This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest due to their potential impact on advancing scientific research and industrial practices by improving predictive models with small- or large-scale datasets and expressive predictive models with useful inductive biases. The survey has two parts. The first considers incorporating physics knowledge on an architectural level through objective functions, structured predictive models, and data augmentation. The second considers data as physics knowledge, which motivates looking at multi-task, meta, and contextual learning as an alternative approach to incorporating physics knowledge in a data-driven fashion. Finally, we also provide an industrial perspective on the application of these methods and a survey of the open-source ecosystem for physics-informed machine learning.

本综述解决了机器学习与物理知识结合以提高预测模型的问题，特别关注偏微分方程的方法。通过在结构、目标函数和数据增强方面引入物理知识，以及将数据视为物理知识，研究提出了多任务、元学习等数据驱动的新方法，展示了这些方法在科学研究和工业实践中的潜在影响。

结合物理知识进行预测的机器学习：一项综述