Search results for: variational method
8087 Variational Iteration Method for the Solution of Boundary Value Problems
Authors: Olayiwola M.O., Gbolagade A .W., Akinpelu F. O.
Abstract:
In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.
Keywords: Variational iteration method, boundary value problems, convergence, restricted variation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20928086 A Descent-projection Method for Solving Monotone Structured Variational Inequalities
Authors: Min Sun, Zhenyu Liu
Abstract:
In this paper, a new descent-projection method with a new search direction for monotone structured variational inequalities is proposed. The method is simple, which needs only projections and some function evaluations, so its computational load is very tiny. Under mild conditions on the problem-s data, the method is proved to converges globally. Some preliminary computational results are also reported to illustrate the efficiency of the method.Keywords: variational inequalities, monotone function, global convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12838085 Proximal Parallel Alternating Direction Method for Monotone Structured Variational Inequalities
Abstract:
In this paper, we focus on the alternating direction method, which is one of the most effective methods for solving structured variational inequalities(VI). In fact, we propose a proximal parallel alternating direction method which only needs to solve two strongly monotone sub-VI problems at each iteration. Convergence of the new method is proved under mild assumptions. We also present some preliminary numerical results, which indicate that the new method is quite efficient.
Keywords: structured variational inequalities, proximal point method, global convergence
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13148084 Variational Evolutionary Splines for Solving a Model of Temporomandibular Disorders
Authors: Alberto Hananel
Abstract:
The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.Keywords: Approximation, evolutionary PDE, finite element method, temporomandibular disorders, variational spline.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15788083 Variational Iteration Method for Solving Systems of Linear Delay Differential Equations
Authors: Sara Barati, Karim Ivaz
Abstract:
In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.
Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24688082 Postbuckling Analysis of End Supported Rods under Self-Weight Using Intrinsic Coordinate Finite Elements
Authors: C. Juntarasaid, T. Pulngern, S. Chucheepsakul
Abstract:
A formulation of postbuckling analysis of end supported rods under self-weight has been presented by the variational method. The variational formulation involving the strain energy due to bending and the potential energy of the self-weight, are expressed in terms of the intrinsic coordinates. The variational formulation is accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method is used to derive a system of nonlinear equations resulting from the stationary of the total potential energy and then Newton-Raphson iterative procedure is applied to solve this system of equations. The numerical results demonstrate the postbluckled configurations of end supported rods under self-weight. This finite element method based on variational formulation expressed in term of intrinsic coordinate is highly recommended for postbuckling analysis of end-supported rods under self-weight.
Keywords: Variational method, postbuckling, finite element method, intrinsic coordinate.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8418081 A New Approximate Procedure Based On He’s Variational Iteration Method for Solving Nonlinear Hyperbolic Wave Equations
Authors: Jinfeng Wang, Yang Liu, Hong Li
Abstract:
In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.
Keywords: Hyperbolic wave equation, Nonlinear, He’s variational iteration method, Transformations
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21298080 An Analytical Method to Analysis of Foam Drainage Problem
Authors: A. Nikkar, M. Mighani
Abstract:
In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.
Keywords: Reconstruction of Variational Iteration Method (RVIM), Foam drainage, nonlinear partial differential equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18068079 Calculation of Wave Function at the Origin (WFO) for the Ground State of Doubly Heavy Mesons Based On the Variational Method
Authors: Maryam Momeni Feili, Mahvash Zandy Navgaran
Abstract:
The wave function at the origin is an important quantity in studying many physical problems concerning heavy quarkonia. This is because that it is using for calculating spin state hyperfine splitting and also crucial to evaluating the production and decay amplitude of the heavy quarkonium. In this paper, we present the variational method by using the single-parameter wave function to estimate the WFO for the ground state of heavy mesons.
Keywords: Wave function at the origin, heavy mesons, bound states, variational method, non-relativistic quark model, potential model, trial wave function.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14848078 Instability of Soliton Solutions to the Schamel-nonlinear Schrödinger Equation
Authors: Sarun Phibanchon, Michael A. Allen
Abstract:
A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schr¨odinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton.
