Solving differential equations using learning-based techniques

Abstract

Physics-based machine learning models are an emerging approach in machine learning to solve differential equations. These models integrate the known physics of a system into the neural network training process, enhancing the efficiency of so- lutions to differential equations. This study will explore the capability of these mod- els to tackle differential equations across various fields, including fluid dynamics, solid mechanics, and heat transfer. It will feature comparative analyses of differ- ent optimisation algorithms, determining under which conditions an algorithm is computationally more effective. In addition, the study will examine the impact of various hyperparameters and training strategies on the performance of these mod- els. The potential of physics-based machine learning models lies in their capability to provide accurate and efficient solutions to differential equations, making them applicable to a wide range of crucial applications in science and engineering.