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

Michihiko Sugawara

doi:10.1016/S0010-4655(01)00286-7

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

Michihiko Sugawara

Department of Chemistry

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	366-380
Number of pages	15
Journal	Computer Physics Communications
Volume	140
Issue number	3
DOIs	https://doi.org/10.1016/S0010-4655(01)00286-7
Publication status	Published - 2001 Nov 1

Fingerprint

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

Sugawara, M. (2001). Numerical solution of the Schrödinger equation by neural network and genetic algorithm. Computer Physics Communications, 140(3), 366-380. https://doi.org/10.1016/S0010-4655(01)00286-7

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 journal › Article

Sugawara, M 2001, 'Numerical solution of the Schrödinger equation by neural network and genetic algorithm', Computer Physics Communications, vol. 140, no. 3, pp. 366-380. https://doi.org/10.1016/S0010-4655(01)00286-7

Sugawara M. Numerical solution of the Schrödinger equation by neural network and genetic algorithm. Computer Physics Communications. 2001 Nov 1;140(3):366-380. https://doi.org/10.1016/S0010-4655(01)00286-7

Sugawara, Michihiko. / Numerical solution of the Schrödinger equation by neural network and genetic algorithm. In: Computer Physics Communications. 2001 ; Vol. 140, No. 3. pp. 366-380.

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Access to Document

10.1016/S0010-4655(01)00286-7