When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning

Machine learning/deep learning models have already achieved tremendous success in a number of domains such as computer vision [1, 2, 3, 4, 5] and natural language processing [6, 7, 8, 9, 10, 11, 12, 13, 14], where large amounts of training data and highly expressive neural network architectures together give birth to solutions outperforming previously dominating methods. As a consequence, researchers have also started exploring the possibility of applying machine learning models to advance scientific discovery and to further improve traditional analytical modeling [15, 16, 17, 18, 19, 20, 21]. While given a set of input and output pairs, deep neural networks are able to extract the complicated relations between the input and output via appropriate optimization over adequate large amount of data, prior knowledge still acts as an important role in finding the optimal solution. As the high level extraction of data distributions and task properties, prior knowledge, if incorporated properly, can provide rich information not existing or hard to extract in limited training data, and helps improve the data efficiency, the ability to generalize, and the plausibility of resulting models. Physics knowledge, which has been collected and validated explicitly both theoretically and empirically in the long history, contains tremendous abstraction and summary of natural phenomena and human behaviours in many important scientific and engineering applications. Thus in this paper, we focus on the topic of integrating prior physics knowledge into machine learning models, i.e. physics-informed machine learning (PIML). Compared to the integration of other types of prior knowledge, such as knowledge graphs, logic rules and human feedback [22], the integration of physics knowledge requires specific design due to its special properties and forms. In this paper, we survey a wide range of recent works in PIML and summarize them from three aspects.