本文主要說明輻狀基底函數(RBF)類神經網路以及微分再生核法(DRKM)之理論基礎，以比較兩者模擬方法上的差異。輻狀基底函數類神經網路主要是以中心點之選取求得標準差，以決定影響寬度來控制整個網路的運算，其模擬方式有二，分別為：1.隨機選取中心點：以控制中心點數目進行分析。2.以垂直最小平方法選取中心點：以指定誤差容忍度進行模擬。而微分再生核法主要是以影響半徑的選取來控制其模擬之準確度。本文並藉以例題討論模擬之準確性以及適用的問題，以作為日後模擬實際問題之參考。
　　其結果顯示RBF隨機選取之中心點數目越多，其內插近似的效果越好，在中心點數目超過一定之比例時，準確度以可超越DRKM之模擬結果；而RBF以垂直最小平方法選取中心點雖然能控制中心點的選取，但計算效率受資料點數目之影響甚大，對於較複雜之問題往往過於耗時。

This study mainly examines the theory of Radial Basis Function (RBF) and Differential Reproducing kernel Approximation Method (DRKM), and compares the differences between them. The entire network calculation of RBF is controlled by the central points. There are two techniques to simulate the procedure: First, select the central point set randomly: to carry out the analysis by controlling the number of central points. Second, select the central points by Orthogonal Least Squares: to carry out the analysis by allocating the tolerance of errors. DKSM controls its accuracy by influencing the selection of radius. This study provides some examples to discuss the accuracy and suitability of this procedure in order to provide references for further studies.
The results reveal that the approximate interpolation outcomes getting better if the RBF numbers of random selection of central points increase. When the numbers of central points go beyond specific percentage, its accuracy can surpass the result of DRKM. Although in the RBF we can control the selection of central points by the Orthogonal Least Squares, the efficiency of calculation is greatly affected by the amount of data. Therefore, it is time-consuming for complicated cases.

【1】Lucy,L.B. , “A numerical approach to the testing of the fission hypothesis.”TheAstron.J.8(12),1013-1024(1977)
【2】Nayroles, B.,Touzot, G .and P .Villon , “Generalizing the finite element method: Diffuse Approximation and Diffuse Element”,Comput.Mech.10,307-318(1992).
【3】Belytschko, T. Gu, L and L .u, Y .Y. ,“Fracture and crack growth by element-free Galerkin methods” ,Model. Simul. Mater. Sci. Engrg.2, 519-534(1994).
【4】Liu, W .K. Jun,S. and Zhang ,Y.F., “Reproducing kernel particle methods” ,Int. J. Numer. Methods in Fluids.20, 1081-1106(1994).
【5】Chen, J .S. Wu,C.T. and Liu W.K., “Reproducing kernel particle methods for Large Deformation Analysis of non-linear structures” ,Computer Methods in Applied Mechanics And Engineering.139,195-227.(1996).
【6】陳禎康,「微分再生核近似法於二維彈力之應用」,碩士論文,國立成功大學土木工程研究所,台南(2002).
【7】蘇俊銘,「微分再生核法之工程應用」,碩士論文,國立台灣科技大學營建工程研究所,台北(2006).
【8】黃家祥,「微分再生核法於雙向彎曲柱設計之運用」,碩士論文,國立台灣科技大學營建工程研究所,台北,(2007).
【9】Warren S. McCulloch and Walter Pitts, “A logical calculus of the ideas immanent in nervous activity.” in the Bulletin of Mathematical Biophysics 5:115-133.(1943).
【10】Rosenblatt, F. “The Perception: a probabilistic model for information storage & organization in the brain.” In the Psychological Review: 65 pp. 386-408.(1958).
【11】J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities.” Proceedings of the National Academy of Sciences of the United States of America, Vol. 79, No. 8, pp. 2554-2558 .(1982).
【12】R.L. Hardy, “Multiquadric equations of topography and other irregular surfaces.” J Geophys Res 76, pp. 1905–1915. (1971).
【13】Powell M.J.D. “Radial Basis Functions for Multivariate Interpolation: A Review. ”In Mason J.C. and Cox M.G. (eds) "Algorithms for Approximation ", Clarendon Press, Oxford, pp. 143-167.(1987).
【14】Broomhead, D. S. and Lowe, David , “Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks.”(1988).
【15】John Moody and Christian J. Darken, “Fast Learning in Networks of Locally-Tuned Processing Units.”(1989)
【16】S .Haykin, “A Comprehensive Foundation, Prentice Hall, Englewood Cliffs.”, NJ (1999).
【17】Chen S. “Orthogonal least squares learning algorithm for radial basis function networks [J].” IEEE Trans on NN,2(2) : 302- 309.(1991).
【18】吳伯壽,「元素釋放法之層狀邊界處理」,碩士論文,國立中央大學土木工程研究所,中壢,(2000).
【19】張斐章,張麗秋,黃浩倫 :類神經網路:理論與實務,東華書局, (2003).
【20】張麗秋、林永堂、張斐章 :結合OLS與SGA建構輻狀基底類神經網路於洪水預測之研究,台灣水利Vol.53,No.4,(2005).