Baike She

Aiping Zhong, Baike She, Philip E. Paré

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.

Lei Xin, Baike She, Qi Dou et al.

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.