Journal
COMPUTER PHYSICS COMMUNICATIONS
Volume 214, Issue -, Pages 31-38Publisher
ELSEVIER
DOI: 10.1016/j.cpc.2017.01.006
Keywords
Artificial neural network; Radial basis function; Coefficients of the potential function; Inverse problems; Eigenvalues of the Schrodinger operator; Finite element method
Funding
- European Unions Horizon research
- Innova-Chile CORFO [l0CEII-9007]
- PIA-CONICYT [PFBasal-01]
- Fondecyt [1140781]
- DIUBB [141709 4/R]
- Fisica de Altas Energias of the Universidad del Bio-Bio
- research and innovation programme under the Marie Sklodowska-Curie [644202]
- Marie Curie Actions (MSCA) [644202] Funding Source: Marie Curie Actions (MSCA)
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A numerical method based on artificial neural networks is used to solve the inverse Schrodinger equation for a multi-parameter class of potentials. First, the finite element method was used to solve repeatedly the direct problem for different parametrizations of the chosen potential function. Then, using the attainable eigenvalues as a training set of the direct radial basis neural network a map of new eigerivalues was obtained. This relationship was later inverted and refined by training an inverse radial basis neural network, allowing the calculation of the unknown parameters and therefore estimating the potential function. Three numerical' examples are presented in order to prove the effectiveness of the method. The results show that the method proposed has the advantage to use less computational resources without a significant accuracy loss. (C) 2017 Elsevier B.V. All rights reserved.
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