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Diffusion approximations are widely used in the analysis of service systems, providing tractable insights into complex models. While heavy-traffic limit theorems justify these approximations asymptotically, they do not quantify the error…

We propose a general framework for studying jump-diffusion systems driven by both Gaussian noise and a jump process with state-dependent intensity. Of particular natural interest are the jump locations: the system evaluated at the jump…

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…

Scene flow estimation is an essential ingredient for a variety of real-world applications, especially for autonomous agents, such as self-driving cars and robots. While recent scene flow estimation approaches achieve a reasonable accuracy,…

Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…

Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…

We consider a queueing network in which there are constraints on which queues may be served simultaneously; such networks may be used to model input-queued switches and wireless networks. The scheduling policy for such a network specifies…

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…

Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove,…

Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…

We present a generative AI algorithm for addressing the pressing task of fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on an end-to-end conditional…

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…

The tandem fluid queueing model is a useful tool for performance analysis and control design for a variety of transportation systems. In this article, we study the joint impact of stochastic capacity and spillback on the long-time…

A gaussian distribution of binding energies, but conditioned to exploit generally available information on packing in liquids, provides a statistical-thermodynamic theory of liquid water that is structurally non-committal, molecularly…

We introduce a novel deep learning approach that harnesses the power of generative artificial intelligence to enhance the accuracy of contextual forecasting in sewerage systems. By developing a diffusion-based model that processes…

We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…

We present a broad literature survey of parameter and state estimation for queueing systems. Our approach is based on various inference activities, queueing models, observations schemes, and statistical methods. We categorize these into…

We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…

In this paper, we present a stochastic queuing model for the road traffic, which captures the stationary density-flow relationships in both uncongested and congestion conditions. The proposed model is based on the $M/g/c/c$ state dependent…

In the setting of a recently developed cellular stochastic traffic flow model, it has shown that the joint per-cell vehicle densities, as a function of time, can be accurately approximated by a Gaussian process, which has the attractive…