[2308.03337] Solving Falkner-Skan type equations via Legendre and Chebyshev Neural Blocks
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Computer Science > Machine Learning

arXiv:2308.03337 (cs)
[Submitted on 7 Aug 2023]

Title:Solving Falkner-Skan type equations via Legendre and Chebyshev Neural Blocks

Authors:Alireza Afzal Aghaei, Kourosh Parand, Ali Nikkhah, Shakila Jaberi
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Abstract:In this paper, a new deep-learning architecture for solving the non-linear Falkner-Skan equation is proposed. Using Legendre and Chebyshev neural blocks, this approach shows how orthogonal polynomials can be used in neural networks to increase the approximation capability of artificial neural networks. In addition, utilizing the mathematical properties of these functions, we overcome the computational complexity of the backpropagation algorithm by using the operational matrices of the derivative. The efficiency of the proposed method is carried out by simulating various configurations of the Falkner-Skan equation.
Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Numerical Analysis (math.NA)
Cite as: arXiv:2308.03337 [cs.LG]
  (or arXiv:2308.03337v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2308.03337

Submission history

From: Kourosh Parand [view email]
[v1] Mon, 7 Aug 2023 06:38:59 UTC (639 KB)
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