TY - JOUR

T1 - Neural network approach for the calculation of potential coefficients in quantum mechanics

AU - Ossandón, Sebastián

AU - Reyes, Camilo

AU - Cumsille, Patricio

AU - Reyes, Carlos M.

N1 - Funding Information:
S. Ossand?n acknowledges support from the European Unions Horizon 2020, research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 644202: Geophysical Exploration using Advanced Galerkin Methods (GEAGAM). C. Reyes thanks the partial support from Project Innova-Chile CORFO No. 10CEII-9007: ?CSIRO-CHILE International Centre of Excellence in Mining and Mineral Processing?, Program 3-Project 1. The work of P. Cumsille was founded by PIA-CONICYT under grant PFBasal-01. Finally, C. M. Reyes acknowledges support from Grant Fondecyt No. 1140781, DIUBB No. 141709 4/R and the group of Fisica de Altas Energias of the Universidad del Bio-Bio.
Publisher Copyright:
© 2017 Elsevier B.V.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - A numerical method based on artificial neural networks is used to solve the inverse Schrödinger 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 eigenvalues 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.

AB - A numerical method based on artificial neural networks is used to solve the inverse Schrödinger 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 eigenvalues 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.

KW - Artificial neural network

KW - Coefficients of the potential function

KW - Eigenvalues of the Schrödinger operator

KW - Finite element method

KW - Inverse problems

KW - Radial basis function

UR - http://www.scopus.com/inward/record.url?scp=85011067232&partnerID=8YFLogxK

U2 - 10.1016/j.cpc.2017.01.006

DO - 10.1016/j.cpc.2017.01.006

M3 - Article

AN - SCOPUS:85011067232

VL - 214

SP - 31

EP - 38

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

ER -