Deep learning has become a popular tool across many scientific fields, including the study of differential equations, particularly partial differential equations. This work introduces the basic principles of deep learning and the Deep Galerkin method, which uses deep neural networks to solve differential equations. This primer aims to provide technical and practical insights into the Deep Galerkin method and its implementation. We demonstrate how to solve the one-dimensional heat equation step-by-step. We also show how to apply the Deep Galerkin method to solve systems of ordinary differential equations and integral equations, such as the Fredholm of the second kind. Additionally, we provide code snippets within the text and the complete source code on Github. The examples are designed so that one can run them on a simple computer without needing a GPU.

翻译：深度学习已成为包括微分方程（尤其是偏微分方程）研究在内的众多科学领域的流行工具。本文介绍了深度学习的基本原理以及使用深度神经网络求解微分方程的Deep Galerkin方法。本入门指南旨在为Deep Galerkin方法及其实现提供技术与实践层面的见解。我们逐步演示了如何求解一维热传导方程，并展示了如何应用Deep Galerkin方法求解常微分方程组和积分方程（例如第二类Fredholm方程）。此外，我们在文中提供了代码片段，并在Github上公开了完整源代码。所有示例均设计为可在无需GPU的普通计算机上运行。