Keywords: Soliton, instability, variational method, spectral method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36908077 Analytical Solutions of Kortweg-de Vries(KdV) Equation
Authors: Foad Saadi, M. Jalali Azizpour, S.A. Zahedi
Abstract:
The objective of this paper is to present a comparative study of Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Homotopy Analysis Method (HAM) for the semi analytical solution of Kortweg-de Vries (KdV) type equation called KdV. The study have been highlighted the efficiency and capability of aforementioned methods in solving these nonlinear problems which has been arisen from a number of important physical phenomenon.Keywords: Variational Iteration Method (VIM), HomotopyPerturbation Method (HPM), Homotopy Analysis Method (HAM), KdV Equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23668076 Inexact Alternating Direction Method for Variational Inequality Problems with Linear Equality Constraints
Abstract:
In this article, a new inexact alternating direction method(ADM) is proposed for solving a class of variational inequality problems. At each iteration, the new method firstly solves the resulting subproblems of ADM approximately to generate an temporal point ˜xk, and then the multiplier yk is updated to get the new iterate yk+1. In order to get xk+1, we adopt a new descent direction which is simple compared with the existing prediction-correction type ADMs. For the inexact ADM, the resulting proximal subproblem has closedform solution when the proximal parameter and inexact term are chosen appropriately. We show the efficiency of the inexact ADM numerically by some preliminary numerical experiments.
Keywords: variational inequality problems, alternating direction method, global convergence
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14938075 Characterization of Solutions of Nonsmooth Variational Problems and Duality
Authors: Juan Zhang, Changzhao Li
Abstract:
In this paper, we introduce a new class of nonsmooth pseudo-invex and nonsmooth quasi-invex functions to non-smooth variational problems. By using these concepts, numbers of necessary and sufficient conditions are established for a nonsmooth variational problem wherein Clarke’s generalized gradient is used. Also, weak, strong and converse duality are established.
Keywords: Variational problem, Nonsmooth pseudo-invex, Nonsmooth quasi-invex, Critical point, Duality
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11348074 Short-Term Load Forecasting Based on Variational Mode Decomposition and Least Square Support Vector Machine
Authors: Jiangyong Liu, Xiangxiang Xu, Bote Luo, Xiaoxue Luo, Jiang Zhu, Lingzhi Yi
Abstract:
To address the problems of non-linearity and high randomness of the original power load sequence causing the degradation of power load forecasting accuracy, a short-term load forecasting method is proposed. The method is based on the least square support vector machine (LSSVM) optimized by an improved sparrow search algorithm combined with the variational mode decomposition proposed in this paper. The application of the variational mode decomposition technique decomposes the raw power load data into a series of intrinsic mode functions components, which can reduce the complexity and instability of the raw data while overcoming modal confounding; the proposed improved sparrow search algorithm can solve the problem of difficult selection of learning parameters in the LSSVM. Finally, through comparison experiments, the results show that the method can effectively improve prediction accuracy.
Keywords: Load forecasting, variational mode decomposition, improved sparrow search algorithm, least square support vector machine.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 238073 Human Action Recognition Using Variational Bayesian HMM with Dirichlet Process Mixture of Gaussian Wishart Emission Model
Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park
Abstract:
In this paper, we present the human action recognition method using the variational Bayesian HMM with the Dirichlet process mixture (DPM) of the Gaussian-Wishart emission model (GWEM). First, we define the Bayesian HMM based on the Dirichlet process, which allows an infinite number of Gaussian-Wishart components to support continuous emission observations. Second, we have considered an efficient variational Bayesian inference method that can be applied to drive the posterior distribution of hidden variables and model parameters for the proposed model based on training data. And then we have derived the predictive distribution that may be used to classify new action. Third, the paper proposes a process of extracting appropriate spatial-temporal feature vectors that can be used to recognize a wide range of human behaviors from input video image. Finally, we have conducted experiments that can evaluate the performance of the proposed method. The experimental results show that the method presented is more efficient with human action recognition than existing methods.
Keywords: Human action recognition, Bayesian HMM, Dirichlet process mixture model, Gaussian-Wishart emission model, Variational Bayesian inference, Prior distribution and approximate posterior distribution, KTH dataset.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9988072 Vibration of a Beam on an Elastic Foundation Using the Variational Iteration Method
Authors: Desmond Adair, Kairat Ismailov, Martin Jaeger
Abstract:
Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.
