Seminario de Informática ‘Mirian Andrés’. Teaching Neural Networks the Laws of Physics: An Introduction to PINNs

This seminar presents an exploratory introduction to Physics-Informed Neural Networks (PINNs) and their possible application to problems in theoretical physics.

Rather than aiming to compete with established numerical methods, the main goal is to investigate PINNs as a proof-of-concept framework capable of incorporating physical laws directly into the training process of neural networks.

After a brief overview of neural networks, optimization, and loss functions, we discuss how differential equations, boundary conditions, and initial conditions can be encoded into the learning procedure.

The methodology is illustrated through several examples of increasing complexity, including the wave equation, the Klein–Gordon equation, and preliminary Einstein–Klein–Gordon systems.

Nota: Esta charla es una actividad conjunta del Seminario Mirian Andrés y del Seminario de Análisis y Matemática Aplicada.