arXiv subjects

Baike She

Publications and source records attributed to Baike She.

15 recordsLinked to original sources

arXiv2025

A Physics-Informed Neural Networks-Based Model Predictive Control Framework for $SIR$ Epidemics

This work introduces a physics-informed neural networks (PINNs)-based model predictive control (MPC) framework for susceptible-infected-recovered ($SIR$) spreading models. Existing studies in MPC design for epidemic control often assume either 1) measurable states of the dynamics, where the parameters are learned, or 2) known parameters of the model, where the states are learned. In this work, we address the joint real-time estimation of states and parameters within the MPC framework using only noisy infected states, under the assumption that 1) only the recovery rate is known, or 2) only the basic reproduction number is known. Under the first assumption, we propose MPC-PINNs and two novel PINNs algorithms, all of which are integrated into the MPC framework. First, we introduce MPC-PINNs, which are designed for $SIR$ models with control. We then propose log-scaled PINNs (MPC-LS-PINNs), which incorporate a log-scaled loss function to improve robustness against noise. Next, we present split-integral PINNs (MPC-SI-PINNs), which leverage integral operators and state coupling in the neural network training process to effectively reconstruct the complete epidemic state information. Building upon these methods, we further extend our framework for the second assumption. We establish the necessary conditions and extend our PINNs algorithms, where MPC-SI-PINNs are simplified as split-PINNs (MPC-S-PINNs). By incorporating these algorithms into the MPC framework, we simultaneously estimate the epidemic states and parameters while generating optimal control strategies. Experiment results demonstrate the effectiveness of the proposed methods under different settings.

cs.LG↗

arXiv2025

Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Data

The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system trajectory under i.i.d. random inputs, and assumes that the underlying dynamics is truly linear. In contrast, we consider the problem of identifying a linearized model when the true underlying dynamics is nonlinear, given that there is a certain constraint on the region where one can initialize the experiments. We provide a multiple trajectories-based deterministic data acquisition algorithm followed by a regularized least squares algorithm, and provide a finite sample error bound on the learned linearized dynamics. Our error bound shows that one can consistently learn the linearized dynamics, and demonstrates a trade-off between the error due to nonlinearity and the error due to noise. We validate our results through numerical experiments, where we also show the potential insufficiency of linear system identification using a single trajectory with i.i.d. random inputs, when nonlinearity does exist.

stat.ML↗

arXiv2025

Scalable Distributed Reproduction Numbers of Network Epidemics with Differential Privacy

Reproduction numbers are widely used for the estimation and prediction of epidemic spreading processes over networks. However, conventional reproduction numbers of an overall network do not indicate where an epidemic is spreading. Therefore, we propose a novel notion of local distributed reproduction numbers to capture the spreading behaviors of each node in a network. We first show how to compute them and then use them to derive new conditions under which an outbreak can occur. These conditions are then used to derive new conditions for the existence, uniqueness, and stability of equilibrium states of the underlying epidemic model. Building upon these local distributed reproduction numbers, we define cluster distributed reproduction numbers to model the spread between clusters composed of nodes. Furthermore, we demonstrate that the local distributed reproduction numbers can be aggregated into cluster distributed reproduction numbers at different scales. However, both local and cluster distributed reproduction numbers can reveal the frequency of interactions between nodes in a network, which raises privacy concerns. Thus, we next develop a privacy framework that implements a differential privacy mechanism to provably protect the frequency of interactions between nodes when computing distributed reproduction numbers. Numerical experiments show that, even under differential privacy, the distributed reproduction numbers provide accurate estimates of the epidemic spread while also providing more insights than conventional reproduction numbers.

eess.SY↗

arXiv2024

A Dissipativity Approach to Analyzing Composite Spreading Networks

The study of spreading processes often analyzes networks at different resolutions, e.g., at the level of individuals or countries, but it is not always clear how properties at one resolution can carry over to another. Accordingly, in this work we use dissipativity theory from control system analysis to characterize composite spreading networks that are comprised by many interacting subnetworks. We first develop a method to represent spreading networks that have inputs and outputs. Then we define a composition operation for composing multiple spreading networks into a larger composite spreading network. Next, we develop storage and supply rate functions that can be used to demonstrate that spreading dynamics are dissipative. We then derive conditions under which a composite spreading network will converge to a disease-free equilibrium as long as its constituent spreading networks are dissipative with respect to those storage and supply rate functions. To illustrate these results, we use simulations of an influenza outbreak in a primary school, and we show that an outbreak can be prevented by decreasing the average interaction time between any pair of classes to less than 79% of the original interaction time.

