Entangling Solid Solutions: Machine Learning of Tensor Networks for Materials Property Prediction

TL;DR

This paper demonstrates that tensor network architectures, adapted from quantum physics, effectively predict materials properties from atomic structures, especially with limited data, by leveraging entanglement and efficient representations.

Contribution

It introduces tensor network models for materials property prediction, showing their strong generalizability and efficiency in learning from atomic structure data.

Findings

Tensor networks outperform traditional models on small datasets.

Strong entanglement correlates with better generalization.

Efficient representations reduce computational complexity.

Abstract

Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning architectures. A large class of atomic structure representations based on expansions of smoothed atomic densities have been shown to correspond to specific choices of basis sets in an abstract many-body Hilbert space. Concurrently, tensor network structures, conventionally the purview of quantum many-body physics and quantum information, have been successfully applied in supervised and unsupervised learning tasks in computer vision and natural language processing. In this work, we argue that architectures based on tensor networks are well-suited to machine learning on Hilbert-space representations of atomic structures. This is demonstrated on supervised learning tasks involving widely available datasets of density functional theory calculations of metal and semiconductor alloys. In particular, we show that certain standard tensor network topologies exhibit strong generalizability even on small training datasets while being parametrically efficient. We further relate this generalizability to the presence of complex entanglement in the trained tensor networks. We also discuss connections to learning with generalized structural kernels and related strategies for compressing large input feature spaces.