Deep learning spinfoam vertex amplitudes: the Euclidean Barrett-Crane model

TL;DR

This paper demonstrates that deep learning can effectively approximate and predict spinfoam vertex amplitudes in the Euclidean Barrett-Crane model, potentially accelerating quantum gravity computations.

Contribution

It introduces a data-driven approach using neural networks to classify and regress spinfoam amplitudes, improving computational efficiency in quantum gravity models.

Findings

Classifier generalizes well outside training data

Regressor achieves high accuracy within training domain

Deep learning accelerates spinfoam amplitude calculations

Abstract

Spinfoam theories propose a well-defined path-integral formulation for quantum gravity and are hoped to provide the dynamics of loop quantum gravity. However, it is computationally hard to calculate spinfoam amplitudes. The well-studied Euclidean Barrett-Crane model provides an excellent setting for testing analytical and numerical tools to probe spinfoam models. We explore a data-driven approach to accelerating spinfoam computations by showing that the vertex amplitude is an object that can be learned from data using deep learning. We divide the learning process into a classification and a regression task: Two networks are independently engineered to decide whether the amplitude is zero or not and to predict the precise numerical value, respectively. The trained networks are tested with several accuracy measures. The classifier in particular demonstrates robust generalisation far outside the training domain, while the regressor demonstrates high predictive accuracy in the domain it is trained on. We discuss limitations, possible improvements, and implications for future work.