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A NOVEL HYBRID SEQUENTIAL DESIGN STRATEGY FOR GLOBAL SURROGATE MODELING OF COMPUTER EXPERIMENTS

SIAM JOURNAL ON SCIENTIFIC COMPUTING 2011年第4期33卷 1948-1974页

作者： Crombecq, Karel Gorissen, Dirk Deschrijver, Dirk Dhaene, Tom Univ Antwerp Dept Math & Comp Sci COMP Res Grp B-2020 Antwerp Belgium Univ Ghent IBBT IBCN Res Grp INTEC B-9050 Ghent Belgium

Many complex real-world systems can be accurately modeled by simulations. However, high-fidelity simulations may take hours or even days to compute. Because this can be impractical, a surrogate model is often used to approximate the dynamic behavior of the original simulator. This model can then be used as a cheap, drop-in replacement for the simulator. Because simulations can be very expensive, the data points, which are required to build the model, must be chosen as optimally as possible. Sequential design strategies offer a huge advantage over one-shot experimental designs because they can use information gathered from previous data points in order to determine the location of new data points. Each sequential design strategy must perform a trade-off between exploration and exploitation, where the former involves selecting data points in unexplored regions of the design space, while the latter suggests adding data points in regions which were previously identified to be interesting (for example, highly nonlinear regions). In this paper, a novel hybrid sequential design strategy is proposed which uses a Monte Carlo-based approximation of a Voronoi tessellation for exploration and local linear approximations of the simulator for exploitation. The advantage of this method over other sequential design methods is that it is independent of the model type, and can therefore be used in heterogeneous modeling environments, where multiple model types are used at the same time. The new method is demonstrated on a number of test problems, showing that it is a robust, competitive, and efficient sequential design strategy.

关键词： sequential design active learning local linear approximation experimental design nonlinear function approximation

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nonlinear function approximation: Computing smooth solutions with an adaptive greedy algorithm

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JOURNAL OF approximation THEORY 2006年第2期143卷 159-175页

作者： Hofinger, Andreas Austrian Acad Sci Johann Radon Inst Computat & Appl Math Linz Austria

In contrast to linear schemes, nonlinear approximation techniques allow for dimension independent rates of convergence. Unfortunately, typical algorithms (such as, e.g., backpropagation) are not only computationally demanding, but also unstable in the presence of data noise. While we can show stability for a weak relaxed greedy algorithm, the resulting method has the drawback that it requires in practise unavailable smoothness information about the data. In this work we propose an adaptive greedy algorithm which does not need this information but rather recovers it iteratively from the available data. We show that the generated approximations are always at least as smooth as the original function and that the algorithm also remains stable, when it is applied to noisy data. Finally, the applicability of this algorithm is demonstrated by numerical experiments. (c) 2006 ***. All rights reserved.

关键词： greedy algorithm nonlinear function approximation data noise regularization theory

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An Improved Cobb-Douglas Production function and its Artificial Neural Network Model

An Improved Cobb-Douglas Production Function and its Artific...

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2011 International Conference on Fuzzy Systems and Neural Computing(FSNC 2011)

作者： Jihong Shen Canxin Zhang Hao Hu Chunbo Lian College of Science Harbin Engineering University College of Automation Harbin Engineering University

For the problem of economic growth,the CobbDouglas(CD)production function is deformed by putting the labor and capital input into the three industries,and then a new production function is created by furtherly improving the *** artificial neural network(ANN)model is also established to simulate the new production *** model can present the economic growth factors,and it can also reflect the highly nonlinear internal relations among industrial structures by simulation of the relations between input elements and total *** show that the results given by this model are reliable and the artificial neural network algorithm is easy to *** model can be widely applied in economic problems.

关键词： Artificial neural network nonlinear function approximation Production function Economic growth.

