Machine Learning Crash Course for Physicists in Three Easy Chapters

Written by Florian Marquardt (originally for the Trieste Summer School 2024 on Frontiers in Nanomechanics).

This online book teaches machine learning to a physicist in three easy chapters. You should be able to work through them in three hours, provided you know how to use python and have worked with numpy before.

This book uses the jax machine learning library, which is really easy to use, since it is directly based on numpy and only adds a handful of useful but powerful commands. jax is also state of the art, being used in famous projects like DeepMind’s AlphaFold. Afterwards, you will already be able to use neural networks to train them on experimental data or simulations, for tasks like rapid experimental calibration or speed-up of simulations, and many more.

• The first chapter shows how to minimize the energy of a mechanical structure, relaxing it to equilibrium. This teaches how to use automatic gradients and adaptive-stepsize gradient descent.

• The second chapter shows how to approximate an arbitrary function using a simple neural network. Training of that network uses the concepts already introduced in chapter 1. In addition, we learn about batch processing and about random numbers in jax.

• The third and final chapter shows how to apply this to an interesting physics case. Suppose you take data in an experiment where you extract the response of a driven nonlinear oscillator. Your goal is to guess the correct underlying system parameters (like resonance frequency and damping) rapidly. A neural network, once trained, can do that for you. It will be much faster and more robust than usual nonlinear curve fitting.