Universal Approximation Using Radial-Basis-Function Networks

By Jooyoung Park, I. Sandberg. 1991

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Citations in the corpus

Surrogate-Assisted Evolutionary Deep Learning Using an End-to-End Random Forest-Based Performance Predictor (2020, background): “This is theoretically evidenced by the universal approximation theorem [56] that the learning curve-based approaches can achieve promising performance only when the learning curve is smooth.”
Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification (2018, neutral): “Popular choices for surrogate models in the literature include, Gaussian processes [11, 12, 13, 14, 15], polynomial chaos expansions [16, 17, 18, 19], radial basis functions [20] and relevance vector machines [21].”
Fix your classifier: the marginal value of training the last weight layer (2018, background): “Past work noted the fact that predeﬁned (Park & Sandberg, 1991) and random (Huang et al., 2006) projections can be used together with a learned afﬁne transformation to achieve competitive results on several tasks.”
Trainability and Accuracy of Artificial Neural Networks: An Interacting Particle System Approach (2018, background): “At the core of our understanding of the approximation properties of neural networks are the well-known “universal approximation theorems” that specify the conditions under which a neural network can represent a target function with arbitrary accuracy [6, 14, 28].”
Applications of classical approximation theory to periodic basis function networks and computational harmonic analysis (2013, background): “Under mild conditions on φ, it was proved by Park and Sandberg [70] that the class of all RBF networks { M ∑ k=1 akφ(| ◦ −xk |) : M ≥ 1, xk ∈ Rq }”
Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks (2021, background): “Since RBFs can be represented in a neural network with a single hidden layer [56, 57], the neural network solution optimizes the location of the centers {xi}i=1 as well as the support-widths {βi}i=1 [56].”
Comparative study on methods of detecting research fronts using different types of citation (2009, methodology): “(RBFN) is an alternative to highly nonlinearity-in-theparameters neural network ( Park & Sandberg, 1991 ), which meansthedeterminantsofneuralcentershavehighnonlinearity.”
Using Cross Validation to Design Conservative Surrogates (2010, background): “With advances in computer throughput, surrogates such as kriging [30,31], radial basis neural networks [50,51], and support vector regression [52,53] increasingly share a place with the traditional polynomial response surface [32,33].”
Mathematical model of liquid–liquid equilibrium for a ternary system using the GMDH-type neural network and genetic algorithm (2012, background): “Giving enough data, they can approximate the underlying function with accuracy [33,34].”
Time series forecasting for nonlinear and non-stationary processes: a review and comparative study (2015, background): “of nonlinearity and are universal approximators (Park and Sandberg, 1991); i.”
A review of analytical techniques for gait data. Part 2: neural network and wavelet methods. (2001, background): “Other proven alternatives such as the radial basis function [10] which also boasts the universal approximation property [47], have not yet been investigated.”
Machine Learning for Wireless Networks with Artificial Intelligence: A Tutorial on Neural Networks (2017, background): “RBF networks have been applied across many applications [149]– [153] including function approximation, stock prediction, classification, and face recognition.”
Training Neural Networks as Learning Data-adaptive Kernels: Provable Representation and Approximation Benefits (2019, background): “Concrete cases for the latter approach include: polynomials (Stone-Weierstrass, Bernstein), radial-basis (Park and Sandberg, 1991; Niyogi and Girosi, 1996), two-layer and multi-layer neural networks (Cybenko, 1989; Hornik et al.”
Adaptive neural control of uncertain MIMO nonlinear systems (2004, methodology): “In control engineering, radial basis function (RBF) NNs are usually used as a tool for modeling nonlinear functions because of their good capabilities in function approximation [35].”
A comprehensive evaluation of random vector functional link networks (2016, methodology): “Single layer feedforward neural networks (SLFN) have been widely applied to solve problems such as classification and regression because of their universal approximation capability [14, 20, 31, 17].”