physics.soc-ph↗

arXiv2024

Control of SIR Epidemics: Sacrificing Optimality for Feasibility

We study the impact of parameter estimation and state measurement errors on a control framework for optimally mitigating the spread of epidemics. We capture the epidemic spreading process using a susceptible-infected-removed (SIR) epidemic model and consider isolation as the control strategy. We use a control strategy to remove (isolate) a portion of the infected population. Our goal is to maintain the daily infected population below a certain level, while minimizing the resource captured by the isolation rate. Distinct from existing works on leveraging control strategies in epidemic spreading, we propose a parameter estimation strategy and further characterize the parameter estimation error bound. In order to deal with uncertainties, we propose a robust control strategy by overestimating the seriousness of the epidemic and study the feasibility of the system. Compared to the optimal control strategy, we establish that the proposed strategy under parameter estimation and measurement errors will sacrifice optimality to flatten the curve.

eess.SY↗

arXiv2023

Modeling Epidemic Spread: A Gaussian Process Regression Approach

Modeling epidemic spread is critical for informing policy decisions aimed at mitigation. Accordingly, in this work we present a new data-driven method based on Gaussian process regression (GPR) to model epidemic spread through the difference on the logarithmic scale of the infected cases. We bound the variance of the predictions made by GPR, which quantifies the impact of epidemic data on the proposed model. Next, we derive a high-probability error bound on the prediction error in terms of the distance between the training points and a testing point, the posterior variance, and the level of change in the spreading process, and we assess how the characteristics of the epidemic spread and infection data influence this error bound. We present examples that use GPR to model and predict epidemic spread by using real-world infection data gathered in the UK during the COVID-19 epidemic. These examples illustrate that, under typical conditions, the prediction for the next twenty days has 94.29% of the noisy data located within the 95% confidence interval, validating these predictions. We further compare the modeling and prediction results with other methods, such as polynomial regression, k-nearest neighbors (KNN) regression, and neural networks, to demonstrate the benefits of leveraging GPR in disease spread modeling.

stat.ML↗

arXiv2023

Reverse Engineering the Reproduction Number: A Framework for Data-Driven Counterfactual Analysis, Strategy Evaluation, and Feedback Control of Epidemics

During the COVID-19 pandemic, different countries, regions, and communities constructed various epidemic models to evaluate spreading behaviors and assist in making mitigation policies. Model uncertainties, introduced by complex transmission behaviors, contact-tracing networks, time-varying spreading parameters, and human factors, as well as insufficient data, have posed arduous challenges for model-based approaches. To address these challenges, we propose a novel framework for data-driven counterfactual analysis, strategy evaluation, and feedback control of epidemics, which leverages statistical information from epidemic testing data instead of constructing a specific model. Through reverse engineering the reproduction number by quantifying the impact of the intervention strategy, this framework tackles three primary problems: 1) How severe would an outbreak have been without the implemented intervention strategies? 2) What impact would varying the intervention strength have had on an outbreak? 3) How can we adjust the intervention intensity based on the current state of an outbreak? Specifically, we consider the epidemic intervention policies such as the testing-for-isolation strategy as an example, which was successfully implemented by the University of Illinois Urbana-Champaign (UIUC) and Purdue University (Purdue) during the COVID-19 pandemic. By leveraging data collected by UIUC and Purdue, we validate the effectiveness of the proposed data-driven framework.

physics.soc-ph↗

arXiv2023

Differentially Private Computation of Basic Reproduction Numbers in Networked Epidemic Models

The basic reproduction number of a networked epidemic model, denoted $R_0$, can be computed from a network's topology to quantify epidemic spread. However, disclosure of $R_0$ risks revealing sensitive information about the underlying network, such as an individual's relationships within a social network. Therefore, we propose a framework to compute and release $R_0$ in a differentially private way. First, we provide a new result that shows how $R_0$ can be used to bound the level of penetration of an epidemic within a single community as a motivation for the need of privacy, which may also be of independent interest. We next develop a privacy mechanism to formally safeguard the edge weights in the underlying network when computing $R_0$. Then we formalize tradeoffs between the level of privacy and the accuracy of values of the privatized $R_0$. To show the utility of the private $R_0$ in practice, we use it to bound this level of penetration under privacy, and concentration bounds on these analyses show they remain accurate with privacy implemented. We apply our results to real travel data gathered during the spread of COVID-19, and we show that, under real-world conditions, we can compute $R_0$ in a differentially private way while incurring errors as low as $7.6\%$ on average.

cs.SI↗

arXiv2023

Modeling Model Predictive Control: A Category Theoretic Framework for Multistage Control Problems

Model predictive control (MPC) is an optimal control technique which involves solving a sequence of constrained optimization problems across a given time horizon. In this paper, we introduce a category theoretic framework for constructing complex MPC problem formulations by composing subproblems. Specifically, we construct a monoidal category - called Para(Conv) - whose objects are Euclidean spaces and whose morphisms represent constrained convex optimization problems. We then show that the multistage structure of typical MPC problems arises from sequential composition in Para(Conv), while parallel composition can be used to model constraints across multiple stages of the prediction horizon. This framework comes equipped with a rigorous, diagrammatic syntax, allowing for easy visualization and modification of complex problems. Finally, we show how this framework allows a simple software realization in the Julia programming language by integrating with existing mathematical programming libraries to provide high-level, graphical abstractions for MPC.

