Predicting ground state configuration of energy landscape ensemble using graph neural network

TL;DR

This paper presents a graph neural network approach to predict ground state configurations in energy landscapes, enabling faster and more accurate searches for large Ising spin glass problems based on small problem training.

Contribution

The study introduces a GNN-based method that generalizes from small to large systems, improving ground state prediction efficiency in complex energy landscapes.

Findings

GNN predicts low-energy configurations more efficiently than simulated annealing.

Model trained on small matrices generalizes to larger systems with better results.

Predicted configurations have significantly lower energies than those from traditional methods.

Abstract

Many scientific problems seek to find the ground state in a rugged energy landscape, a task that becomes prohibitively difficult for large systems. Within a particular class of problems, however, the short-range correlations within energy minima might be independent of system size. Can these correlations be inferred from small problems with known ground states to accelerate the search for the ground states of larger problems? Here, we demonstrate the strategy on Ising spin glasses, where the interaction matrices are drawn from protein contact maps. We use graph neural network to learn the mapping from an interaction matrix $J$ to a ground state configuration, yielding guesses for the set of most probable configurations. Given these guesses, we show that ground state configurations can be searched much faster than in vanilla simulated annealing. For large problems, a model trained on small $J$ matrices predicts a configurations whose energy is much lower than those obtained by simulated annealing, indicating the size generalizability of the strategy.