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

arXiv: https://arxiv.org/abs/2308.03337 · HTML: https://mlsanity.com/paper/2308.03337/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 30 references that are in the map.
- First posted on arXiv 7 Aug 2023.

## Built on by (most cited first, 3 of 3)

- [rKAN: Rational Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.14495/) (2024)
- [A Multimodal Physics-Informed Neural Network Approach for Mean Radiant Temperature Modeling](https://mlsanity.com/paper/2503.08482/) (2025)
- [PINNIES: An Efficient Physics-Informed Neural Network Framework to Integral Operator Problems](https://mlsanity.com/paper/2409.01899/) (2024)

## Abstract (arXiv)

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.