An introduction to Neural Networks for Physicists

TL;DR

This paper provides a practical introduction to neural networks for physicists, illustrating their application through four diverse examples involving the simple pendulum, and discusses recent advances at the intersection of machine learning and physics.

Contribution

It offers an accessible overview of neural network concepts and demonstrates their application to physics problems, including parameter fitting, PINNs, autoencoders, and SINDy for the pendulum.

Findings

Neural networks can effectively model and analyze physical systems.

Multiple machine learning techniques are applicable to pendulum problems.

The paper bridges machine learning methods with physics applications.

Abstract

Machine learning techniques have emerged as powerful tools to tackle various challenges. The integration of machine learning methods with Physics has led to innovative approaches in understanding, controlling, and simulating physical phenomena. This article aims to provide a practical introduction to neural network and their basic concepts. It presents some perspectives on recent advances at the intersection of machine learning models with physical systems. We introduce practical material to guide the reader in taking their first steps in applying neural network to Physics problems. As an illustrative example, we provide four applications of increasing complexity for the problem of a simple pendulum, namely: parameter fitting of the pendulum's ODE for the small-angle approximation; Application of Physics-Inspired Neural Networks (PINNs) to find solutions of the pendulum's ODE in the small-angle regime; Autoencoders applied to an image dataset of the pendulum's oscillations for estimating the dimensionality of the parameter space in this physical system; and the use of Sparse Identification of Non-Linear Dynamics (SINDy) architectures for model discovery and analytical expressions for the nonlinear pendulum problem (large angles).