arXiv subjects

Mehdi Dehghan

Publications and source records attributed to Mehdi Dehghan.

17 recordsLinked to original sources

arXiv2025

Mixed FEM for coupled unsteady fluid flow problems with $p$-type Brinkman-Forchheimer framework and its application for reverse-osmosis desalination

This work analyzes a fully discrete mixed finite element method in a Banach space framework for solving nonstationary coupled fluid flow problems modeled by the Brinkman-Forchheimer equations, with applications to reverse osmosis. The model couples unsteady $p$-type convective Brinkman-Forchheimer and transport equations with nonlinear boundary conditions across a semi-permeable membrane. A mixed formulation is used for the fluid equation (pseudostress-velocity) and for the transport equation (concentration, its gradient, and a Lagrange multiplier from the membrane condition). The continuous problem is reformulated in Banach spaces as a fixed-point problem, enabling a well-posedness analysis via differential-algebraic system theory. Spatial discretization employs lowest-order Raviart-Thomas elements for fluxes and piecewise constants for primal variables, while linear elements are used for the Lagrange multiplier. A fully discrete Galerkin scheme with backward Euler time-stepping is proposed. Its well-posedness and stability are proven using a fixed-point argument, and optimal convergence rates are established. Numerical results confirm the theoretical error estimates and demonstrate the method's effectiveness.

math.NA↗

arXiv2024

Analysis of weak Galerkin mixed FEM based on the velocity--pseudostress formulation for Navier--Stokes equation on polygonal meshes

The present article introduces, mathematically analyzes, and numerically validates a new weak Galerkin (WG) mixed-FEM based on Banach spaces for the stationary Navier--Stokes equation in pseudostress-velocity formulation. More precisely, a modified pseudostress tensor, called $ \boldsymbolσ $, depending on the pressure, and the diffusive and convective terms has been introduced in the proposed technique, and a dual-mixed variational formulation has been derived where the aforementioned pseudostress tensor and the velocity, are the main unknowns of the system, whereas the pressure is computed via a post-processing formula. Thus, it is sufficient to provide a WG space for the tensor variable and a space of piecewise polynomial vectors of total degree at most 'k' for the velocity. Moreover, in order to define the weak discrete bilinear form, whose continuous version involves the classical divergence operator, the weak divergence operator as a well-known alternative for the classical divergence operator in a suitable discrete subspace is proposed. The well-posedness of the numerical solution is proven using a fixed-point approach and the discrete versions of the Babuška-Brezzi theory and the Banach-Nečas-Babuška theorem. Additionally, an a priori error estimate is derived for the proposed method. Finally, several numerical results illustrating the method's good performance and confirming the theoretical rates of convergence are presented.

math.NA↗

arXiv2023

The sine and cosine diffusive representations for the Caputo fractional derivative

As we are aware, various types of methods have been proposed to approximate the Caputo fractional derivative numerically. A common challenge of the methods is the non-local property of the Caputo fractional derivative which leads to the slow and memory consuming methods. Diffusive representation of fractional derivative is an efficient tool to overcome the mentioned challenge. This paper presents two new diffusive representations to approximate the Caputo fractional derivative of order $0<α<1$. Error analysis of the newly presented methods together with some numerical examples are provided at the end.

math.NA↗

arXiv2022

Optimal error estimates of coupled and divergence-free virtual element methods for the Poisson--Nernst--Planck/Navier--Stokes equations

In this article, we propose and analyze a fully coupled, nonlinear, and energy-stable virtual element method (VEM) for solving the coupled Poisson-Nernst-Planck (PNP) and Navier--Stokes (NS) equations modeling microfluidic and electrochemical systems (diffuse transport of charged species within incompressible fluids coupled through electrostatic forces). A mixed VEM is employed to discretize the NS equations whereas classical VEM in primal form is used to discretize the PNP equations. The stability, existence and uniqueness of solution of the associated VEM are proved by fixed point theory. Global mass conservation and electric energy decay of the scheme are also proved. Also, we obtain unconditionally optimal error estimates for both the electrostatic potential and ionic concentrations of PNP equations in the $H^{1}$-norm, as well as for the velocity and pressure of NS equations in the $\mathbf{H}^{1}$- and $L^{2}$-norms, respectively. Finally, several numerical experiments are presented to support the theoretical analysis of convergence and to illustrate the satisfactory performance of the method in simulating the onset of electrokinetic instabilities in ionic fluids, and studying how they are influenced by different values of ion concentration and applied voltage. These tests relate to applications in the desalination of water.

