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.

翻译：本文提出了一种求解非线性Falkner-Skan方程的新型深度学习架构。该方法利用Legendre和Chebyshev神经模块，展示了如何在神经网络中应用正交多项式以提高人工神经网络的逼近能力。此外，通过利用这些函数的数学性质，我们采用导数运算矩阵克服了反向传播算法的计算复杂性。通过对Falkner-Skan方程多种配置的数值模拟，验证了所提方法的高效性。