# Physics-informed Neural Networks approach to solve the Blasius function

arXiv: https://arxiv.org/abs/2301.00106 · HTML: https://mlsanity.com/paper/2301.00106/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 33 references that are in the map.
- First posted on arXiv 31 Dec 2022.

## Builds on (most cited first, 5 of 5)

- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method](https://mlsanity.com/paper/2110.15832/) (2021)
- [Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equations](https://mlsanity.com/paper/2107.10711/) (2021)
- [To go deep or wide in learning?](https://mlsanity.com/paper/1402.5634/) (2014)
- [A Neural Network Study of Blasius Equation](https://mlsanity.com/paper/1811.08936/) (2018)

## Built on by (most cited first, 1 of 1)

- [Adaptive Physics-Informed Neural Networks for the Blasius Boundary-Layer Problem](https://mlsanity.com/paper/2609.22185/) (2026)

## Abstract (arXiv)

Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to solve the Blasius function. This method eliminates the process of changing the non-linear differential equation to an initial value problem. Also, it tackles the convergence issue arising in the conventional series solution. It is seen that this method produces results that are at par with the numerical and conventional methods. The solution is extended to the negative axis to show that PINNs capture the singularity of the function at η=-5.69