Keywords: Timoshenko beam, variational iteration method, two-parameter elastic foundation model.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9638071 Investigation of a Transition from Steady Convection to Chaos in Porous Media Using Piecewise Variational Iteration Method
Authors: Mohamed M. Mousa, Aidarkhan Kaltayev Shahwar F. Ragab
Abstract:
In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.
Keywords: Variational iteration method, free convection, Chaos, Lorenz equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15258070 Optimal Control of Piezo-Thermo-Elastic Beams
Authors: Marwan Abukhaled, Ibrahim Sadek
Abstract:
This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a distributed piezoelectric actuators. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combination of modal expansion and variational approaches. The modal expansion approach is used to convert the optimal control of distributed parameter system into the optimal control of lumped parameter system. By utilizing the variational approach, an explicit optimal control law is derived and the determination of the corresponding displacement and velocity is reduced to solving a set of ordinary differential equations.
Keywords: Optimal control, Thermoelastic beam, variational approach, modal expansion approach
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14128069 Accurate Optical Flow Based on Spatiotemporal Gradient Constancy Assumption
Authors: Adam Rabcewicz
Abstract:
Variational methods for optical flow estimation are known for their excellent performance. The method proposed by Brox et al. [5] exemplifies the strength of that framework. It combines several concepts into single energy functional that is then minimized according to clear numerical procedure. In this paper we propose a modification of that algorithm starting from the spatiotemporal gradient constancy assumption. The numerical scheme allows to establish the connection between our model and the CLG(H) method introduced in [18]. Experimental evaluation carried out on synthetic sequences shows the significant superiority of the spatial variant of the proposed method. The comparison between methods for the realworld sequence is also enclosed.Keywords: optical flow, variational methods, gradient constancy assumption.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21728068 Single Image Defogging Method Using Variational Approach for Edge-Preserving Regularization
Authors: Wan-Hyun Cho, In-Seop Na, Seong-ChaeSeo, Sang-Kyoon Kim, Soon-Young Park
Abstract:
In this paper, we propose the variational approach to solve single image defogging problem. In the inference process of the atmospheric veil, we defined new functional for atmospheric veil that satisfy edge-preserving regularization property. By using the fundamental lemma of calculus of variations, we derive the Euler-Lagrange equation foratmospheric veil that can find the maxima of a given functional. This equation can be solved by using a gradient decent method and time parameter. Then, we can have obtained the estimated atmospheric veil, and then have conducted the image restoration by using inferred atmospheric veil. Finally we have improved the contrast of restoration image by various histogram equalization methods. The experimental results show that the proposed method achieves rather good defogging results.
Keywords: Image defogging, Image restoration, Atmospheric veil, Transmission, Variational approach, Euler-Lagrange equation, Image enhancement.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 29358067 An Analytical Solution for Vibration of Elevator Cables with Small Bending Stiffness
Authors: R. Mirabdollah Yani, E. Darabi
Abstract:
Responses of the dynamical systems are highly affected by the natural frequencies and it has a huge impact on design and operation of high-rise and high-speed elevators. In the present paper, the variational iteration method (VIM) is employed to investigate better understanding the dynamics of elevator cable as a single-degree-of-freedom (SDOF) swing system. Comparisons made among the results of the proposed closed-form analytical solution, the traditional numerical iterative time integration solution, and the linearized governing equations confirm the accuracy and efficiency of the proposed approach. Furthermore, based on the results of the proposed closed-form solution, the linearization errors in calculating the natural frequencies in different cases are discussed.
