Wave‐net

a multiresolution, hierarchical neural network with localized learning

Bhavik R. Bakshi, George Stephanopoulos

Research output: Contribution to journalArticle

182 Citations (Scopus)

Abstract

A Wave‐Net is an artificial neural network with one hidden layer of nodes, whose basis functions are drawn from a family of orthonormal wavelets. The good localization characteristics of the basis functions, both in the input and frequency domains, allow hierarchical, multiresolution learning of input‐output maps from experimental data. Furthermore, Wave‐Nets allow explicit estimation for global and local prediction error‐bounds, and thus lend themselves to a rigorous and explicit design of the network. This article presents the mathematical framework for the development of Wave‐Nets and discusses the various aspects of their practical implementation. Computational complexity arguments prove that the training and adaptation efficiency of Wave‐Nets is at least an order of magnitude better than other networks. In addition, it presents two examples on the application of Wave‐Nets; (a) the prediction of a chaotic time‐series, representing population dynamics, and (b) the classification of experimental data for process fault diagnosis.

Original languageEnglish (US)
Pages (from-to)57-81
Number of pages25
JournalAICHE Journal
Volume39
Issue number1
DOIs
StatePublished - Jan 1 1993
Externally publishedYes

Fingerprint

Population Dynamics
Learning
Neural networks
Efficiency
Population dynamics
Failure analysis
Computational complexity

ASJC Scopus subject areas

  • Biotechnology
  • Environmental Engineering
  • Chemical Engineering(all)

Cite this

Wave‐net : a multiresolution, hierarchical neural network with localized learning. / Bakshi, Bhavik R.; Stephanopoulos, George.

In: AICHE Journal, Vol. 39, No. 1, 01.01.1993, p. 57-81.

Research output: Contribution to journalArticle

@article{6898f1f87f024f28b062d01c4454cac9,
title = "Wave‐net: a multiresolution, hierarchical neural network with localized learning",
abstract = "A Wave‐Net is an artificial neural network with one hidden layer of nodes, whose basis functions are drawn from a family of orthonormal wavelets. The good localization characteristics of the basis functions, both in the input and frequency domains, allow hierarchical, multiresolution learning of input‐output maps from experimental data. Furthermore, Wave‐Nets allow explicit estimation for global and local prediction error‐bounds, and thus lend themselves to a rigorous and explicit design of the network. This article presents the mathematical framework for the development of Wave‐Nets and discusses the various aspects of their practical implementation. Computational complexity arguments prove that the training and adaptation efficiency of Wave‐Nets is at least an order of magnitude better than other networks. In addition, it presents two examples on the application of Wave‐Nets; (a) the prediction of a chaotic time‐series, representing population dynamics, and (b) the classification of experimental data for process fault diagnosis.",
author = "Bakshi, {Bhavik R.} and George Stephanopoulos",
year = "1993",
month = "1",
day = "1",
doi = "10.1002/aic.690390108",
language = "English (US)",
volume = "39",
pages = "57--81",
journal = "AICHE Journal",
issn = "0001-1541",
publisher = "American Institute of Chemical Engineers",
number = "1",

}

TY - JOUR

T1 - Wave‐net

T2 - a multiresolution, hierarchical neural network with localized learning

AU - Bakshi, Bhavik R.

AU - Stephanopoulos, George

PY - 1993/1/1

Y1 - 1993/1/1

N2 - A Wave‐Net is an artificial neural network with one hidden layer of nodes, whose basis functions are drawn from a family of orthonormal wavelets. The good localization characteristics of the basis functions, both in the input and frequency domains, allow hierarchical, multiresolution learning of input‐output maps from experimental data. Furthermore, Wave‐Nets allow explicit estimation for global and local prediction error‐bounds, and thus lend themselves to a rigorous and explicit design of the network. This article presents the mathematical framework for the development of Wave‐Nets and discusses the various aspects of their practical implementation. Computational complexity arguments prove that the training and adaptation efficiency of Wave‐Nets is at least an order of magnitude better than other networks. In addition, it presents two examples on the application of Wave‐Nets; (a) the prediction of a chaotic time‐series, representing population dynamics, and (b) the classification of experimental data for process fault diagnosis.

AB - A Wave‐Net is an artificial neural network with one hidden layer of nodes, whose basis functions are drawn from a family of orthonormal wavelets. The good localization characteristics of the basis functions, both in the input and frequency domains, allow hierarchical, multiresolution learning of input‐output maps from experimental data. Furthermore, Wave‐Nets allow explicit estimation for global and local prediction error‐bounds, and thus lend themselves to a rigorous and explicit design of the network. This article presents the mathematical framework for the development of Wave‐Nets and discusses the various aspects of their practical implementation. Computational complexity arguments prove that the training and adaptation efficiency of Wave‐Nets is at least an order of magnitude better than other networks. In addition, it presents two examples on the application of Wave‐Nets; (a) the prediction of a chaotic time‐series, representing population dynamics, and (b) the classification of experimental data for process fault diagnosis.

UR - http://www.scopus.com/inward/record.url?scp=0027147212&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027147212&partnerID=8YFLogxK

U2 - 10.1002/aic.690390108

DO - 10.1002/aic.690390108

M3 - Article

VL - 39

SP - 57

EP - 81

JO - AICHE Journal

JF - AICHE Journal

SN - 0001-1541

IS - 1

ER -