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Incorporating statistical and neural network approaches for student course satisfaction analysis and prediction

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EXPERT SYSTEMS WITH APPLICATIONS 2010年第4期37卷 3358-3365页

作者： Guo, William W. Cent Queensland Univ Fac Arts Business Informat & Educ Rockhampton Qld 4702 Australia

Students' perception on course satisfaction through student surveys has become more influential in institutional operations because their experience in study may affect not only the prospective student's decision in choosing the institution for their tertiary education, but also the retention of existing students. Student course satisfaction is a multivariate nonlinear problem. Neural network (NN) techniques have been successfully applied to approximating nonlinear functions in many disciplines, but there has been little information available in applying NN to the modelling of student course satisfaction. In this paper, based on the student survey results collected from 43 courses in 11 semesters from 2002 to 2007, statistical analysis and NN techniques are incorporated for establishing some dynamic models for analysing and predicting student course satisfaction. The factors identified from this process also allow new strategies to be drawn for improving course satisfaction in the future. This study shows that both the number of students (NS) enrolled to a course and the high distinction (HD) rate in final grading are the two most influential factors to student course satisfaction. The three-layer multilayer perceptron (MLP) models outperform the linear regressions in predicting student course satisfaction, with the best outcome being achieved by combining both NS and HD as the input to the networks. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Neural networks Multilayer perceptron Linear regression Student course satisfaction nonlinear function approximation

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Approximating nonlinear Relations Between Susceptibility and Magnetic Contents in Rocks Using Neural Networks

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Tsinghua Science and Technology 2010年第3期15卷 281-287页

作者： William W Guo Michael Li Zhengxiang Li Greg Whymark Faculty of Arts Business lnformatics and Education Central Queensland University Rockhampton QLD 4701 Australia The Institute for Geoscience Research (TIGER) Curtin University of Technology Perth WA 6845 Australia

Correlations between magnetic susceptibility and contents of magnetic minerals in rocks are important in interpreting magnetic anomalies in geophysical exploration and understanding magnetic behaviors of rocks in rock magnetism studies. Previous studies were focused on describing such correlations using a sole expression or a set of expressions through statistical analysis. In this paper, we use neural network techniques to approximate the nonlinear relations between susceptibility and magnetite and/or hematite contents in rocks. This is the first time that neural networks are used for such study in rock magnetism and magnetic petrophysics. Three multilayer perceptrons are trained for producing the best possible estimation on susceptibility based on magnetic contents. These trained models are capable of producing accurate mappings between susceptibility and magnetite and/or hematite contents in rocks. This approach opens a new way of quantitative simulation using neural networks in rock magnetism and petrophysical research and applications.

关键词： neural networks nonlinear function approximation rock magnetism magnetic susceptibility magnetic contents

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Generalized neuron: Feedforward and recurrent architectures

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NEURAL NETWORKS 2009年第7期22卷 1011-1017页

作者： Kulkarni, Raghavendra V. Venayagamoorthy, Ganesh K. Missouri Univ Sci & Technol Real Time Power & Intelligent Syst Lab Dept Elect & Comp Engn Rolla MO USA

Feedforward neural networks such as multilayer perceptrons (MLP) and recurrent neural networks are widely used for pattern classification, nonlinear function approximation, density estimation and time series prediction. A large number of neurons are usually required to perform these tasks accurately, which makes the MLPs less attractive for computational implementations on resource constrained hardware platforms. This paper highlights the benefits of feedforward and recurrent forms of a compact neural architecture called generalized neuron (GN). This paper demonstrates that GN and recurrent GN (RGN) can perform good classification, nonlinear function approximation, density estimation and chaotic time series prediction. Due to two aggregation functions and two activation functions, GN exhibits resilience to the nonlinearities of complex problems. Particle swarm optimization (PSO) is proposed as the training algorithm for GN and RGN. Due to a small number of trainable parameters, GN and RGN require less memory and Computational resources. Thus, these structures are attractive choices for fast implementations on resource constrained hardware platforms. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Density estimation Generalized neuron nonlinear function approximation Particle swarm optimization (PSO) Classification Recurrent generalized neuron

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Performance Improvement of Direct Torque Control System Based on Dynamic Parameter Identification Technology

Performance Improvement of Direct Torque Control System Base...

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21st Chinese Control and Decision Conference

作者： Liu Hua Zhao Wei Li Zhanfeng Hebei Univ Engn Handan 056038 Peoples R China

ISBN: (纸本)9781424427239

In traditional direct torque control system, the torque and flux are directly controlled by means of optimum voltage vectors, where the stator resistance variation deteriorates the dynamic performance. It is necessary to improve estimation accuracy for stator flux and torque. Considering the effects of the stator resistance variation on direct torque control, a novel approach of stator resistance identification based on wavelet network is presented for dynamic performance in low speed status, optimizing the inverter control strategy. The wavelet transform decomposes the signal using dilated and translated wavelets in time-frequency domain into a series of correlation factors or wavelet coefficients. The wavelet network combines the mathematical feature of wavelet transform with learning scheme of conventional neural network into an organic unit, which has been applied to nonlinear function approximation and dynamical system modeling. The improved training algorithm is utilized to fulfill the network parameter initialization, increasing the network stabilization and convergence property. Therefore, the stator voltage vector can be obtained from the stator resistance identification result of wavelet network output, reducing the number of voltage sensors. The simulation results show that the steady state and dynamic performance was improved.

