Using Radial Basis Function Networks for Function Approximation and Classification

Wu, Yue; Wang, Hui; Zhang, Biaobiao; Du, Ke-Lin

doi:10.5402/2012/324194

Cited by 154 publications

(84 citation statements)

References 132 publications

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“…No que diz respeito às técnicas, várias são as abordagens de cálculo numérico e métodos estatísticos utilizados para a resolução desse problema, tais como: interpolação, splines, séries de potências, regressão por funções de núcleo, entre outros. Há ainda abordagens baseadas em Inteligência Computacional, como Multilayer Perceptron (MLP) [10], Radial Basis Function Network (RBFN) [11], Neuro-fuzzy Systems [12].…”

Section: Aproximação De Funçãounclassified

‘Wolf-Pack Approximation’ utilizando funções de núcleo

Pessoa¹,

Neto²,

Menezes³

2016

Anais Do 11. Congresso Brasileiro De Inteligência Computacional

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Abstract-Through metaphors of natural phenomena, one can construct computational models that are able to simulate or solve complex problems. Often, those are more intuitive to use and less computationally expensive to run . Within complex problems, function approximation features as a very important class of problems, since functions are good ways to represent real-world problems or to describe reality from a sparse set of entries (e.g. points). Even though the vast range of techniques in existence for dealing with approximation of functions such as linear programming, e.g, the SIMPLEX algorithm, in the worst case, they are of exponential complexity O(2 n ). On the other hand, the very good approach of some metaheuristic such as artificial neural networks, completely lack in explanatory power towards the underlying relationships with the data.. In this context Wolf-Pack Approximation (WPA), although another metaheuristic, features as a new computational alternative to the approximation problem of a given set of entry points. This paper put forward an enlarged and restructured version of WPA, which had some important limitations in its inception, namely, (i) the lack of communication between the wolves and (ii) the use of simple function (i.e. circles) for modeling the contour of the input points of the problems. Thus, in this work we propose mechanisms to increase the effectiveness of the initial version of WPA. To validate the current proposition, WPA2 was used in complex tasks of digital image representation, where several analyses and comparison were performed. Keywords-Multiagent I. INTRODUÇÃODiversas são as técnicas e algoritmos inspirados no comportamento de animais na natureza para a resolução de problemas que surgiram nas últimas décadas. Essa abordagem mostra-se promissora e já apresentou resultados pelo seu poder de abstração e eficácia, porém ela é desafiadora, já que requer conhecimento em diferentes áreas de conhecimento. Através de metáforas com os fenômenos da Natureza, pode-se construir um modelo computacional que se proponha a simular o ambiente e resolver problemas complexos, geralmente de forma mais intuitiva O motivo para a existência de técnicas e abordagens diferentes dessa área é a sua aplicabilidade (e efetividade) em problemas específicos. Cada uma delas possui vantagens para resolver problemas com características em comum. No que diz respeito a problemas complexos, a aproximação de função é uma classe de problemas bastante importante, uma vez que funções podem representar problemas do mundo real ou descrever alguma realidade a partir de um conjunto de pontos. Além disso, a aproximação de funções é bastante utilizada para a resolução de problemas de classificação e reconhecimento de padrões [4], predição, compressão de dados [5], aprendizagem por reforço, processamento e reconstrução de imagens [6]. A Programação Linear utilizando o algoritmo SIMPLEX possui, no pior caso, complexidade exponencial O(2n) [7] (i.e. escala exponencialmente com o tamanho da entrada do problema de aproximação...

