Fictitious Domain Approach Via Lagrange Multipliers with Least Squares Spectral Element Method

We consider the application of Fictitious Domain approach combined with Least Squares Spectral Elements for the numerical solution of partial differential equations. Fictitious Domain methods allow problems formulated on a complicated shaped domain Ω to be solved on a simpler domain Π containing Ω. Least Squares Spectral Element Method has been used to develop the discrete model, as this scheme combines the generality of finite element methods with the accuracy of spectral methods. Moreover the least squares methods have theoretical and computational advantages in the algorithmic design and implementation. This paper presents the formulation and validation of the Fictitious Domain/Least Squares Spectral Element approach. The convergence of the relative energy norm η is verified computing smooth solutions to two-dimensional first and second-order differential equations, demonstrating the predictive capability of the proposed formulation.     

对极几何估计的鲁棒性新算法

以８参数模型的Ｆ矩阵为基础,深入研究的Ｆ阵的稳定性求解中的若干问题,将求解对极点的问题归结为求解二元六次非线性方程的最优解问题,并将所求最优解作为进上步计算的最佳修造对极点,最后以余差最小准则获得Ｆ阵的全局最优解,实验结果表明,该方法不但使对极点的稳定性有较大提高,也能高精度地估计祟Ｆ阵。     

Simulating free surface problems using Discrete Least Squares Meshless method

A Discrete Least Squares Meshless (DLSM) method is presented here for the simulation of incompressible free surface flows. The governing equations of the mass and momentum conservations are solved in a Lagrangian form using a pressure projection method. Since there are no particles in the outer region of the free surface, the particle density will drop significantly. Free surfaces are, therefore, resolved by tracking particles with highly reduced density. A fully least squares approach is used in both function approximation and the discretization of the governing differential equations in space. The meshless shape functions are derived using the Moving Least Squares (MLS) method of function approximation. The discretized equations are obtained via a discrete least squares method in which the sum of the squared residuals are minimized with respect to unknown nodal parameters. The method enjoys the advantage of producing symmetric, positive definite matrixes for the cases considered. The method can be viewed as a truly meshless method since it does not need any mesh for both field variable approximation and the construction of system matrices. Two free surface problems namely dam break and evolution of a drop with an initial known velocity are solved to test the accuracy of the proposed method. The results show the ability of the proposed method to solve complex fluid dynamic problems with moving free surface boundaries.     

最小二乘迁移生成对抗网络

现有的生成对抗网络（Generative Adversarial Networks，GAN）损失函数已经被成功地应用在迁移学习方法中。然而，发现这种损失函数在学习过程中可能会出现梯度消失的问题。为了克服该问题，提出了一种学习领域不变特征的新方法，即最小二乘迁移生成对抗网络（Least Squares Transfer Generative Adversarial Networks，LSTGAN）。LSTGAN采用最小二乘生成对抗网络（Least Squares Generative Adversarial Networks，LSGAN）损失函数，通过单领域判别的训练方式来减少领域分布之间的差异。通过研究表明，所提方法与其他有竞争力的算法相比较具有一定的优越性。     

一种快速最小二乘支持向量机分类算法

最小二乘支持向量机不需要求解凸二次规划问题,通过求解一组线性方程而获得最优分类面,但是,最小二乘支持向量机失去了解的稀疏性,当训练样本数量较大时,算法的计算量非常大。提出了一种快速最小二乘支持向量机算法,在保证支持向量机推广能力的同时,算法的速度得到了提高,尤其是当训练样本数量较大时算法的速度优势更明显。新算法通过选择那些支持值较大样本作为训练样本,以减少训练样本数量,提高算法的速度;然后,利用最小二乘支持向量机算法获得近似最优解。实验结果显示,新算法的训练速度确实较快。     

A discontinuous Galerkin front tracking method for two-phase flows with surface tension

A discontinuous Galerkin method for solving hyperbolic systems of conservation laws involving interfaces is presented. The interfaces are represented by a collection of element boundaries and their position is updated using an arbitrary Lagrangian-Eulerian method. The motion of the interfaces and the numerical fluxes are obtained by solving a Riemann problem. As the interface is propagated, a simple and effective remeshing technique based on distance functions regenerates the grid to preserve its quality. Compared to other interface capturing techniques, the proposed approach avoids smearing of the jumps across the interface which leads to an improvement in accuracy. Numerical results are presented for several typical two-dimensional interface problems, including flows with surface tension.     

