本文为论文Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications的阅读笔记。
Abstract
Recent advances of data-driven machine learning have revolutionized fields like computer vision, reinforcement learning, and many scientific and engineering domains.
数据驱动机器学习的最新进展给许多领域带来巨大变革（CV、强化学习等）。
In many real-world and scientific problems, systems that generate data are governed by physical laws.Recent work shows that it provides potential benefits for machine learning models by incorporating the physical prior and collected data, which makes the intersection of machine learning and physics become a prevailing paradigm.
在现实世界与科学问题中，数据生成受到物理定律的限制。现有研究表明，融合物理先验知识与数据的机器学习模型具有一定的潜力，物理学与机器学习的交叉也成为一种主流范式。
By integrating the data and mathematical physics models seamlessly, it can guide the machine learning model towards solutions that are physically plausible, improving accuracy and efficiency even in uncertain and high-dimensional contexts.
通过集成数据和数学物理模型，可以引导机器学习模型向物理上合理的方向发展，在不确定的高维环境中也能保证准确性和效率。
In this survey, we present this learning paradigm called Physics-Informed Machine Learning (PIML) which is to build a model that leverages empirical data and available physical prior knowledge to improve performance on a set of tasks that involve a physical mechanism.
本研究提出了PIML的学习范式，旨在利用数据和物理先验知识来提高模型在涉及物理机制的一系列任务上的性能。
We systematically review the recent development of physics-informed machine learning from three perspectives of machine learning tasks, representation of physical prior, and methods for incorporating physical prior. We also propose several important open research problems based on the current trends in the field.
从机器学习任务、物理先验知识表示、物理先验知识的集成方法三个角度回顾了PIML的进展，并提出了几个开放性研究问题。
We argue that encoding different forms of physical prior into model architectures, optimizers, inference algorithms, and significant domain-specific applications like inverse engineering design and robotic control is far from being fully explored in the field of physics-informed machine learning.
将不同形式的物理先验信息编码到模型架构、优化器、推理算法或其他重要领域还有广阔前景。
We believe that the interdisciplinary research of physics-informed machine learning will significantly propel research progress, foster the creation of more effective machine learning models, and also offer invaluable assistance in addressing long-standing problems in related disciplines.
PIML会促进更有效的机器学习模型的构建。