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Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
With an increasing high penetration of solar photovoltaic generation in electric power grids, voltage phasors and branch power flows experience more severe fluctuations. In this context, probabilistic power flow (PPF) study aims at…
In this study, the ducted propeller has been numerically investigated under oblique flow, which is crucial and challenging for the design and safe operation of thruster driven vessel and dynamic positioning (DP) system. A Reynolds-Averaged…
We propose a consistency model based on the optimal-transport flow. A physics-informed design of partially input-convex neural networks (PICNN) plays a central role in constructing the flow field that emulates the displacement…
Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty. However, tracking uncertainty for iterative, multi-step predictions in general leads to an analytically intractable…
We introduce a rigorous framework for stochastic cell transmission models for general traffic networks. The performance of traffic systems is evaluated based on preference functionals and acceptable designs. The numerical implementation…
The Direct Simulation Monte Carlo (DSMC) method is widely employed for simulating rarefied nonequilibrium gas flows. With advances in aerospace engineering and micro/nano-scale technologies, gas flows exhibit the coexistence of rarefied and…
Balancing safety and efficiency when planning in crowded scenarios with uncertain dynamics is challenging where it is imperative to accomplish the robot's mission without incurring any safety violations. Typically, chance constraints are…
Many state-of-the-art methods for safety assessment and motion planning for automated driving require estimation of the probability of collision (POC). To estimate the POC, a shape approximation of the colliding actors and probability…
In order to achieve a virtual certification process and robust designs for turbomachinery, the uncertainty bounds for Computational Fluid Dynamics have to be known. The formulation of turbulence closure models implies a major source of the…
Cascading failure of a power transmission system are initiated by an exogenous event that disable a set of elements (e.g., lines) followed by a sequence of interrelated failures (or more precisely, trips) of overloaded elements caused by…
In this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity $c(t)$ and changing direction at instants distributed…
Gliding offers small fixed-wing UAVs extended endurance and silent operation but requires accurate energy management, especially under wind disturbances and obstacle constraints. Traditional Total Energy Control Systems based controllers…
In this paper, we introduce a traffic flow model based on a microscopic follow-the-leader model, while enforcing maximal constraints on the density and velocity of the flow. The related macroscopic model can be represented in conservative…
We study probabilistic protocols for concurrent threshold-based load balancing in networks. There are n resources or machines represented by nodes in an undirected graph and m >> n users that try to find an acceptable resource by moving…
We provide attainable analytical tools to estimate the error of flow-based generative models under the Wasserstein metric and to establish the optimal sampling iteration complexity bound with respect to dimension as $O(\sqrt{d})$. We show…
In this paper, we present a novel cascade control structure with formal guarantees of uniform almost global asymptotic stability for the state tracking error dynamics of a quadcopter. The proposed approach features a model predictive…
In the context of dynamic emission tomography, the conventional processing pipeline consists of independent image reconstruction of single time frames, followed by the application of a suitable kinetic model to time activity curves (TACs)…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…