Electrification can help to reduce the carbon footprint of aviation. The transition away from the jet fuel-powered conventional airplane towards battery-powered electrified aircraft will impose extra charging requirements on airports. In this paper, we first quantify the increase in energy demands at several airports across the United States (US), when commercial airline carriers partially deploy hybrid electric aircraft (HEA). We then illustrate that smart charging and minor modifications to flight schedules can substantially reduce peak power demands, and in turn the needs for grid infrastructure upgrade. Motivated by our data analysis, we then formulate an optimization problem for flight rescheduling that incorporates HEA charging considerations. This problem jointly decides flight schedules and charging profiles to manage airport congestion and peak power demands. We further consider mechanisms via which airlines and airports can negotiate HEA assignments using said optimization problem. Finally, we illustrate the efficacy of our formulation through a case study on the John F. Kennedy International Airport.

Conditional mean embedding (CME) operators encode conditional probability densities within Reproducing Kernel Hilbert Space (RKHS). In this paper, we present a decentralized algorithm for a collection of agents to cooperatively approximate CME over a network. Communication constraints limit the agents from sending all data to their neighbors; we only allow sparse representations of covariance operators to be exchanged among agents, compositions of which defines CME. Using a coherence-based compression scheme, we present a consensus-type algorithm that preserves the average of the approximations of the covariance operators across the network. We theoretically prove that the iterative dynamics in RKHS is stable. We then empirically study our algorithm to estimate CMEs to learn spectra of Koopman operators for Markovian dynamical systems and to execute approximate value iteration for Markov decision processes (MDPs).

Transfer operators provide a rich framework for representing the dynamics of very general, nonlinear dynamical systems. When interacting with reproducing kernel Hilbert spaces (RKHS), descriptions of dynamics often incur prohibitive data storage requirements, motivating dataset sparsification as a precursory step to computation. Further, in practice, data is available in the form of trajectories, introducing correlation between samples. In this work, we present a method for sparse learning of transfer operators from $\beta$-mixing stochastic processes, in both discrete and continuous time, and provide sample complexity analysis extending existing theoretical guarantees for learning from non-sparse, i.i.d. data. In addressing continuous-time settings, we develop precise descriptions using covariance-type operators for the infinitesimal generator that aids in the sample complexity analysis. We empirically illustrate the efficacy of our sparse embedding approach through deterministic and stochastic nonlinear system examples.