Solving Falkner-Skan type equations via Legendre and Chebyshev Neural Blocks
This work addresses computational challenges in solving specific fluid dynamics equations, representing an incremental improvement for researchers in numerical methods and applied mathematics.
The paper tackled solving non-linear Falkner-Skan equations by proposing a new deep-learning architecture using Legendre and Chebyshev neural blocks, which improved approximation capabilities and reduced computational complexity, achieving efficient simulations across various equation configurations.
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.