基于物理信息神经网络的随机系统演化分析  

Evolutionary analysis of stochastic systems based on physical informationneural networks

作　　者：曹瑞 裔扬[1] 刘燕斌 CAO Rui;YI Yang;LIU Yan-bin(College of Information Engineering,Yangzhou University,Yangzhou 225127,China;College of Astronautics,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China)

机构地区：[1]扬州大学信息工程学院,江苏扬州225127 [2]南京航空航天大学航天学院,南京211106

出　　处：《控制与决策》2024年第9期3013-3022,共10页Control and Decision

基　　金：江苏省自然科学基金青年项目(BK20230560);国家自然科学基金项目(62303400,52272369)。

摘　　要：提出一个概率深度学习框架,通过基于物理信息的神经网络对非线性微分系统中的不确定性进行量化和演化分析.算法使用潜在变量模型(即噪声/随机变量模型)构建系统状态的概率表示,并将偏微分方程描述的物理定律引入训练过程中,建立约束关系,为基于小样本数据集的训练提供一种有效的机制.所提出的概率物理学信息神经网络算法能够提供一种灵活的框架,表征由输入中的随机性或观测中的噪声引起的物理系统输出的不确定性,避免重复采样昂贵的实验或数值模拟器的需要.最后,通过包含随机变量的非线性系统示例对所提出算法进行验证,以表明算法的有效性.This study presents a probabilistic deep learning framework that analyzes the uncertainty in nonlinear differential systems using a physics-informed neural network.The framework utilizes a latent variable model(i.e.noise/random variable model),to create a probability-based model of the system state.Physical laws that are described using partial differential equations are incorporated into the training process to establish constraint relationships,which provides an effective way to train using small samples.The proposed probabilistic physics information neural network(PPINN)algorithm provides a flexible framework,representing the uncertainty of the physical system output caused by the randomness in the input or the noise in the observation,which helps avoid the high costs associated with repeated sampling or expensive experiments.Finally,the effectiveness of the proposed algorithm is demonstrated through some nonlinear system examples containing random variables.

关 键 词：物理信息 神经网络 随机系统 小样本数据 概率神经网络 演化分析 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]