LS-SVM approximate solution to linear time varying descriptor systems

This paper discusses a numerical method based on Least Squares Support Vector Machines (LS-SVMs) for solving linear time varying initial and boundary value problems in Differential Algebraic Equations (DAEs). The method generates a closed form (model-based) approximate solution. The results of numerical experiments on different systems with index from $0$ to $3$, are presented and compared with analytic solutions to confirm the validity and applicability of the proposed method.     

The plane stress/strain analysis of non-homogeneous continua by the boundary integral equation method

The numerical analysis of non-homogeneous bodies by the Boundary Integral Equation method is discussed. The body is divided into subregions where the material properties are constant, and each subregion is enclosed within its own boundary. Quadratic shape functions are used to interpolate the variables defined on these boundaries. At corners, either on the external boundaries or on the subregion interfaces, the tractions are discontinuous which can cause numerical difficulties. Particular attention is given to overcoming this problem by using either a set of auxiliary equations, or a number of auxiliary nodes at these corner points. In addition, the elegant method of calculating the body force terms by boundary integration, instead of the more conventional domain integration, is discussed. Finally, two examples are presented which examine the performance of the BIEM for problems of this type.     

A parallel method for the numerical solution of integro-differential equation with positive memory

An efficient parallel numerical method is proposed for an integro-differential equation with positive memory. Instead of solving the equation in classical time-marching methods which require massive storage of solutions of previous time steps in order to advance to a next time step, the Fourier–Laplace transformation in time is applied to obtain a set of complex-valued, elliptic problems parameterized by points on a contour in the complex plane. Using the independence of an elliptic problem corresponding to one contour point is independent of those elliptic problems corresponding to other contour points, all elliptic problems can be solved in parallel essentially without data communications. Then the time domain solution can be obtained by the Fourier–Laplace inversion formula. An error analysis and the numerical implementation of this parallel method is presented.     

A new numerical learning approach to solve general Falkner–Skan model

A new numerical learning approach namely Rational Gegenbauer Least Squares Support Vector Machines (RG_LS_SVM), is introduced in this paper. RG_LS_SVM method is a combination of collocation method based on rational Gegenbauer functions and LS_SVM method. This method converts a nonlinear high order model on a semi-infinite domain to a set of linear/nonlinear equations with equality constraints which decreases computational costs. Blasius, Falkner–Skan and MHD Falkner–Skan models and the effects of various parameters over them are investigated to satisfy accuracy, validity and efficiency of the proposed method. Both Primal and Dual forms of the problems are considered and the nonlinear models are converted to linear models by applying quasilinearization method to get the better results. Comparing the results of RG_LS_SVM method with available analytical and numerical solutions show that the present methods are efficient and have fast convergence rate and high accuracy.

     

基于改进支持向量机的快速稳健代理模型研究

最小二乘支持向量机代理模型具有较好的泛化能力和强大的非线性处理能力,但其对实际工程中不可避免的异常样本十分敏感,而传统的加权最小二乘支持向量机易产生过度拟合并且未考虑到回归误差分布特性,针对这一问题提出正态分布概率密度函数加权方法,并且采用回归误差的中值作为计算权值的衡量标准,增强了加权算法的稳健性;提出了迭代加权最小二乘支持向量机快速递推算法,利用矩阵关系进行迭代递推计算,减少了计算量,节约了建模时间。通过数值实例验证了该方法的可行性、有效性。     

Online adaptive utilization control for real-time embedded multiprocessor systems

Many embedded systems have stringent real-time constraints. An effective technique for meeting real-time constraints is to keep the processor utilization on each node at or below the schedulable utilization bound, even though each task’s actual execution time may have large uncertainties and deviate a lot from its estimated value. Recently, researchers have proposed solutions based on Model Predictive Control (MPC) for the utilization control problem. Although these approaches can handle a limited range of execution time estimation errors, the system may suffer performance deterioration or even become unstable with large estimation errors. In this paper, we present two online adaptive optimal control techniques, one is based on Recursive Least Squares (RLS) based model identification plus Linear Quadratic (LQ) optimal controller; the other one is based on Adaptive Critic Design (ACD). Simulation experiments demonstrate both the LQ optimal controller and ACD-based controller have better performance than the MPC-based controller and the ACD-based controller has the smallest aggregate tracking errors.     

