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

2023/08/07 by Alireza Afzal Aghaei, Aghaei, Alireza Afzal, Kourosh Parand +5
Computer Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Neural Networks and Applications #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2308.03337

openalex publication_date 2023/08/07 · openalex created_date 2023/08/09 · openalex updated_date 2026/07/28

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.

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