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The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows.…
We study growing open Jackson networks where each station is a single-server queue that follows the first-come first-served discipline with Poisson arrivals and exponentially distributed service times, characterized by node-specific rates.…
Turbulent flows are chaotic and unsteady, but their statistical distribution converges to a statistical steady state. Engineering quantities of interest typically take the form of time-average statistics such as $ \frac{1}{t} \int_0^t f (…
The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop-on-demand (DoD)…
A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
The class of nonlinear Markov processes is characterized by the dependence of the current state of the process on its current distribution in addition to the dependence on the previous state. Due to this feature, these processes are…
Estimating the transition dynamics of controlled Markov chains is crucial in fields such as time series analysis, reinforcement learning, and system exploration. Traditional non-parametric density estimation methods often assume independent…
Dynamic wetting processes inherently manifest as multiscale phenomena. While the capillary length is typically millimeters, solid-liquid interactions occur at the nanometer scale. These short-range interactions significantly affect…
Ordinary Differential Equations (ODE) based models have become popular as foundation models for solving many time series problems. Combining neural ODEs with traditional RNN models has provided the best representation for irregular time…
In this paper, we propose a data-based methodology to solve a multi-period stochastic optimal water flow (OWF) problem for water distribution networks (WDNs). The framework explicitly considers the pump schedule and water network head level…
One of the key performance measures in queueing systems is the exponential decay rate of the steady-state tail probabilities of the queue lengths. It is known that if a corresponding fluid model is stable and the stochastic primitives have…
Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation…
We study the stability of the Kolmogorov flows which are stationary solutions to the two-dimensional Navier-Stokes equations in the presence of the shear external force. We establish the linear stability estimate when the viscosity…
We introduce a unified framework to estimate the convergence of Markov chains to equilibrium in Wasserstein distance. The framework can provide convergence bounds with rates ranging from polynomial to exponential, all derived from a…
For over 30 years, mode-coupling theory (MCT) has been the de facto theoretic description of dense fluids and the liquid-glass transition. MCT, however, is limited by its ad hoc construction and lacks a mechanism to institute corrections.…
Historically, traffic modelling approaches have taken either a particle-like (microscopic) approach, or a gas-like (meso- or macroscopic) approach. Until recently with the introduction of mean-field games to the controls community, there…
We propose in this paper a new nonlinear mathematical model of an oscillating water column (OWC). The one-dimensional shallow water equations in the presence of this device is reformulated as a transmission problem related to the…
We present an alternative view for the study of optimal control of partially observed Markov Decision Processes (POMDPs). We first revisit the traditional (and by now standard) separated-design method of reducing the problem to fully…
Much recent interest has focused on the design of optimization algorithms from the discretization of an associated optimization flow, i.e., a system of differential equations (ODEs) whose trajectories solve an associated optimization…