2011
DOI: 10.1002/qua.22572
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Using neural networks to solve nonlinear differential equations in atomic and molecular physics

Abstract: ABSTRACT:To represent the solution of a differential equation by an artificial neural network (ANN) was an idea introduced by Lagaris. Sugawara applied this concept to solve Schrödinger's equation for select systems. We have submitted their method to a new kind of application. Here, for the first time, the approach is applied to the equations derived from density functional theory (DFT). At first, we have tested the procedure for two simple systems: the double harmonic oscillator and the hydrogen atom. The ANN… Show more

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Cited by 21 publications
(23 citation statements)
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“…We refer the interested readers to for example, refs. [22][23][24][25][26][27][28][29][34][35][36][37][38]49,50,53,107].…”
Section: Hubbard Modelmentioning
confidence: 99%
See 2 more Smart Citations
“…We refer the interested readers to for example, refs. [22][23][24][25][26][27][28][29][34][35][36][37][38]49,50,53,107].…”
Section: Hubbard Modelmentioning
confidence: 99%
“…Since 2001, researchers have been trying to use machine learning techniques, especially neural networks, to deal with the quantum problems, for example, solving the Schrödinger equations . Later, in 2016, neural networks were introduced as a variational ansatz for representing quantum many‐body ground states .…”
Section: Introductionmentioning
confidence: 99%
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“…In recent years many authors have used nature and biologically inspired based computation techniques as an alternative for solving nonlinear ODEs arising in diverse fields of engineering and science [6][7][8][9][10][11][12][13][14][15][16]. Very recently Malik et al [6,7] employed heuristic technique based on hybrid genetic algorithm for numerically solving the nonlinear singular boundary value problems in physiology and the Bratu problem.…”
Section: Introductionmentioning
confidence: 99%
“…Arqub et al [8] used genetic algorithm (GA) based method for solving linear and nonlinear singular boundary value problems (BVPs). Caetano et al [9] used genetic algorithm (GA) based neural network (NN) for the solution of nonlinear ODEs arising in atomic and molecular physics. Khan et al [10] used particle swarm optimization (PSO) based NN technique for solving nonlinear ODEs including Wessinger's equation.…”
Section: Introductionmentioning
confidence: 99%