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Mathematics > Numerical Analysis

arXiv:2402.10649 (math)
[Submitted on 16 Feb 2024]

Title:Hermite Neural Network Simulation for Solving the 2D Schrodinger Equation

Authors:Kourosh Parand, Aida Pakniyat
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Abstract:The Schrodinger equation is a mathematical equation describing the wave function's behavior in a quantum-mechanical system. It is a partial differential equation that provides valuable insights into the fundamental principles of quantum mechanics. In this paper, the aim was to solve the Schrodinger equation with sufficient accuracy by using a mixture of neural networks with the collocation method base Hermite functions. Initially, the Hermite functions roots were employed as collocation points, enhancing the efficiency of the solution. The Schrodinger equation is defined in an infinite domain, the use of Hermite functions as activation functions resulted in excellent precision. Finally, the proposed method was simulated using MATLAB's Simulink tool. The results were then compared with those obtained using Physics-informed neural networks and the presented method.
Subjects: Numerical Analysis (math.NA); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE); Analysis of PDEs (math.AP)
Report number: 2402.10649
Cite as: arXiv:2402.10649 [math.NA]
  (or arXiv:2402.10649v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2402.10649

Submission history

From: Aida Pakniyat [view email]
[v1] Fri, 16 Feb 2024 12:51:25 UTC (1,087 KB)
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