### 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 |
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Pages (from-to) | 366-380 |

Number of pages | 15 |

Journal | Computer Physics Communications |

Volume | 140 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2001 Nov 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Computer Science Applications
- Physics and Astronomy(all)

### Cite this

*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.

Research output: Contribution to journal › Article

*Computer Physics Communications*, vol. 140, no. 3, pp. 366-380. https://doi.org/10.1016/S0010-4655(01)00286-7

}

TY - JOUR

T1 - Numerical solution of the Schrödinger equation by neural network and genetic algorithm

AU - Sugawara, Michihiko

PY - 2001/11/1

Y1 - 2001/11/1

N2 - 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.

AB - 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.

KW - Eigenvalue problems

KW - Genetic Algorithm

KW - Neural network

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=0035501084&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035501084&partnerID=8YFLogxK

U2 - 10.1016/S0010-4655(01)00286-7

DO - 10.1016/S0010-4655(01)00286-7

M3 - Article

VL - 140

SP - 366

EP - 380

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

IS - 3

ER -