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Damped-driven systems are ubiquitous in engineering and science. Despite the diversity of physical processes observed in a broad range of applications, the underlying instabilities observed in practice have a universal characterization…
Linear stability of horizontal and inclined stratified channel flows of Newtonian/non-Newtonian shear-thinning fluids is investigated with respect to all wavelength perturbations. The Carreau model has been chosen for the modeling of the…
In this paper we consider Deep Neural Networks (DNNs) with a smooth activation function as surrogates for high-dimensional functions that are somewhat smooth but costly to evaluate. We consider the standard (non-periodic) DNNs as well as…
The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual based pore scale network modeling method…
In the consideration of steady-state flow of gas in pipeline networks, the exclusion of gravity and nonlinear inertial effects (convective acceleration) leads to a fortuitous simplification in the governing equations to yield a system of…
Infrastructure monitoring is critical for safe operations and sustainability. Water distribution networks (WDNs) are large-scale networked critical systems with complex cascade dynamics which are difficult to predict. Ubiquitous monitoring…
Optimal control theory extending from the calculus of variations has not been used to study the wind turbine power system (WTPS) control problem, which aims at achieving two targets: (i) maximizing power generation in lower wind speed…
An innovative \textit{deep learning} approach has been adopted to formulate the eddy-viscosity for large eddy simulation (LES) of wall-bounded turbulent flows. A deep neural network (DNN) is developed which learns to evaluate the…
We propose the Diffusion-Inversion-Net (DIN) framework for inverse modeling of groundwater flow and solute transport processes. DIN utilizes an offline-trained Denoising Diffusion Probabilistic Model (DDPM) as a powerful prior leaner, which…
We study convergence in networks of piecewise-smooth (PWS) systems that commonly arise in applications to model dynamical systems whose evolution is affected by macroscopic events such as switches and impacts. Existing approaches were…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Water distribution networks (WDNs) expand their service areas over time. These growth dynamics are poorly understood. One facet of WDNs is that they have loops in general, and closing loops may be a functionally important process for…
A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
Among many unsolved puzzles in theories of Deep Neural Networks (DNNs), there are three most fundamental challenges that highly demand solutions, namely, expressibility, optimisability, and generalisability. Although there have been…
Effective SDN control relies on the network data collecting capability as well as the quality and timeliness of the data. As open programmable data plane is becoming a reality, we further enhance it with the support of runtime interactive…
Software-Defined Networking (SDN) is an emerging paradigm that promises to change this state of affairs, by breaking vertical integration, separating the network's control logic from the underlying routers and switches, promoting (logical)…
As it stands, a robust mathematical framework to analyse and study various topics in deep learning is yet to come to the fore. Nonetheless, viewing deep learning as a dynamical system allows the use of established theories to investigate…
Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge due to the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward…
This paper considers the network flow stabilization problem in power systems and adopts an output regulation viewpoint. Building upon the structure of a heterogeneous port-Hamiltonian model, we integrate network aspects and develop a…