Multifidelity surrogate modeling based on radial basis functions

Multiple models of a physical phenomenon are sometimes available with different levels of approximation. The high fidelity model is more computationally demanding than the coarse approximation. In this context, including information from the lower fidelity model to build a surrogate model is desirable. Here, the study focuses on the design of a miniaturized photoacoustic gas sensor which involves two numerical models. First, a multifidelity metamodeling method based on Radial Basis Function, the co-RBF, is proposed. This surrogate model is compared with the classical co-kriging method on two analytical benchmarks and on the photoacoustic gas sensor. Then an extension to the multifidelity framework of an already existing RBF-based optimization algorithm is applied to optimize the sensor efficiency. The co-RBF method does not bring better results than co-kriging but can be considered as an alternative for multifidelity metamodeling.     

An efficient truss structure optimization framework based on CAD/CAE integration and sequential radial basis function metamodel

In order to improve the performance and efficiency of truss structure optimization, this paper presents a general framework that embeds and seamlessly integrates commercial CAD and CAE software through common programming languages and application programming interface (API). Along with the automatic CAD/CAE integration, an adaptive metamodel-based optimization called sequential radial basis function (SRBF) is applied to truss structure optimization involving sizing, geometry and topology variables. SRBF distinguishingly features two-loops searching strategy, the “inner loop” and the “outer loop”. The “inner loop” aims to search a feasible point through updating the factors of the augmented Lagrangian function. With the improved significant sampling space (ISSS) method, the “outer loop” sequentially generates new additional samples to update the RBF model. The continuous relaxation method is developed to deal with the mixed-discrete variables during the truss structure optimization. Applied to practical truss structure optimization problems from small scale to large scale, the proposed framework demonstrates feasibility of the CAD/CAE integration system during the structure modeling and analysis, and facilitates the truss structure optimization process. The comparison results between the SRBF and other approaches show that SRBF improves merit of searching global optimum and reduces the computation cost.     

基于动态径向基神经网络的人脸识别算法研究

提出了一个通用而且有效的方法来设计RBF神经网络分类器用于人脸识别。为了避免过拟合和减少计算量,用主元分析法和Fisher线性判别技术来降低维数,以提取人脸特征;利用一个混合的学习算法来训练RBF神经网络,使梯度下降法的搜索空间大大减少;采用一种基于训练样本类别信息的新的聚类算法,所有同类的数据可被聚集在一起,尽量减少不同类数据混杂在一起,同时选取结构尽可能紧凑的RBF神经网络分类器。在ORL数据库上进行了仿真,实验结果表明,该算法具有高效性和有效性。     

Robustness of radial basis functions

Neural networks are intended to be used in future nanoelectronic technology since these architectures seem to be robust to malfunctioning elements and noise in its inputs and parameters. In this work, the robustness of radial basis function networks is analyzed in order to operate in noisy and unreliable environment. Furthermore, upper bounds on the mean square error under noise contaminated parameters and inputs are determined if the network parameters are constrained. To achieve robuster neural network architectures fundamental methods are introduced to identify sensitive parameters and neurons.     

Sequential improvement for robust optimization using an uncertainty measure for radial basis functions

The performance of the sequential metamodel based optimization procedure depends strongly on the chosen building blocks for the algorithm, such as the used metamodeling method and sequential improvement criterion. In this study, the effect of these choices on the efficiency of the robust optimization procedure is investigated. A novel sequential improvement criterion for robust optimization is proposed, as well as an improved implementation of radial basis function interpolation suitable for sequential optimization. The leave-one-out cross-validation measure is used to estimate the uncertainty of the radial basis function metamodel. The metamodeling methods and sequential improvement criteria are compared, based on a test with Gaussian random fields as well as on the optimization of a strip bending process with five design variables and two noise variables. For this process, better results are obtained in the runs with the novel sequential improvement criterion as well as with the novel radial basis function implementation, compared to the runs with conventional sequential improvement criteria and kriging interpolation.     

Global optimization based on active preference learning with radial basis functions

Machine Learning - This paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such...     

紧支径向基函数插值实现多维数据可视化

通过分析某城市空气质量数值预报数据的时空组织结构,构建出了多维空间数据的整体框架。论述了几种插值方法的优缺点,在比较的基础上,将新的紧支径向基函数局部径向点插值方法引入到多维数据处理中,在空间、时间维度上对数据进行局部插值,从而实现数据的重构。以新的基于封装回调函数的多线程方法实现了大规模空气质量预报数据的三维动态可视化。实验结果表明,以上方法应用于大规模数据可视化时,其质量和运算速度都能满足实际需要。     

全局正定径向基函数在图像分割中的应用

将全局正定径向基函数和图像分割中基于偏微分方程水平集方法的发展方程相结合,提出了一种基于全局正定径向基函数的图像分割算法。用全局正定径向基函数插值发展方程中的水平集函数,得到的插值函数具有较高的精度和光滑性,克服了传统水平集方法中复杂费时的重新初始化过程和水平集对初始轮廓位置敏感等缺点,非线性发展方程最终被转化成常微分方程组并用Euler法求解。实验结果表明该算法不需要重新初始化过程,并且在没有初始轮廓时也能够快速正确地分割图像。     

Using radial basis functions to approximate a function and itserror bounds

A novel network called the validity index network (VI net) is presented. The VI net, derived from radial basis function networks, fits functions and calculates confidence intervals for its predictions, indicating local regions of poor fit and extrapolation     

