Introduction to Partial Differential Equations and Machine Learning Solutions

Kawino Charles K.

Faculty of Engineering Kampala International University Uganda

ABSTRACT

Partial differential equations (PDEs) are foundational tools in modeling various physical phenomena in science and engineering. Traditional numerical methods such as finite difference, finite volume, and finite element methods have been the primary approaches for solving PDEs. However, these methods often struggle with high-dimensional and nonlinear problems. Recently, machine learning (ML) has emerged as a promising tool for enhancing the efficiency and accuracy of PDE solutions. This paper provides an overview of PDEs, traditional numerical methods for solving them, and the integration of ML techniques in these methods. We explore how ML, particularly deep learning, can address challenges such as the curse of dimensionality and computational inefficiency. The discussion includes various ML approaches, including physics-informed neural networks (PINNs) and data-driven discretizations, and their applications in fields such as fluid dynamics and medical physics.

Keywords: Partial Differential Equations, Machine Learning, Numerical Methods, Deep Learning and Physics-Informed Neural Networks

CITE AS: Kawino Charles K. (2024). Introduction to Partial Differential Equations and Machine Learning Solutions. RESEARCH INVENTION JOURNAL OF ENGINEERING AND PHYSICAL SCIENCES 3(1):52-61.