TY - JOUR
T1 - Numerical solution of the Schrödinger equation by neural network and genetic algorithm
AU - Sugawara, M.
N1 - Funding Information:
This work is supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture and, in part, by “Research and Development Applying Advanced Computational Science and Technology” of Japan Science and Technology Corporation. Authors are grateful to Dr. D.L. Carroll for his Fortran GA driver, which is open to the public on the Internet.
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
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U2 - 10.1016/S0010-4655(01)00286-7
DO - 10.1016/S0010-4655(01)00286-7
M3 - Article
AN - SCOPUS:0035501084
VL - 140
SP - 366
EP - 380
JO - Computer Physics Communications
JF - Computer Physics Communications
SN - 0010-4655
IS - 3
ER -