近日，美国加州大学的Rose Yu及其研究团队取得一项新进展。他们通过物理引导深度学习介绍从数据中学习动态系统。相关研究成果已于2024年6月24日在国际知名学术期刊《美国科学院院刊》上发表。

据悉，复杂物理动力学建模是科学和工程中的一项基本任务。传统的基于物理的模型是第一性原则的、可解释的、样本高效的。然而，它们通常依赖于强大的建模假设和昂贵的数值积分，需要大量的计算资源和领域专业知识。虽然深度学习(DL)为复杂动态建模提供了有效的替代方案，但它们需要大量标记的训练数据。

此外，它的预测可能不符合主导的物理定律，难以解释。物理引导的深度学习旨在将第一性物理知识整合到数据驱动的方法中。它拥有两全其美的优势，并且有能力更好地解决科学问题。最近，这一领域取得了很大的进展，并引起了跨学科的极大兴趣。

该研究团队介绍了物理引导下的深度学习框架，特别强调学习动态系统。研究人员描述了学习管道，并在此框架下对最先进的方法进行了分类。研究人员还就公开的挑战和新出现的机遇提出了自己的观点。

附：英文原文

Title: Learning dynamical systems from data: An introduction to physics-guided deep learning

Author: Yu, Rose, Wang, Rui

Issue&Volume: 2024-6-24

Abstract: Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are first-principled, explainable, and sample-efficient. However, they often rely on strong modeling assumptions and expensive numerical integration, requiring significant computational resources and domain expertise. While deep learning (DL) provides efficient alternatives for modeling complex dynamics, they require a large amount of labeled training data. Furthermore, its predictions may disobey the governing physical laws and are difficult to interpret. Physics-guided DL aims to integrate first-principled physical knowledge into data-driven methods. It has the best of both worlds and is well equipped to better solve scientific problems. Recently, this field has gained great progress and has drawn considerable interest across discipline Here, we introduce the framework of physics-guided DL with a special emphasis on learning dynamical systems. We describe the learning pipeline and categorize state-of-the-art methods under this framework. We also offer our perspectives on the open challenges and emerging opportunities.

DOI: 10.1073/pnas.2311808121

Source: https://www.pnas.org/doi/abs/10.1073/pnas.2311808121