math.NA↗

arXiv2020

Deep Neural Review Text Interaction for Recommendation Systems

Users' reviews contain valuable information which are not taken into account in most recommender systems. According to the latest studies in this field, using review texts could not only improve the performance of recommendation, but it can also alleviate the impact of data sparsity and help to tackle the cold start problem. In this paper, we present a neural recommender model which recommends items by leveraging user reviews. In order to predict user rating for each item, our proposed model, named MatchPyramid Recommender System (MPRS), represents each user and item with their corresponding review texts. Thus, the problem of recommendation is viewed as a text matching problem such that the matching score obtained from matching user and item texts could be considered as a good representative of their joint extent of similarity. To solve the text matching problem, inspired by MatchPyramid (Pang, 2016), we employed an interaction-based approach according to which a matching matrix is constructed given a pair of input texts. The matching matrix, which has the property of hierarchical matching patterns, is then fed into a Convolutional Neural Network (CNN) to compute the matching score for the given user-item pair. Our experiments on the small data categories of Amazon review dataset show that our proposed model gains from 1.76% to 21.72% relative improvement compared to DeepCoNN model, and from 0.83% to 3.15% relative improvement compared to TransNets model. Also, on two large categories, namely AZ-CSJ and AZ-Mov, our model achieves relative improvements of 8.08% and 7.56% compared to the DeepCoNN model, and relative improvements of 1.74% and 0.86% compared to the TransNets model, respectively.

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arXiv2019

Analysis of a Legendre spectral element method (LSEM) for the two-dimensional system of a nonlinear stochastic advection-reaction-diffusion models

In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection-reaction-diffusion models. The used basis functions are based on a class of Legendre functions such that their mass and diffuse matrices are tridiagonal and diagonal, respectively. The temporal variable is discretized by a Crank--Nicolson finite difference formulation. In the stochastic direction, we also employ a random variable $W$ based on the $Q-$Wiener process. We inspect the rate of convergence and the unconditional stability for the achieved semi-discrete formulation. Then, the Legendre spectral element technique is used to obtain a full-discrete scheme. The error estimation of the proposed numerical scheme is substantiated based upon the energy method. The numerical results confirm the theoretical analysis.

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arXiv2019

Generalized moving least squares and moving kriging least squares approximations for solving the transport equation on the sphere

In this work, we apply two meshless methods for the numerical solution of the time-dependent transport equation defined on the sphere in spherical coordinates. The first technique, which was introduced by Mirzaei (BIT Numerical Mathematics, 54 (4) 1041-1063, 2017) in Cartesian coordinates is a generalized moving least squares approximation, and the second one, which is developed here, is moving kriging least squares interpolation on the sphere. These methods do not depend on the background mesh or triangulation, and they can be implemented on the transport equation in spherical coordinates easily using different distribution points. Furthermore, the time variable is approximated by a second-order backward differential formula. The obtained fully discrete scheme is solved via the biconjugate gradient stabilized algorithm with zero-fill incomplete lower-upper (ILU) preconditioner at each time step. Three well-known test problems namely solid body rotation, vortex roll-up, and deformational flow are solved to demonstrate our developments.

math.NA↗

arXiv2019

Augmentation Scheme for Dealing with Imbalanced Network Traffic Classification Using Deep Learning

One of the most important tasks in network management is identifying different types of traffic flows. As a result, a type of management service, called Network Traffic Classifier (NTC), has been introduced. One type of NTCs that has gained huge attention in recent years applies deep learning on packets in order to classify flows. Internet is an imbalanced environment i.e., some classes of applications are a lot more populated than others e.g., HTTP. Additionally, one of the challenges in deep learning methods is that they do not perform well in imbalanced environments in terms of evaluation metrics such as precision, recall, and $\mathrm{F_1}$ measure. In order to solve this problem, we recommend the use of augmentation methods to balance the dataset. In this paper, we propose a novel data augmentation approach based on the use of Long Short Term Memory (LSTM) networks for generating traffic flow patterns and Kernel Density Estimation (KDE) for replicating the numerical features of each class. First, we use the LSTM network in order to learn and generate the sequence of packets in a flow for classes with less population. Then, we complete the features of the sequence with generating random values based on the distribution of a certain feature, which will be estimated using KDE. Finally, we compare the training of a Convolutional Recurrent Neural Network (CRNN) in large-scale imbalanced, sampled, and augmented datasets. The contribution of our augmentation scheme is then evaluated on all of the datasets through measurements of precision, recall, and F1 measure for every class of application. The results demonstrate that our scheme is well suited for network traffic flow datasets and improves the performance of deep learning algorithms when it comes to above-mentioned metrics.

