Novel approach of using Unsupervised Machine Learning in Physics

A team of researchers report on a method that unsupervised machine learning, based on anomaly detection.

Machine Learning has the main goal of analyzing and interpreting data structures and patterns in order to learn from them, reason and carry out a decision-making task that is completely independent of human reasoning and engagement. Even though this field of study started in the mid-1900s, recent developments in the area have revolutionized the way on how we can process and find correlations in complex data.

ICREA Professors at ICFO Antonio Acín and Maciej Lewenstein, together with ICFO researchers Korbinian Kottmann and Patrick Huembeli, published an article at the journal Physical Review Letters. The study describes a method that uses an unsupervised machine learning technique based on anomaly detection to automatically map out the phase diagram of a quantum many-body systems given unlabeled data.

The anomaly detection method

In machine learning, the most common and known classification task example is to discriminate, for instance, images of cats and dogs. In this study, researchers used a method called anomaly detection, which separates dogs from everything that is not a dog, approaching the system is an entirely different perspective. The idea is to train a special neural network – called an autoencoder-  to efficiently compress and reproduce images of dogs. Those networks are computational models or systems, inspired in animal’s brains, and based on a collection of connected units or nodes called artificial neurons. Once the network is trained, it is later fed with images of cats. As the features of those pictures are not the same as the dog’s ones, it won’t be able to compress them efficiently, so it will be able to tell from the higher reconstruction loss that it is not a dog.

Quantum many-body systems

This method was used in the context of quantum many-body systems. In these quantum systems, the interactions between the particles create quantum correlations or entanglement. As a consequence, the wave function of the system is a complicated object that contains a large amount of information, making exact or analytical calculations impossible in practice. Many-body problems are generally addressed with a series of approaches specific to the problem under study. Using the anomaly detection method, the images become observables, wave-functions or entanglement properties and the classes dogs and cats become different quantum phases.

The model that they looked at – the extended Bose-Hubbard model-  offered four different phases in the parameter space of interest. Since the researchers did not know the phases in their task a priori, they started by defining a region around the origin of the phase diagram as their starting point to train the neural network. Already from there, they were able to map the system in one training iteration, where all four phases of the system were easily distinguishable.

This method allowed the researchers to detect a previously unknown phenomenon in a quantum many-body context, being the first time that a machine is able to do so.

 

Reference: Korbinian Kottmann, Patrick Huembeli, Maciej Lewenstein, and Antonio Acín. Phys. Rev. Lett. 125, 170603. DOI: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.170603

Read more: ICFO’s newsroom