Keywords: variational iteration method (VIM), cable vibration, closed-form solution
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22918066 Dynamic Variational Multiscale LES of Bluff Body Flows on Unstructured Grids
Authors: Carine Moussaed, Stephen Wornom, Bruno Koobus, Maria Vittoria Salvetti, Alain Dervieux,
Abstract:
The effects of dynamic subgrid scale (SGS) models are investigated in variational multiscale (VMS) LES simulations of bluff body flows. The spatial discretization is based on a mixed finite element/finite volume formulation on unstructured grids. In the VMS approach used in this work, the separation between the largest and the smallest resolved scales is obtained through a variational projection operator and a finite volume cell agglomeration. The dynamic version of Smagorinsky and WALE SGS models are used to account for the effects of the unresolved scales. In the VMS approach, these effects are only modeled in the smallest resolved scales. The dynamic VMS-LES approach is applied to the simulation of the flow around a circular cylinder at Reynolds numbers 3900 and 20000 and to the flow around a square cylinder at Reynolds numbers 22000 and 175000. It is observed as in previous studies that the dynamic SGS procedure has a smaller impact on the results within the VMS approach than in LES. But improvements are demonstrated for important feature like recirculating part of the flow. The global prediction is improved for a small computational extra cost.Keywords: variational multiscale LES, dynamic SGS model, unstructured grids, circular cylinder, square cylinder.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18198065 Multinomial Dirichlet Gaussian Process Model for Classification of Multidimensional Data
Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park
Abstract:
We present probabilistic multinomial Dirichlet classification model for multidimensional data and Gaussian process priors. Here, we have considered efficient computational method that can be used to obtain the approximate posteriors for latent variables and parameters needed to define the multiclass Gaussian process classification model. We first investigated the process of inducing a posterior distribution for various parameters and latent function by using the variational Bayesian approximations and important sampling method, and next we derived a predictive distribution of latent function needed to classify new samples. The proposed model is applied to classify the synthetic multivariate dataset in order to verify the performance of our model. Experiment result shows that our model is more accurate than the other approximation methods.Keywords: Multinomial dirichlet classification model, Gaussian process priors, variational Bayesian approximation, Importance sampling, approximate posterior distribution, Marginal likelihood evidence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16078064 Variational EM Inference Algorithm for Gaussian Process Classification Model with Multiclass and Its Application to Human Action Classification
Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park
Abstract:
In this paper, we propose the variational EM inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multiclass. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.
Keywords: Bayesian rule, Gaussian process classification model with multiclass, Gaussian process prior, human action classification, laplace approximation, variational EM algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17518063 Large Amplitude Free Vibration of a Very Sag Marine Cable
Authors: O. Punjarat, S. Chucheepsakul, T. Phanyasahachart
Abstract:
This paper focuses on a variational formulation of large amplitude free vibration behavior of a very sag marine cable. In the static equilibrium state, the marine cable has a very large sag configuration. In the motion state, the marine cable is assumed to vibrate in in-plane motion with large amplitude from the static equilibrium position. The total virtual work-energy of the marine cable at the dynamic state is formulated which involves the virtual strain energy due to axial deformation, the virtual work done by effective weight, and the inertia forces. The equations of motion for the large amplitude free vibration of marine cable are obtained by taking into account the difference between the Euler’s equation in the static state and the displaced state. Based on the Galerkin finite element procedure, the linear and nonlinear stiffness matrices, and mass matrices of the marine cable are obtained and the eigenvalue problem is solved. The natural frequency spectrum and the large amplitude free vibration behavior of marine cable are presented.
Keywords: Axial deformation, free vibration, Galerkin Finite Element Method, large amplitude, variational method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8158062 Distributed Generator Placement and Sizing in Unbalanced Radial Distribution System
Authors: J. B. V. Subrahmanyam, C. Radhakrishna
Abstract:
To minimize power losses, it is important to determine the location and size of local generators to be placed in unbalanced power distribution systems. On account of some inherent features of unbalanced distribution systems, such as radial structure, large number of nodes, a wide range of X/R ratios, the conventional techniques developed for the transmission systems generally fail on the determination of optimum size and location of distributed generators (DGs). This paper presents a simple method for investigating the problem of contemporaneously choosing best location and size of DG in three-phase unbalanced radial distribution system (URDS) for power loss minimization and to improve the voltage profile of the system. Best location of the DG is determined by using voltage index analysis and size of DG is computed by variational technique algorithm according to available standard size of DGs. This paper presents the results of simulations for 25-bus and IEEE 37- bus Unbalanced Radial Distribution system.Keywords: Distributed generator, unbalanced radial distributionsystem, voltage index analysis, variational algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 37328061 Variational Explanation Generator: Generating Explanation for Natural Language Inference Using Variational Auto-Encoder