cs.NI↗

arXiv2018

Distributed Power Control for Delay Optimization in Energy Harvesting Cooperative Relay Networks

We consider cooperative communications with energy harvesting (EH) relays, and develop a distributed power control mechanism for the relaying terminals. Unlike prior art which mainly deal with single-relay systems with saturated traffic flow, we address the case of bursty data arrival at the source cooperatively forwarded by multiple half-duplex EH relays. We aim at optimizing the long-run average delay of the source packets under the energy neutrality constraint on power consumption of each relay. While EH relay systems have been predominantly optimized using either offline or online methodologies, we take on a more realistic learning-theoretic approach. Hence, our scheme can be deployed for real-time operation without assuming acausal information on channel realizations, data/energy arrivals as required by offline optimization, nor does it rely on precise statistics of the system processes as is the case with online optimization. We formulate the problem as a partially observable identical payoff stochastic game (PO-IPSG) with factored controllers, in which the power control policy of each relay is adaptive to its local source-to-relay/relay-to-destination channel states, its local energy state as well as to the source buffer state information. We derive a multi-agent reinforcement learning algorithm which is convergent to a locally optimal solution of the formulated PO-IPSG. The proposed algorithm operates without explicit message exchange between the relays, while inducing only little source-relay signaling overhead. By simulation, we contrast the delay performance of the proposed method against existing heuristics for throughput maximization. It is shown that compared with these heuristics, the systematic approach adopted in this paper has a smaller sub-optimality gap once evaluated against a centralized optimal policy armed with perfect statistics.

cs.NI↗

arXiv2018

To overhear or not to overhear: a dilemma between network coding gain and energy consumption in multi-hop wireless networks

Any properly designed network coding technique can result in increased throughput and reliability of multi-hop wireless networks by taking advantage of the broadcast nature of wireless medium. In many inter-flow network coding schemes nodes are encouraged to overhear neighbours traffic in order to improve coding opportunities at the transmitter nodes. A study of these schemes reveal that some of the overheard packets are not useful for coding operation and thus this forced overhearing increases energy consumption dramatically. In this paper, we formulate network coding aware sleep/wakeup scheduling as a semi Markov decision process (SMDP) that leads to an optimal node operation. In the proposed solution for SMDP, the network nodes learn when to switch off their transceiver in order to conserve energy and when to stay awake to overhear some useful packets. One of the main challenges here is the delay in obtaining reward signals by nodes. We employ a modified Reinforcement Learning (RL) method based on continuous-time Q-learning to overcome this challenge in the learning process. Our simulation results confirm the optimality of the new methodology.

cs.NI↗

arXiv2017

To Send or Not to Send: An Optimal Stopping Approach to Network Coding in Multi-hop Wireless Networks

Network coding is all about combining a variety of packets and forwarding as much packets as possible in each transmission operation. The network coding technique improves the throughput efficiency of multi-hop wireless networks by taking advantage of the broadcast nature of wireless channels. However, there are some scenarios where the coding cannot be exploited due to the stochastic nature of the packet arrival process in the network. In these cases, the coding node faces two critical choices: forwarding the packet towards the destination without coding, thereby sacrificing the advantage of network coding, or, waiting for a while until a coding opportunity arises for the packets. Current research works have addressed this challenge for the case of a simple and restricted scheme called reverse carpooling where it is assumed that two flows with opposite directions arrive at the coding node. In this paper the issue is explored in a general sense based on the COPE architecture requiring no assumption about flows in multi-hop wireless networks. In particular, we address this sequential decision making problem by using the solid framework of optimal stopping theory, and derive the optimal stopping rule for the coding node to choose the optimal action to take, i.e. to wait for more coding opportunity or to stop immediately (and send packet). Our simulation results validate the effectiveness of the derived optimal stopping rule and show that the proposed scheme outperforms existing methods in terms of network throughput and energy consumption.

