Title: A Practical Guide to Solving Differential Equations with Deep Learning

Abstract:

The integration of deep learning into scientific disciplines, particularly the analysis of partial differential equations (PDEs), has become increasingly prevalent. This paper offers a concise and approachable overview of fundamental deep learning principles, such as backpropagation, neural network architectures, and the universal approximation theorem. The primary focus is on applying these techniques to the resolution of differential equations.

The target audience includes undergraduate and graduate students in mathematics, physics, and adjacent fields, for whom this text serves as a tutorial on leveraging deep learning for PDE solutions. Additionally, educators in these domains may utilize this work to introduce concepts like the Deep Galerkin method and the broader field of scientific machine learning.

Key topics addressed include: * Defining deep learning and illustrating its utility in resolving mathematical and physical challenges. * Practical steps for implementing neural networks and selecting appropriate numerical strategies for differential equations. * Strategies for optimizing hyperparameters. * Techniques for enhancing model accuracy and accelerating convergence rates.

Notably, every example and problem presented in this article is designed to be solvable on standard hardware without the need for a GPU, ensuring that the methodology is accessible to all students.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC