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Comparative Analysis of Finite Difference Method (FDM) and Physics-Informed Neural Networks (PINNs)

Wasif Khan*, Shahbaz Ahmad**

*-**Department of Mathematics, Government College University, Lahore, Pakistan.

Periodicity:January - June'2024
DOI : https://doi.org/10.26634/jmat.13.1.20383

Abstract

In this analysis, the solutions of the Linear and Non-Linear models are explored and compared using two distinct methods: the Finite Difference Method (FDM) and the Physics-Informed Neural Networks (PINNs). Initially, the solution is derived employing the principles of FDM, followed by solving the same problem using the methodology of PINNs. Subsequently, a comparative examination of the solution graphs with the exact solution is conducted.

Keywords

Differential Equations, Finite Differences, Finite Difference Method, Least Squares Error, Neural Networks, Physics-Informed Neural Networks.

How to Cite this Article?

Khan, W., and Ahmad, S. (2024). Comparative Analysis of Finite Difference Method (FDM) and Physics-Informed Neural Networks (PINNs). i-manager’s Journal on Mathematics, 13(1), 27-37. https://doi.org/10.26634/jmat.13.1.20383

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