math.OC↗

arXiv2023

Characterizing Compositionality of LQR from the Categorical Perspective

Composing systems is a fundamental concept in modern control systems, yet it remains challenging to formally analyze how controllers designed for individual subsystems can differ from controllers designed for the composition of those subsystems. To address this challenge, we propose a novel approach to composing control systems based on resource sharing machines, a concept from applied category theory. We use resource sharing machines to investigate the differences between (i) the linear-quadratic regulator (LQR) designed directly for a composite system and (ii) the LQR that is attained through the composition of LQRs designed for each subsystem. We first establish novel formalisms to compose LQR control designs using resource sharing machines. Then we develop new sufficient conditions to guarantee that the LQR designed for a composite system is equal to the LQR attained through composition of LQRs for its subsystems. In addition, we reduce the developed condition to that of checking the controllability and observability of a certain linear, time-invariant system, which provides a simple, computationally efficient procedure for evaluating the equivalence of controllers for composed systems.

eess.SY↗

arXiv2023

Leveraging Opinions and Vaccination to Eradicate Networked Epidemics

We introduce a multi-layer networked compartmental $SIRS-V_o$ model that captures opinion dynamics, disease spread, risk perception, and self-interest vaccine-uptake behavior in an epidemic process. We characterize the target vaccination criterion of the proposed model and conditions that guarantee the criterion is obtainable by influencing opinions on disease prevalence. We leverage this result to design an eradication strategy that leverages opinions and vaccination. Through numerical simulations, we show that the proposed eradication strategy is able to stabilize the epidemic process around a healthy state equilibrium, and the outbreak rebounds after the control signal is relaxed.

physics.soc-ph↗

arXiv2023

Distributed Reproduction Numbers of Networked Epidemics

Reproduction numbers are widely used for the estimation and prediction of epidemic spreading processes over networks. However, reproduction numbers do not enable estimation and prediction in individual communities within networks, and they can be difficult to compute due to the aggregation of infection data that is required to do so. Therefore, in this work we propose a novel concept of distributed reproduction numbers to capture the spreading behaviors of each entity in the network, and we show how to compute them using certain parameters in networked SIS and SIR epidemic models. We use distributed reproduction numbers to derive new conditions under which an outbreak can occur. These conditions are then used to derive new conditions for the existence, uniqueness, and stability of equilibrium states. Finally, in simulation we use synthetic infection data to illustrate how distributed reproduction numbers provide more fine-grained analyses of networked spreading processes than ordinary reproduction numbers.

eess.SY↗

arXiv2022

Optimal Mitigation of SIR Epidemics Under Model Uncertainty

We study the impact of model parameter uncertainty on optimally mitigating the spread of epidemics. We capture the epidemic spreading process using a susceptible-infected-removed (SIR) epidemic model and consider testing for isolation as the control strategy. We use a testing strategy to remove (isolate) a portion of the infected population. Our goal is to maintain the daily infected population below a certain level, while minimizing the total number of tests. Distinct from existing works on leveraging control strategies in epidemic spreading, we propose a testing strategy by overestimating the seriousness of the epidemic and study the feasibility of the system under the impact of model parameter uncertainty. Compared to the optimal testing strategy, we establish that the proposed strategy under model parameter uncertainty will flatten the curve effectively but require more tests and a longer time period.

eess.SY↗

arXiv2021

Peak Infection Time for a Networked SIR Epidemic with Opinion Dynamics

We propose an SIR epidemic model coupled with opinion dynamics to study an epidemic and opinions spreading in a network of communities. Our model couples networked SIR epidemic dynamics with opinions towards the severity of the epidemic, and vice versa. We develop an epidemic-opinion based threshold condition to capture the moment when a weighted average of the epidemic states starts to decrease exponentially fast over the network, namely the peak infection time. We define an effective reproduction number to characterize the behavior of the model through the peak infection time. We use both analytical and simulation-based results to illustrate that the opinions reflect the recovered levels within the communities after the epidemic dies out.

eess.SY↗

arXiv2021

On a Network SIS Epidemic Model with Cooperative and Antagonistic Opinion Dynamics

We propose a mathematical model to study coupled epidemic and opinion dynamics in a network of communities. Our model captures SIS epidemic dynamics whose evolution is dependent on the opinions of the communities toward the epidemic, and vice versa. In particular, we allow both cooperative and antagonistic interactions, representing similar and opposing perspectives on the severity of the epidemic, respectively. We propose an Opinion-Dependent Reproduction Number to characterize the mutual influence between epidemic spreading and opinion dissemination over the networks. Through stability analysis of the equilibria, we explore the impact of opinions on both epidemic outbreak and eradication, characterized by bounds on the Opinion-Dependent Reproduction Number. We also show how to eradicate epidemics by reshaping the opinions, offering researchers an approach for designing control strategies to reach target audiences to ensure effective epidemic suppression.

eess.SY↗