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Section: Aproximação De Funçãounclassified

‘Wolf-Pack Approximation’ utilizando funções de núcleo

Pessoa¹,

Neto²,

Menezes³

2016

Anais Do 11. Congresso Brasileiro De Inteligência Computacional

View full text Add to dashboard Cite

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“…Gaussian RBFs are local and are the most commonly used across several applications. Other type of kernels for RBF can also be used with more specific purposes (Wu et al, 2012).…”

Section: Dimensionality Reduction Via Proper Orthogonal Decompositionmentioning

confidence: 99%

“…Choosing all points as RBF centers will therefore lead to an unnecessarily large network involving long training and computation times. An effective way of reducing the number of nodes in the hidden layer is by clustering the input points such that each point falls into one of the hyperspheres which collectively span the entire input space (Wu et al, 2012). Each of the RBF centers are then to be located at the centroid of each cluster.…”

Section: Dimensionality Reduction Via Proper Orthogonal Decompositionmentioning

confidence: 99%

“…We will address the time dependent formulation in a separate work. In any case, we should remark that RBF networks have been successfully applied in the context of modeling dynamical systems (Wu et al, 2012). Figure 7 depicts in more detail the proposed workflow.…”

Section: Dimensionality Reduction Via Proper Orthogonal Decompositionmentioning

confidence: 99%

“…The non-intrusive character of our approach resides in the reconstruction of the high-dimensional interactions via a Radial Basis Function (RBF) network (Haykin et al, 2009;Kecman, 2001;Wu et al, 2012). RBF networks are particularly convenient in the present work given their computational efficiency and local character to approximate input/output interactions as opposed to multi-layered artificial neural networks (Haykin et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

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Unlocking Fast Reservoir Predictions via Non-Intrusive Reduced Order Models

Klíe

2013

All Days

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The present paper proposes a novel non-intrusive model reduction approach based on Proper Orthogonal Decomposition (POD), the Discrete Empirical Interpolation Method (DEIM) and Radial Basis Function (RBF) networks to efficiently predict production of oil and gas reservoirs. Provided a representative set of training reservoir scenarios, either POD or DEIM allows for effectively projecting input parameters (e.g., permeability, porosity), states (e.g., pressure, saturations) and outputs (e.g., well production curves) into a much lower dimension that retains the main features contained in the simulation system. In this work, these projections are applied across multiple levels to be able to collapse a large number of spatio-temporal correlations. It is observed that these projections can be effectively performed at a large extent regardless of the underlying geological complexity and operational constraints associated with the reservoir model. The RBF network provides a powerful means for developing learning functions from input-output relationships described by the reservoir dynamics entailed by multiple combinations of inputs and controls. In order to achieve a high degree of predictability from the resulting reduced model, the RBF network exploits locality by a means of Gaussian basis functions that are maximal at the sampled point and decrease monotonically with distance. Compared to multilayer perceptron networks (i.e., traditional artificial neural networks) RBF networks require less training and are less sensitive to the presence of noise in the data. In this regard, POD or DEIM acts as a data filter that additionally aids at designing a more compact RBF network representation suitable for targeting fast reservoir predictions. Numerical results show significant accelerations with respect to running the original simulation model on a set of field-motivated cases.

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Radial basis function‐based Pareto optimization of an outer rotor brushless DC motor

Rahmani,

Sadrossadat,

Noohi

et al. 2024

Int J Numerical Modelling

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This paper presents the development of an optimization and modeling method for the objective functions of output power, efficiency and weight of an outer rotor permanent magnet brushless DC (BLDC) motor based on radial basis function (RBF) approximation technique. The proposed RBF‐based Pareto optimization method requires less knowledge about electric/magnetic formulas and can replace conventional optimizations based on these equations with higher accuracy. To apply the proposed optimization method, the initial design should be developed using such equations. Therefore, RBFs are used to model and predict engine behavior. To optimize the objective functions, we used a genetic algorithm optimization technique with nonlinear electric and magnetic constraints to find the Pareto front set. The design obtained by the proposed radial basis function Pareto optimization (RBFPO) method was finally verified by Ansoft Maxwell. The results of optimal design using the RBFPO method have higher output power and efficiency. Also, in addition to the advantage of a favorable accuracy, RBF‐based models are significantly faster than models available in simulation tools.

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Using Radial Basis Function Networks for Function Approximation and Classification

Cited by 154 publications

References 132 publications

‘Wolf-Pack Approximation’ utilizando funções de núcleo

‘Wolf-Pack Approximation’ utilizando funções de núcleo

Unlocking Fast Reservoir Predictions via Non-Intrusive Reduced Order Models

Radial basis function‐based Pareto optimization of an outer rotor brushless DC motor

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