基于偏最小二乘的SIFT误匹配校正方法

针对尺度不变特征变换（SIFT）描述子仅利用特征点的局部邻域信息而对图像内具有相似结构的特征点易产生误匹配的现象,提出一种基于偏最小二乘的SIFT误匹配校正方法。该方法首先利用SIFT算法进行匹配,得到初始匹配对,然后利用偏最小二乘方法对匹配后初始匹配点的空间分布信息进行重新描述,并通过定义影响函数,剔除影响程度大的特征点对,最后得到精确匹配点对,对图像进行配准。实验结果表明,该方法能够有效地剔除误匹配点,提高图像配准的精度。     

Application of the Galerkin and Least-Squares Finite Element Methods in the solution of 3D Poisson and Helmholtz equations

This paper presents the numerical solution, by the Galerkin and Least Squares Finite Element Methods, of the three-dimensional Poisson and Helmholtz equations, representing heat diffusion in solids. For the two applications proposed, the analytical solutions found in the literature review were used to compare with the numerical solutions. The analysis of results was made from the L₂ norm (average error throughout the domain) and L_∞ norm (maximum error in the entire domain). The results of the two applications (Poisson and Helmholtz equations) are presented and discussed for testing of the efficiency of the methods.     

1-Norm least squares twin support vector machines

During the last few years, nonparallel plane classifiers, such as Multisurface Proximal Support Vector Machine via Generalized Eigenvalues (GEPSVM), and Least Squares TWSVM (LSTSVM), have attracted much attention. However, there are not any modifications of them that have been presented to automatically select the input features. This motivates the rush towards new classifiers. In this paper, we develop a new nonparallel plane classifier, which is designed for automatically selecting the relevant features. We first introduce a Tikhonov regularization (TR) term that is usually used for regularizing least squares into the LSTSVM learning framework, and then convert this formulation to a linear programming (LP) problem. By minimizing an exterior penalty (EP) problem of the dual of the LP formulation and using a fast generalized Newton algorithm, our method yields very sparse solutions, such that it generates a classifier that depends on only a smaller number of input features. In other words, this approach is capable of suppressing input features. This makes the classifier easier to store and faster to compute in the classification phase. Lastly, experiments on both toy and real problems disclose the effectiveness of our method.     

Robust Optic Flow Computation

This paper formulates the optic flow problem as a set of over-determined simultaneous linear equations. It then introduces and studies two new robust optic flow methods. The first technique is based on using the Least Median of Squares (LMedS) to detect the outliers. Then, the inlier group is solved using the least square technique. The second method employs a new robust statistical method named the Least Median of Squares Orthogonal Distances (LMSOD) to identify the outliers and then uses total least squares to solve the optic flow problem. The performance of both methods are studied by experiments on synthetic and real image sequences. These methods outperform other published methods both in accuracy and robustness.     

A Higher-Order Chimera Method for Finite Volume Schemes

In this work a higher-order accurate finite volume method for the resolution of the Euler/Navier–Stokes equations using Chimera grid techniques is presented. The formulation is based on the use of Moving Least Squares approximations in order to obtain higher-order accurate reconstruction and connectivity between the overlapped grids. The accuracy and performance of the proposed methodology is demonstrated by solving different benchmark problems.     

基于粒子群优化算法的LS-SVM财务预警

提出一种基于粒子群优化算法优化有关参数的最小二乘支持向量机的财务预警模型。通过提出适当的验证性能指标,用粒子群优化算法优化最小二乘支持向量机的有关参数,利用上市公司的财务数据对该方法进行实证财务预警分析。仿真结果表明,该模型的精确度令人满意,该方法是可行且有效的。     

Numerical solution of a class of quasilinear hyperbolic equations by reduction to the wave equation

An iterative method of solving quasilinear hyperbolic equations of the type $$ - [p_1 (u_x ,x,t)]_x + [p_2 (u_t ,x,t)]_t = f(x,t)$$ in the domain (0, 1)×(0,T) is proposed. For each given initial-boundary-value problem of this type with boundary conditions of the first kind (second kind), a conjugate problem of the same type that has boundary conditions of the second kind (first kind) is defined. From the relations connecting the solutions of a pair of conjugate problems, a series of wave equations is created. The method proposed consists in calculating the solutions of the wave equations of this series. Theoretical proof of the convergence of the solutions of the wave equations to the solutions of the conjugate quasilinear problems is left as an open question. However, numerical results are presented to demonstrate that, under favorable circumstances, the solutions of the wave equations do converge to the solutions of the conjugate quasilinear problems.     

PLS-LSSVM模型在锌净化中的应用

在锌净化除钴过程中,生产数据存在噪声且变量间具有多重相关性,从而难以准确预测钴离子浓度。为此,采用偏最小二乘方法去除数据中的噪声,降低各参数间的多重相关性。通过为不同时期的样本数据赋予不同的权值,提高了最小二乘支持向量机(LSSVM)模型预测的准确性。利用改进的粒子群优化算法优化选择LSSVM模型的惩罚因子和核函数参数,以避免人为选择参数的盲目性。仿真结果表明,PLS- LSSVM模型的预测精度高于偏最小二乘回归和LSSVM。