cs.NI↗

arXiv2017

Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations

Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Gr\"unwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.

math.NA↗

arXiv2015

Cognitive Forwarding Control in Wireless Ad-Hoc Networks with Slow Fading Channels

We propose a decentralized stochastic control solution for the broadcast message dissemination problem in wireless ad hoc networks with slow fading channels. We formulate the control problem as a dynamic robust game which is well justified by two key observations; first, the shared nature of the wireless medium which inevitably cross-couples the nodes' forwarding decisions, thus binding them together as strategic players; second, the stochastic dynamics associated with the link qualities which renders the transmission costs noisy, thus motivating a robust formulation. Given the non stationarity induced by the fading process, an online solution for the formulated game would then require an adaptive procedure capable of both convergence to and tracking strategic equilibria as the environment changes. To this end, we deploy the strategic and non stationary learning algorithm of regret tracking, the temporally adaptive variant of the celebrated regret matching algorithm, to guarantee the emergence and active tracking of the correlated equilibria in the dynamic robust forwarding game. We also make provision for exploiting the channel state information, when available, to enhance the convergence speed of the learning algorithm by conducting an accurate transmission cost estimation. This cost estimate can basically serve as a model which spares the algorithm from extra action exploration, thus rendering the learning process more sample efficient. Simulation results reveal that our proposed solution excels in terms of both the number of transmissions and load distribution while also maintaining near perfect delivery ratio, especially in dense crowded environments.

cs.NI↗

arXiv2015

Learning Stationary Correlated Equilibria in Constrained General-Sum Stochastic Games

We study constrained general-sum stochastic games with unknown Markovian dynamics. A distributed constrained no-regret Q-learning scheme (CNRQ) is presented to guarantee convergence to the set of stationary correlated equilibria of the game. Prior art addresses the unconstrained case only, is structured with nested control loops, and has no convergence result. CNRQ is cast as a single-loop three-timescale asynchronous stochastic approximation algorithm with set-valued update increments. A rigorous convergence analysis with differential inclusion arguments is given which draws on recent extensions of the theory of stochastic approximation to the case of asynchronous recursive inclusions with set-valued mean fields. Numerical results are given for the exemplary application of CNRQ to decentralized resource control in heterogeneous wireless networks (HetNets).

cs.GT↗

arXiv2014

Decentralized Adaptive Helper Selection in Multi-channel P2P Streaming Systems

In Peer-to-Peer (P2P) multichannel live streaming, helper peers with surplus bandwidth resources act as micro-servers to compensate the server deficiencies in balancing the resources between different channel overlays. With deployment of helper level between server and peers, optimizing the user/helper topology becomes a challenging task since applying well-known reciprocity-based choking algorithms is impossible due to the one-directional nature of video streaming from helpers to users. Because of selfish behavior of peers and lack of central authority among them, selection of helpers requires coordination. In this paper, we design a distributed online helper selection mechanism which is adaptable to supply and demand pattern of various video channels. Our solution for strategic peers' exploitation from the shared resources of helpers is to guarantee the convergence to correlated equilibria (CE) among the helper selection strategies. Online convergence to the set of CE is achieved through the regret-tracking algorithm which tracks the equilibrium in the presence of stochastic dynamics of helpers' bandwidth. The resulting CE can help us select proper cooperation policies. Simulation results demonstrate that our algorithm achieves good convergence, load distribution on helpers and sustainable streaming rates for peers.

cs.NI↗

arXiv2013

A numerical method based on the reproducing kernel Hilbert space method for the solution of fifth-order boundary-value problems

In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the equations have been obtained in terms of convergent series with easily computable components. We compare our results with spline methods, decomposition method, variational iteration method, Sinc-Galerkin method and homotopy perturbation methods. The comparison of the results with exact ones is made to confirm the validity and efficiency.

math.NA↗

arXiv2010

An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method

In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value problems. The proposed approach is based on a Hermite function collocation (HFC) method. To illustrate the reliability of the method, some special cases of the equations are solved as test examples. The new method reduces the solution of a problem to the solution of a system of algebraic equations. Hermite functions have prefect properties that make them useful to achieve this goal. We compare the present work with some well-known results and show that the new method is efficient and applicable.

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