Toward fast, accurate and robust AI prediction of ground states in rotating BEC

TL;DR

This paper introduces an unsupervised deep learning method for accurately and efficiently computing the ground state of rotating Bose-Einstein condensates, effectively handling various physical conditions and phase transitions.

Contribution

It presents a novel normalized loss function and a virtual rotation acceleration training strategy, improving prediction accuracy and avoiding local minima in ground state computations.

Findings

Effective prediction of ground states across different rotation speeds.

Accurate modeling of phase transitions in Bose-Einstein condensates.

Rapid generalization of physical parameters using a unified operator network.

Abstract

We propose an unsupervised deep learning approach for computing the ground state (GS) of rotating Bose-Einstein condensation. To minimize the energy under a mass constraint, our approach introduces two key and novel ingredients: a normalized loss function that exactly enforces the mass constraint, and a training strategy named virtual rotation acceleration that is essential for avoiding local minima and guiding the learning process to the correct quantized vortex phase. Extensive numerical experiments demonstrate the proposed approach as an effective and accurate method to predict GS across physical conditions--from slow to fast rotation and from isotropic to anisotropic confinement. Through further distillation, we establish a unified operator network capable of efficiently generalizing physical parameters across different phases. It enables rapid GS predictions while correctly capturing phase transitions and is applied for inverse problems.