Metamodeling using extended radial basis functions: a comparative approach

The process of constructing computationally benign approximations of expensive computer simulation codes, or metamodeling, is a critical component of several large-scale multidisciplinary design optimization (MDO) approaches. Such applications typically involve complex models, such as finite elements, computational fluid dynamics, or chemical processes. The decision regarding the most appropriate metamodeling approach usually depends on the type of application. However, several newly proposed kernel-based metamodeling approaches can provide consistently accurate performance for a wide variety of applications. The authors recently proposed one such novel and effective metamodeling approach—the extended radial basis function (E-RBF) approach—and reported highly promising results. To further understand the advantages and limitations of this new approach, we compare its performance to that of the typical RBF approach, and another closely related method—kriging. Several test functions with varying problem dimensions and degrees of nonlinearity are used to compare the accuracies of the metamodels using these metamodeling approaches. We consider several performance criteria such as metamodel accuracy, effect of sampling technique, effect of sample size, effect of problem dimension, and computational complexity. The results suggest that the E-RBF approach is a potentially powerful metamodeling approach for MDO-based applications, as well as other classes of computationally intensive applications.     

A novel model modification method for support vector regression based on radial basis functions

Structural and Multidisciplinary Optimization - There are some inherent limitations to the performance of support vector regression (SVR), such as (i) the loss function, penalty parameter, and...     

Indexed families of functionals and gaussian radial basis functions

We report on results concerning the capabilities of gaussian radial basis function networks in the setting of inner product spaces that need not be finite dimensional. Specifically, we show that important indexed families of functionals can be uniformly approximated, with the approximation uniform also with respect to the index. Applications are described concerning the classification of signals and the synthesis of reconfigurable classifiers.     

Fast evaluation of radial basis functions: I

This paper describes some new techniques for the rapid evaluation and fitting of radial basic functions. The techniques are based on the hierarchical and multipole expansions recently introduced by several authors for the calculation of many-body potentials. Consider in particular the N term thin-plate spline, s(x) = Σ_j=1^N d_jφ(x−x_j), where φ(u) = |u|²log|u|, in 2-dimensions. The direct evaluation of s at a single extra point requires an extra O(N) operations. This paper shows that, with judicious use of series expansions, the incremental cost of evaluating s(x) to within precision ε, can be cut to O(1+|log ε|) operations. In particular, if A is the interpolation matrix, a_i,j = φ(x_i−x_j, the technique allows computation of the matrix-vector product Ad in O(N), rather than the previously required O(N²) operations, and using only O(N) storage. Fast, storage-efficient, computation of this matrix-vector product makes pre-conditioned conjugate-gradient methods very attractive as solvers of the interpolation equations, Ad = y, when N is large.     

A new class of oscillatory radial basis functions

Radial basis functions (RBFs) form a primary tool for multivariate interpolation, and they are also receiving increased attention for solving PDEs on irregular domains. Traditionally, only nonoscillatory radial functions have been considered. We find here that a certain class of oscillatory radial functions (including Gaussians as a special case) leads to nonsingular interpolants with intriguing features especially as they are scaled to become increasingly flat. This flat limit is important in that it generalizes traditional spectral methods to completely general node layouts. Interpolants based on the new radial functions appear immune to many or possibly all cases of divergence that in this limit can arise with other standard types of radial functions (such as multiquadrics and inverse multiquadratics).     

Hybrid metamodel of radial basis function and polynomial chaos expansions with orthogonal constraints for global sensitivity analysis

Structural and Multidisciplinary Optimization - In this study, a hybrid metamodel using the orthogonal constraints of radial basis function and sparse polynomial chaos expansions is proposed for...     

An interactive approach for CBIR using a network of radial basis functions

An important requirement for constructing effective content-based image retrieval (CBIR) systems is accurate characterization of visual information. Conventional nonadaptive models, which are usually adopted for this task in simple CBIR systems, do not adequately capture all aspects of the characteristics of the human visual system. An effective way of addressing this problem is to adopt a "human-computer" interactive approach, where the users directly teach the system about what they regard as being significant image features and their own notions of image similarity. We propose a machine learning approach for this task, which allows users to directly modify query characteristics by specifying their attributes in the form of training examples. Specifically, we apply a radial-basis function (RBF) network for implementing an adaptive metric which progressively models the notion of image similarity through continual relevance feedback from users. Experimental results show that the proposed methods not only outperform conventional CBIR systems in terms of both accuracy and robustness, but also previously proposed interactive systems.     

Approximation of insurance liability contracts using radial basis functions

ABSTRACT

We introduce the Option Interpolation Model (OIM) for accurate approximation of embedded option values in insurance liabilities. Accurate approximation is required for ex-ante risk management applications. The OIM is based on interpolation with radial basis functions, which can interpolate scattered data, and does not suffer from the curse of dimensionality. To reduce computation time we present an inversion method to determine the interpolation function weights. The robustness, accuracy and efficiency of the OIM are investigated in several numerical experiments. We show that the OIM results in highly accurate approximations.     

Unified uncertainty representation and quantification based on insufficient input data

Uncertainty quantification accuracy of system performance has an important influence on the results of reliability-based design optimization (RBDO). A new uncertain identification and quantification methodology is proposed considering the strong statistical variables, sparse variables, and interval variables simultaneously. Maximum likelihood function and Akaike information criterion (AIC) methods are used to identify the best-fitted distribution types and distribution parameters of sparse variables. The interval variables are represented with evidence theory. Finally, a unified uncertainty quantification framework considering the three types of uncertain design variables is put forward, and then the failure probability of system performance is quantified with belief and plausibility measures. The Kriging metamodel and random sampling method are used to reduce the computational complexity. Three examples are illustrated to verify the effectiveness of the proposed methodology.     

Fuzzy entropy functions based on perceived uncertainty

Knowledge and Information Systems - The paper presents fuzzy entropy functions based on perceived vagueness. The proposed entropy functions are based on the principle that different agents may...