近日，法国PASQAL公司的Vincent E. Elfving与德国巴斯夫数字化解决方案公司的Horst Weiss等人合作并取得一项新进展。经过不懈努力，他们对量子科学机器学习在天气建模中的应用潜力进行 研究。相关研究成果已于2024年11月18日在国际知名学术期刊《物理评论A》上发表。

本文探讨了如何利用量子科学机器学习来应对天气建模的挑战。研究人员采用参数化量子电路作为机器学习模型，并考虑了两种范式：一是从天气数据进行监督学习，二是基于物理原理求解大气动力学的基本方程。在第一种情况下，研究人员展示了如何训练量子模型以4°的分辨率准确再现真实世界的全球流函数动态，并详细介绍了为实现这一结果所采用的多种针对特定问题的经典和量子架构选择。

随后，研究人员引入了正压涡度方程（BVE）作为大气模型，该方程在流函数表述中是一个三阶偏微分方程（PDE）。利用可微量子电路算法，研究人员成功地在适当边界条件下求解了BVE，并使用训练好的模型根据人工设定的初始天气状态，以高精度预测了未来未见过的动态。尽管仍存在挑战，但这项研究结果在量子科学机器学习求解PDE的复杂性方面取得了进展。

附：英文原文

Title: Potential of quantum scientific machine learning applied to weather modeling

Author: Ben Jaderberg, Antonio A. Gentile, Atiyo Ghosh, Vincent E. Elfving, Caitlin Jones, Davide Vodola, John Manobianco, Horst Weiss

Issue&Volume: 2024/11/18

Abstract: In this paper we explore how quantum scientific machine learning can be used to tackle the challenge of weather modeling. Using parametrized quantum circuits as machine learning models, we consider two paradigms: supervised learning from weather data and physics-informed solving of the underlying equations of atmospheric dynamics. In the first case, we demonstrate how a quantum model can be trained to accurately reproduce real-world global stream function dynamics at a resolution of 4°. We detail a number of problem-specific classical and quantum architecture choices used to achieve this result. Subsequently, we introduce the barotropic vorticity equation (BVE) as our model of the atmosphere, which is a third-order partial differential equation (PDE) in its stream function formulation. Using the differentiable quantum circuits algorithm, we successfully solve the BVE under appropriate boundary conditions and use the trained model to predict unseen future dynamics to high accuracy given an artificial initial weather state. While challenges remain, our results mark an advancement in terms of the complexity of PDEs solved with quantum scientific machine learning.

DOI: 10.1103/PhysRevA.110.052423

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.052423