关键词： Torque and flux voltage vector resistance variation wavelet network optimization strategy nonlinear function approximation system modeling

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Incomplete series expansion for function approximation

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2007年第1期34卷 21-40页

作者： Groenwold, Albert A. Etman, L. F. P. Snyman, J. A. Rooda, J. E. Univ Stellenbosch Dept Mech Engn ZA-7602 Matieland South Africa Eindhoven Univ Technol Dept Mech Engn Syst Engn Grp NL-5600 MB Eindhoven Netherlands Univ Pretoria Dept Mech & Aeronaut Engn ZA-0002 Pretoria South Africa

We present an incomplete series expansion (ISE) as a basis for function approximation. The ISE is expressed in terms of an approximate Hessian matrix, which may contain second, third, and even higher order "main" or diagonal terms, but which excludes "interaction" or off-diagonal terms. From the ISE, a family of approximation functions may be derived. The approximation functions may be based on an arbitrary number of previously sampled points, and any of the function and gradient values at suitable previously sampled points may be enforced when deriving the approximation functions. When function values only are enforced, the storage requirements are minimal. However, irrespective of the conditions enforced, the approximate Hessian matrix is a sparse diagonal matrix. In addition, the resultant approximations are separable. Hence, the proposed approximation functions are very well-suited for use in gradient-based sequential approximate optimization requiring computationally expensive simulations;a typical example is structural design problems with many design variables and constraints. We derived a wide selection of approximations from the family of ISE approximating functions;these include approximations based on the substitution of reciprocal and exponential intervening variables. A comparison with popular approximating functions previously proposed illustrates the accuracy and flexibility of the new family of approximation functions. In fact, a number of popular approximating functions previously proposed for structural optimization applications derive from our ISE.

关键词： nonlinear function approximation sequential approximate optimization (SAO) incomplete series expansion (ISE)

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A spiking neural network architecture for nonlinear function approximation

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NEURAL NETWORKS 2001年第6-7期14卷 933-939页

作者： Iannella, N Back, AD RIKEN Brain Sci Inst Wako Saitama 3510198 Japan

Multilayer perceptrons have received much attention in recent years due to their universal approximation capabilities. Normally, such models use real valued continuous signals, although they are loosely based on biological neuronal networks that encode signals using spike trains. Spiking neural networks are of interest both from a biological point of view and in terms of a method of robust signaling in particularly noisy or difficult environments. It is important to consider networks based on spike trains. A basic question that needs to be considered however, is what type of architecture can be used to provide universal function approximation capabilities in spiking networks? In this paper, we propose a spiking neural network architecture using both integrate-and-fire units as well as delays, that is capable of approximating a real valued function mapping to within a specified degree of accuracy. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： spiking neurons integrate-and-fire units delays neural architecture nonlinear function approximation

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High-order neural network structure selection for function approximation applications using genetic algorithms

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS 2004年第1期34卷 150-158页

作者： Rovithakis, GA Chalkiadakis, I Zervakis, ME Aristotle Univ Thessaloniki Dept Elect & Comp Engn GR-54006 Thessaloniki Greece Tech Univ Crete Dept Elect & Comp Engn Iraklion 73100 Greece

Neural network literature for function approximation is by now sufficiently rich. In its complete form, the problem entails both parametric (i.e., weights determination) and structural learning (i.e., structure selection). The majority of works deal with parametric uncertainty assuming knowledge of the appropriate neural structure. In this paper we present an algorithmic approach to determine the structure of High Order Neural Networks (HONNs), to solve function approximation problems. The method is based on a Genetic Algorithm (GA) and is equipped with a stable update law to guarantee parametric learning. Simulation results on an illustrative example highlight the performance and give some insight of the proposed approach.

关键词： genetic algorithms neural networks nonlinear function approximation structure determination

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