DPSO Based Machine Learning-driven Approach for the Solution of PDEs: A Case Study of Burger Equation

Abstract

Burger's equation represents a nonlinear second-order partial differential equation that is instrumental in characterizing the behavior of shock waves within the realm of gas dynamics. This research article examines the classical formulation of Burger's equation and its conversion into the linear heat equation. An artificial neural network (ANN) that is directed by the hybrid fractional order particle swarm optimisation (FO-PSO) technique is used to solve this partial differential equation (PDE). FO-PSO is a novel computer approach that finds optimal solutions by using a fractional order for the velocity of moving particles. By including optimised weights, the ANN framework is mainly used to reduce absolute errors (AE) in the approximation solutions. This research article's main goal is to solve the PDE using an ANN structure that was trained with the FO-PSO technique. The outcomes are contrasted with other modern methods to assess the efficacy of our methodology. Additionally, a supervised learning technique is implemented for the training, testing, and validation of our proposed outcomes, which are presented graphically.

Conflict of interest:
The authors have declared no potential conflicts of interest and falsification/fabrication of data with respect to the research, authorship, and/or publication of this article.

Funding:
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.