Numerical solution of the Schrödinger equation by neural network and genetic algorithm

Michihiko Sugawara

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

A new approach for solving the Schrödinger equation based on genetic algorithm (GA) and artificial neural network (NN) is presented. Feed-forward perceptron-type network is used to represent the wavefunction, while network parameters are optimized by micro-genetic algorithm so that the NN satisfies the Schrödinger equation. In the GA breeding process, random point evaluation method (RPEM) for fitness evaluation is introduced to improve the convergence. Final solution is obtained by invoking deterministic optimizer which corresponds to a "learning process" of the NN. The present method is tested in the calculation of one-dimensional harmonic oscillator and other model potentials.

Original languageEnglish
Pages (from-to)366-380
Number of pages15
JournalComputer Physics Communications
Volume140
Issue number3
DOIs
Publication statusPublished - 2001 Nov 1

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genetic algorithms
Genetic algorithms
Neural networks
Wave functions
Random processes
self organizing systems
fitness
random processes
evaluation
harmonic oscillators
learning

Keywords

  • Eigenvalue problems
  • Genetic Algorithm
  • Neural network
  • Schrödinger equation

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

Numerical solution of the Schrödinger equation by neural network and genetic algorithm. / Sugawara, Michihiko.

In: Computer Physics Communications, Vol. 140, No. 3, 01.11.2001, p. 366-380.

Research output: Contribution to journalArticle

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