Fast analysis of large-scale problems by modified multilevel compressed block decomposition combined with high order hierarchical basis functions

2017 ◽  
Vol 55 (1) ◽  
pp. 167-175
Author(s):  
Zhaoneng Jiang ◽  
Qingchun Zhang ◽  
Liping Zha ◽  
Xiaoyu Yang
Keyword(s):  
Large Scale ◽  
High Order ◽  
Basis Functions ◽  
Block Decomposition ◽  
Fast Analysis ◽  
Hierarchical Basis ◽  
Large Scale Problems

scholarly journals A well-conditioned and efficient implementation of dual reciprocity method for Poisson equation

2021 ◽  
Vol 6 (11) ◽  
pp. 12560-12582
Author(s):  
Suliman Khan ◽  
◽  
M. Riaz Khan ◽  
Aisha M. Alqahtani ◽  
Hasrat Hussain Shah ◽  
...  
Keyword(s):  
Radial Basis Functions ◽  
Poisson Equation ◽  
Large Scale ◽  
Basis Functions ◽  
Dual Reciprocity Method ◽  
Reciprocity Method ◽  
Interpolation Matrix ◽  
Large Scale Problems ◽  
Radial Basis ◽  
Governing Differential Equation

<abstract><p>One of the attractive and practical techniques to transform the domain integrals to equivalent boundary integrals is the dual reciprocity method (DRM). The success of DRM relies on the proper treatment of the non-homogeneous term in the governing differential equation. For this purpose, radial basis functions (RBFs) interpolations are performed to approximate the non-homogeneous term accurately. Moreover, when the interpolation points are large, the global RBFs produced dense and ill-conditioned interpolation matrix, which poses severe stability and computational issues. Fortunately, there exist interpolation functions with local support known as compactly supported radial basis functions (CSRBFs). These functions produce a sparse and well-conditioned interpolation matrix, especially for large-scale problems. Therefore, this paper aims to apply DRM based on multiquadrics (MQ) RBFs and CSRBFs for evaluation of the Poisson equation, especially for large-scale problems. Furthermore, the convergence analysis of DRM with MQ and CSRBFs is performed, along with error estimate and stability analysis. Several experiments are performed to ensure the well-conditioned, efficient, and accurate behavior of the CSRBFs compared to the MQ-RBFs, especially for large-scale interpolation points.</p></abstract>

A new method to predict anomaly in brain network based on graph deep learning

2020 ◽  
Vol 31 (6) ◽  
pp. 681-689
Author(s):  
Jalal Mirakhorli ◽  
Hamidreza Amindavar ◽  
Mojgan Mirakhorli
Keyword(s):  
Deep Learning ◽  
Large Scale ◽  
Brain Plasticity ◽  
Brain Network ◽  
High Order ◽  
Brain Diseases ◽  
Simultaneous Occurrence ◽  
Generative Adversarial Network ◽  
The Brain ◽  
Brain Connections

AbstractFunctional magnetic resonance imaging a neuroimaging technique which is used in brain disorders and dysfunction studies, has been improved in recent years by mapping the topology of the brain connections, named connectopic mapping. Based on the fact that healthy and unhealthy brain regions and functions differ slightly, studying the complex topology of the functional and structural networks in the human brain is too complicated considering the growth of evaluation measures. One of the applications of irregular graph deep learning is to analyze the human cognitive functions related to the gene expression and related distributed spatial patterns. Since a variety of brain solutions can be dynamically held in the neuronal networks of the brain with different activity patterns and functional connectivity, both node-centric and graph-centric tasks are involved in this application. In this study, we used an individual generative model and high order graph analysis for the region of interest recognition areas of the brain with abnormal connection during performing certain tasks and resting-state or decompose irregular observations. Accordingly, a high order framework of Variational Graph Autoencoder with a Gaussian distributer was proposed in the paper to analyze the functional data in brain imaging studies in which Generative Adversarial Network is employed for optimizing the latent space in the process of learning strong non-rigid graphs among large scale data. Furthermore, the possible modes of correlations were distinguished in abnormal brain connections. Our goal was to find the degree of correlation between the affected regions and their simultaneous occurrence over time. We can take advantage of this to diagnose brain diseases or show the ability of the nervous system to modify brain topology at all angles and brain plasticity according to input stimuli. In this study, we particularly focused on Alzheimer’s disease.

Decentralized adaptive tracking control for high-order interconnected stochastic nonlinear time-varying delay systems with stochastic input-to-state stable inverse dynamics by neural networks

2019 ◽  
Vol 41 (13) ◽  
pp. 3612-3625 ◽  
Author(s):  
Wang Qian ◽  
Wang Qiangde ◽  
Wei Chunling ◽  
Zhang Zhengqiang
Keyword(s):  
Neural Networks ◽  
Tracking Control ◽  
Large Scale ◽  
Inverse Dynamics ◽  
Small Neighborhood ◽  
High Order ◽  
Interconnected Systems ◽  
Delay Systems ◽  
Rbf Neural Networks ◽  
Stochastic Input

The paper solves the problem of a decentralized adaptive state-feedback neural tracking control for a class of stochastic nonlinear high-order interconnected systems. Under the assumptions that the inverse dynamics of the subsystems are stochastic input-to-state stable (SISS) and for the controller design, Radial basis function (RBF) neural networks (NN) are used to cope with the packaged unknown system dynamics and stochastic uncertainties. Besides, the appropriate Lyapunov-Krosovskii functions and parameters are constructed for a class of large-scale high-order stochastic nonlinear strong interconnected systems with inverse dynamics. It has been proved that the actual controller can be designed so as to guarantee that all the signals in the closed-loop systems remain semi-globally uniformly ultimately bounded, and the tracking errors eventually converge in the small neighborhood of origin. Simulation example has been proposed to show the effectiveness of our results.

scholarly journals Investigation of Improved Cooperative Coevolution for Large-Scale Global Optimization Problems

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 146
Author(s):  
Aleksei Vakhnin ◽  
Evgenii Sopov
Keyword(s):  
Global Optimization ◽  
Evolutionary Algorithms ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
State Of The Art ◽  
Fixed Number ◽  
High Dimensional ◽  
Cooperative Coevolution ◽  
Large Scale Problems

Modern real-valued optimization problems are complex and high-dimensional, and they are known as “large-scale global optimization (LSGO)” problems. Classic evolutionary algorithms (EAs) perform poorly on this class of problems because of the curse of dimensionality. Cooperative Coevolution (CC) is a high-performed framework for performing the decomposition of large-scale problems into smaller and easier subproblems by grouping objective variables. The efficiency of CC strongly depends on the size of groups and the grouping approach. In this study, an improved CC (iCC) approach for solving LSGO problems has been proposed and investigated. iCC changes the number of variables in subcomponents dynamically during the optimization process. The SHADE algorithm is used as a subcomponent optimizer. We have investigated the performance of iCC-SHADE and CC-SHADE on fifteen problems from the LSGO CEC’13 benchmark set provided by the IEEE Congress of Evolutionary Computation. The results of numerical experiments have shown that iCC-SHADE outperforms, on average, CC-SHADE with a fixed number of subcomponents. Also, we have compared iCC-SHADE with some state-of-the-art LSGO metaheuristics. The experimental results have shown that the proposed algorithm is competitive with other efficient metaheuristics.

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