Renewable-based charging in green ride-sharing.

Governments, regulatory bodies, and manufacturers are proposing plans to accelerate the adoption of electric vehicles (EVs), with the goal of reducing the impact of greenhouse gases and pollutants from internal combustion engines on human health and climate change. In this context, the paper considers a scenario where ride-sharing enterprises utilize a 100%-electrified fleet of vehicles, and seeks responses to the following key question: How can renewable-based EV charging be maximized without disrupting the quality of the ride-sharing services? We propose a new mechanism to promote EV charging during hours of high renewable generation, and we introduce the concept of charge request, which is issued by a power utility company. Our mechanism is inspired by a game-theoretic approach where the power utility company proposes incentives and the ride-sharing platform assigns vehicles to both ride and charge requests; the bargaining mechanism leads to prices and EV assignments that are aligned with the notion of Nash equilibria. Numerical results show that it is possible to shift the EV charging during periods of high renewable generation and adapt to intermittent generation while minimizing the impact on the quality of service. The paper also investigates how the users' willingness to ride-share affects the charging strategy and the quality of service.

Novel use of online optimization in a mathematical model of COVID-19 to guide the relaxation of pandemic mitigation measures.

Since early 2020, non-pharmaceutical interventions (NPIs)-implemented at varying levels of severity and based on widely-divergent perspectives of risk tolerance-have been the primary means to control SARS-CoV-2 transmission. This paper aims to identify how risk tolerance and vaccination rates impact the rate at which a population can return to pre-pandemic contact behavior. To this end, we developed a novel mathematical model and we used techniques from feedback control to inform data-driven decision-making. We use this model to identify optimal levels of NPIs across geographical regions in order to guarantee that hospitalizations will not exceed given risk tolerance thresholds. Results are shown for the state of Colorado, United States, and they suggest that: coordination in decision-making across regions is essential to maintain the daily number of hospitalizations below the desired limits; increasing risk tolerance can decrease the number of days required to discontinue NPIs, at the cost of an increased number of deaths; and if vaccination uptake is less than 70%, at most levels of risk tolerance, return to pre-pandemic contact behaviors before the early months of 2022 may newly jeopardize the healthcare system. The sooner we can acquire population-level vaccination of greater than 70%, the sooner we can safely return to pre-pandemic behaviors.

Online Weak-form Sparse Identification of Partial Differential Equations.

This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in the sense that if performs the identification task by processing solution snapshots that arrive sequentially. The core of the method combines a weak-form discretization of candidate PDEs with an online proximal gradient descent approach to the sparse regression problem. In particular, we do not regularize the ℓ0-pseudo-norm, instead finding that directly applying its proximal operator (which corresponds to a hard thresholding) leads to efficient online system identification from noisy data. We demonstrate the success of the method on the Kuramoto-Sivashinsky equation, the nonlinear wave equation with time-varying wavespeed, and the linear wave equation, in one, two, and three spatial dimensions, respectively. In particular, our examples show that the method is capable of identifying and tracking systems with coefficients that vary abruptly in time, and offers a streaming alternative to problems in higher dimensions.