Scanning probe experiments such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM) on strongly correlated electronic systems often reveal complex pattern formation on multiple length scales. By studying the universal scaling in these images, we have shown in several distinct correlated electronic systems that the pattern formation is driven by proximity to a disorder-driven critical point, revealing a unification of the pattern formation in these materials. As an alternative approach to this image classification problem of novel materials, here we report an investigation of the machine learning method to determine which underlying physical model is driving pattern formation in a system. Using a neural network architecture, we are able to achieve $97\%$ accuracy on classifying configuration images from three models with Ising symmetry. This investigation also demonstrates that machine learning can capture the implicit universal behavior of a physical system. This broadens our understanding of what machine learning can do, and we expect more synergy between machine learning and condensed matter physics in the future.

• Received 3 February 2017
• Revised 2 October 2018

DOI:https://doi.org/10.1103/PhysRevMaterials.3.033805