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

TL;DR

This paper introduces Physics-Informed Neural Networks (PINNs) as an accessible educational tool for solving differential equations, enhancing physics learning through interactive virtual simulations suitable for undergraduate and graduate students.

Contribution

It presents PINNs at an elementary level tailored for physics education, highlighting their potential to improve understanding of complex physical concepts.

Findings

PINNs can create effective virtual physics simulations.

They enhance student engagement and comprehension.

Suitable for undergraduate and graduate education.

Abstract

The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community last years. Physics Informed Neural Networks (PINNs) is one of this methods and represent a contemporary technique that is based on the fundamentals of neural networks to solve differential equations. These kind of networks have the potential to 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 so 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 where differential equations are involved. 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.