Machine learning and the physical sciences

TL;DR

The paper surveys the burgeoning interface between machine learning and the physical sciences, tracing how physics-inspired theory informs learning and how ML accelerates discovery across statistical and quantum physics, high-energy physics, cosmology, and materials science. It highlights concrete advances such as neural-network quantum states, likelihood-free and simulation-based inference, jet tagging and photometric redshift in astronomy, and ML-driven acceleration of quantum Monte Carlo and tomography, while candidly addressing limitations in generalization, uncertainty quantification, and data efficiency. By weaving together theoretical insights, practical applications, and hardware considerations, the authors argue for physics-informed ML, open benchmarks, and hardware-software co-design to scale these methods. The work emphasizes a reciprocal, collaborative trajectory where physics motivates new ML ideas and ML provides powerful tools to tackle otherwise intractable scientific problems, forecasting substantial impact across disciplines.

Abstract

Machine learning encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. We review in a selective way the recent research on the interface between machine learning and physical sciences. This includes conceptual developments in machine learning (ML) motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross-fertilization between the two fields. After giving basic notion of machine learning methods and principles, we describe examples of how statistical physics is used to understand methods in ML. We then move to describe applications of ML methods in particle physics and cosmology, quantum many body physics, quantum computing, and chemical and material physics. We also highlight research and development into novel computing architectures aimed at accelerating ML. In each of the sections we describe recent successes as well as domain-specific methodology and challenges.

Figures (8)

• Figure 1: Dark matter distribution in three cubes produced using different sets of parameters. Each cube is divided into small sub- cubes for training and prediction. Note that although cubes in this figure are produced using very different cosmological parameters in our constrained sampled set, the effect is not visually discernible. Reproduced from 2017arXiv171102033R.
• Figure 2: A schematic of machine learning based approaches to likelihood-free inference in which the simulation provides training data for a neural network that is subsequently used as a surrogate for the intractable likelihood during inference. Reproduced from Brehmer:2018kdj.
• Figure 3: Samples from the GALAXY-ZOO dataset versus generated samples using conditional generative adversarial network. Each synthetic image is a 128$\times$128 colored image (here inverted) produced by conditioning on a set of features $y \in [0,1]^{37}$ . The pair of observed and generated images in each column correspond to the same $y$ value. Reproduced from 2016arXiv160905796R.
• Figure 4: (Top) Example of a shallow convolutional neural network used to represent the many-body wave-function of a system of spin $1/2$ particles on a square lattice. (Bottom) Filters of a fully-connected convolutional RBM found in the variational learning of the ground-state of the two-dimensional Heisenberg model, adapted from carleo_solving_2017.
• Figure 5: Example of machine learning approach to the classification of experimental images from scanning tunneling microscopy of high-temperature superconductors. Images are classified according to the predictions of distinct types of periodic spatial modulations. Reproduced from zhang_using_2018