Built on by (most cited first, 1 of 1)

- [An Interpretable Approach to Load Profile Forecasting in Power Grids using Galerkin-Approximated Koopman Pseudospectra](https://mlsanity.com/paper/2304.07832/) (2023)

## Abstract (arXiv)

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.