Journal of Engineering Mathematics & Statistics

Author: Arjun Verma

Abstract: Machine learning (ML) techniques have emerged as a promising tool for solving complex partial differential equations (PDEs) that frequently arise in engineering applications. Traditional numerical methods for solving PDEs can be computationally expensive, time-consuming, and require specialized domain knowledge. In contrast, ML algorithms can offer more efficient, scalable, and flexible solutions to these challenges. This paper explores the application of ML algorithms in solving PDEs in various engineering fields, including fluid dynamics, heat transfer, structural analysis, and electromagnetics. The paper highlights the key ML models used, such as neural networks, deep learning, and reinforcement learning, and their implementation strategies in solving both linear and nonlinear PDEs. We also discuss the advantages and limitations of using ML for PDE solutions and the potential future directions for this evolving area of research.

Keywords: Machine Learning, Partial Differential Equations, Engineering, Neural Networks, Deep Learning, Reinforcement Learning, Computational Methods, Nonlinear PDEs, Numerical Solutions, Engineering Applications.