Physics-informed Neural Networks:Recent Advances and Prospects

Physical-informed neural networks (PINN) are a class of neural networks used to solve supervised learning tasks.They not only try to follow the distribution law of the training data, but also follow the physical laws described by partial diffe-rential equations.Compared with pure data-driven neural networks, PINN imposes physical information constraints during the training process, so that more generalized models can be acquired with fewer training data.In recent years, PINN has gradually become a research hotspot in the interdisciplinary field of machine learning and computational mathematics, and has obtained relatively in-depth research in both theory and application, and has made considerable progress.However, due to the unique network structure of PINN, there are some problems such as slow training or even non-convergence and low precision in practical application.On the basis of summarizing the current research of PINN, this paper explores the network/system design and its application in many fields such as fluid mechanics, and looks forward to the further research directions.