Surface Fitting with Radial Basis Functions and Applications to Neural Networks.

Abstract

Summary. The following is a summary of the research of F. J. Narcowich and J. D. Ward supported by the Air Force during the period 6-92 through 8-95. Results dealing with center placement and stability for neural networks that employ radial basis functions (RBFs) were obtained, and led to convergent RBF identification algorithms with persistently excited regressor vector. A class of RBF-based methods that are grid-free and dimension-blind and that allow one to solve virtually any surface-fitting problem involving derivative information at scattered sites was discovered. For situations where the underlying geometries are noneuclidean-spheres or tori, for example, basis functions analogous to RBFs were developed; these provide tools to fit not only scattered data, but also scattered derivative-data. A class of nonstationary, orthogonal, well-localized periodic scaling functions and wavelets were constructed out of these bases, so that an integrated approach to handling both the representation and analysis of periodic data, even when the data are scattered or noisy, is provided.

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Document Details

Document Type
Technical Report
Publication Date
Oct 12, 1995
Accession Number
ADA312790

Entities

People

  • Francis J. Narcowich
  • Joseph D. Ward

Organizations

  • Texas Engineering Experiment Station

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Applied Mathematics
  • Artificial Intelligence
  • Computational Science
  • Convolution Integrals
  • Data Sets
  • Differential Equations
  • Engineering
  • Equations
  • Geometry
  • Identification
  • Mathematics
  • Neural Networks
  • Partial Differential Equations
  • Real Variables
  • Universities

Readers

  • Approximation Theory.
  • Neural Network Machine Learning.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms