Solving differential equations with Deep Learning: a beginner's guide

Abstract 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.