Harnessing Machine Learning for Fluid Dynamics: A Neural Network Approach to the Blasius Equation

Abstract

The paper represents a recent supervised learning-based neural network model of solving the classical Blasius equation, a fundamental theory of fluid dynamics, the basis of the boundary layer of a flat plate laminar flow. Computational cost and convergence stability is typically a challenge to traditional analytical and numerical approaches to such nonlinear differential equations. The proposed study will address these limitations by taking the strength of machine learning based on a supervised neural architecture to learn the solution to the Blasius equation with great accuracy and efficiency.

The Mean Squared Error (MSE) is used as the optimization criterion of the neural network model, the gradient behavior and adaptive learning rate (μ), is noticed to reveal convergence properties and is used to guarantee a strong training dynamics. The evaluation of the performance is conducted to the full extent relying on the error histograms, regression, and fitness plots, and with their help, the predictive ability of the network and the generalization ability are quantified and visualized.

Besides, the proposed supervised learning model is highly scalable to nonlinear boundary value problems in fluid mechanics that can provide smooth, physically consistent, and computationally efficient solutions. The results validate the claim that implementing the machine learning paradigms on classical fluid dynamics does not just augment the precision of the solutions but contributes to better convergence and eliminates excessive computing.