The research in artificial intelligence methods with potential applications in science has become an essential task in the scientific community in recent years. Physics-informed neural networks (PINNs) is one of these methods and represents a contemporary technique based on neural network fundamentals to solve differential equations. These networks can potentially improve or complement classical numerical methods in computational physics, making them an exciting area of study. In this paper, we introduce PINNs at an elementary level, mainly oriented to physics education, making them suitable for educational purposes at both undergraduate and graduate levels. PINNs can be used to create virtual simulations and educational tools that aid in understating complex physical concepts and processes involving differential equations. By combining the power of neural networks with physics principles, PINNs can provide an interactive and engaging learning experience that can improve students’ understanding and retention of physics concepts in higher education.

中文翻译：

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使用深度学习求解微分方程：初学者指南


研究具有科学潜在应用价值的人工智能方法已成为近年来科学界的一项重要任务。物理信息神经网络 (PINN) 就是其中一种方法，代表了一种基于神经网络基础来求解微分方程的当代技术。这些网络可以潜在地改进或补充计算物理中的经典数值方法，使它们成为一个令人兴奋的研究领域。在本文中，我们在初级阶段介绍了 PINN，主要面向物理教育，使其适用于本科和研究生水平的教育目的。 PINN 可用于创建虚拟模拟和教育工具，帮助理解涉及微分方程的复杂物理概念和过程。通过将神经网络的力量与物理原理相结合，PINN 可以提供互动且引人入胜的学习体验，从而提高学生对高等教育中物理概念的理解和保留。