Authors: Zhen Cheng, Xinyu Dai, Shujian Huang, Jiajun Chen
Abstract:
Recently, explanatory natural language inference has attracted much attention for the interpretability of logic relationship prediction, which is also known as explanation generation for Natural Language Inference (NLI). Existing explanation generators based on discriminative Encoder-Decoder architecture have achieved noticeable results. However, we find that these discriminative generators usually generate explanations with correct evidence but incorrect logic semantic. It is due to that logic information is implicitly encoded in the premise-hypothesis pairs and difficult to model. Actually, logic information identically exists between premise-hypothesis pair and explanation. And it is easy to extract logic information that is explicitly contained in the target explanation. Hence we assume that there exists a latent space of logic information while generating explanations. Specifically, we propose a generative model called Variational Explanation Generator (VariationalEG) with a latent variable to model this space. Training with the guide of explicit logic information in target explanations, latent variable in VariationalEG could capture the implicit logic information in premise-hypothesis pairs effectively. Additionally, to tackle the problem of posterior collapse while training VariaztionalEG, we propose a simple yet effective approach called Logic Supervision on the latent variable to force it to encode logic information. Experiments on explanation generation benchmark—explanation-Stanford Natural Language Inference (e-SNLI) demonstrate that the proposed VariationalEG achieves significant improvement compared to previous studies and yields a state-of-the-art result. Furthermore, we perform the analysis of generated explanations to demonstrate the effect of the latent variable.Keywords: Natural Language Inference, explanation generation, variational auto-encoder, generative model.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6778060 A Meshfree Solution of Tow-Dimensional Potential Flow Problems
Authors: I. V. Singh, A. Singh
Abstract:
In this paper, mesh-free element free Galerkin (EFG) method is extended to solve two-dimensional potential flow problems. Two ideal fluid flow problems (i.e. flow over a rigid cylinder and flow over a sphere) have been formulated using variational approach. Penalty and Lagrange multiplier techniques have been utilized for the enforcement of essential boundary conditions. Four point Gauss quadrature have been used for the integration on two-dimensional domain (Ω) and nodal integration scheme has been used to enforce the essential boundary conditions on the edges (┌). The results obtained by EFG method are compared with those obtained by finite element method. The effects of scaling and penalty parameters on EFG results have also been discussed in detail.
Keywords: Meshless, EFG method, potential flow, Lagrange multiplier method, penalty method, penalty parameter and scaling parameter
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14928059 A Parallel Approach for 3D-Variational Data Assimilation on GPUs in Ocean Circulation Models
Authors: Rossella Arcucci, Luisa D’Amore, Simone Celestino, Giuseppe Scotti, Giuliano Laccetti
Abstract:
This work is the first dowel in a rather wide research activity in collaboration with Euro Mediterranean Center for Climate Changes, aimed at introducing scalable approaches in Ocean Circulation Models. We discuss designing and implementation of a parallel algorithm for solving the Variational Data Assimilation (DA) problem on Graphics Processing Units (GPUs). The algorithm is based on the fully scalable 3DVar DA model, previously proposed by the authors, which uses a Domain Decomposition approach (we refer to this model as the DD-DA model). We proceed with an incremental porting process consisting of 3 distinct stages: requirements and source code analysis, incremental development of CUDA kernels, testing and optimization. Experiments confirm the theoretic performance analysis based on the so-called scale up factor demonstrating that the DD-DA model can be suitably mapped on GPU architectures.Keywords: Data Assimilation, Parallel Algorithm, GPU architectures, Ocean Models.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20038058 Unsupervised Texture Segmentation via Applying Geodesic Active Regions to Gaborian Feature Space
Authors: Yuan He, Yupin Luo, Dongcheng Hu
Abstract:
In this paper, we propose a novel variational method for unsupervised texture segmentation. We use a Gabor filter bank to extract texture features. Some of the filtered channels form a multidimensional Gaborian feature space. To avoid deforming contours directly in a vector-valued space we use a Gaussian mixture model to describe the statistical distribution of this space and get the boundary and region probabilities. Then a framework of geodesic active regions is applied based on them. In the end, experimental results are presented, and show that this method can obtain satisfied boundaries between different texture regions.
Keywords: Texture segmentation, Gabor filter, snakes, Geodesicactive regions
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1764