Deep learning neural network for approaching Schrödinger problems with arbitrary two-dimensional confinement

被引:0
|
作者
Radu, A. [1 ]
Duque, C. A. [2 ]
机构
[1] Univ Politehn Bucuresti, Dept Phys, 313 Splaiul Independentei, RO-060042 Bucharest, Romania
[2] Univ Antioquia UdeA, Fac Ciencias Exactas & Nat, Grp Mat Condensada UdeA, Inst Fis, Calle 70 52-21, Medellin, Colombia
来源
MACHINE LEARNING-SCIENCE AND TECHNOLOGY | 2023年 / 4卷 / 03期
关键词
artificial intelligence; neural network; deep learning; stochastic gradient descent; Schrodinger equation; quantum well; FINITE-ELEMENT-ANALYSIS; SCHRODINGER-EQUATION; NUMERICAL-SOLUTION; QUANTUM DOTS; ASYMPTOTIC ITERATION; WIRES; MODEL;
D O I
10.1088/2632-2153/acf55b
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
This article presents an approach to the two-dimensional Schrodinger equation based on automatic learning methods with neural networks. It is intended to determine the ground state of a particle confined in any two-dimensional potential, starting from the knowledge of the solutions to a large number of arbitrary sample problems. A network architecture with two hidden layers is proposed to predict the wave function and energy of the ground state. Several accuracy indicators are proposed for validating the estimates provided by the neural network. The testing of the trained network is done by applying it to a large set of confinement potentials different from those used in the learning process. Some particular cases with symmetrical potentials are solved as concrete examples, and a good network prediction accuracy is found.
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页数:24
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