基于物理信息的神经网络:最新进展与展望  

Physics-informed Neural Networks:Recent Advances and Prospects

作　　者：李野 陈松灿[1] LI Ye;CHEN Song-can(College of Computer Science and Technology/Artificial Intelligence,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China)

机构地区：[1]南京航空航天大学计算机科学与技术学院/人工智能学院,南京211106

出　　处：《计算机科学》2022年第4期254-262,共9页Computer Science

基　　金：南京航空航天大学新教师工作启动基金(90YAH20131);中央高校基本科研业务费(NJ2020023)。

摘　　要：基于物理信息的神经网络(Physics-informed Neural Networks,PINN),是一类用于解决有监督学习任务的神经网络,它不仅尽力遵循训练数据样本的分布规律,而且遵守由偏微分方程描述的物理定律。与纯数据驱动的神经网络学习相比,PINN在训练过程中施加了物理信息约束,因此能用更少的数据样本学习得到更具泛化能力的模型。近年来,PINN已逐渐成为机器学习和计算数学交叉学科的研究热点,并在理论和应用方面都获得了相对深入的研究,取得了可观的进展。但PINN独特的网络结构在实际应用中也存在训练缓慢甚至不收敛、精度低等问题。文中在总结当前PINN研究的基础上,对其网络/体系设计及其在流体力学等多个领域中的应用进行了探究,并展望了进一步的研究方向。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 differential 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.

关 键 词：人工智能 机器学习 神经网络 物理模型 偏微分方程 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]