论文标题
基于转移学习的多余物理学知情的深神经网络
Transfer learning based multi-fidelity physics informed deep neural network
论文作者
论文摘要
对于许多科学和工程领域的系统，管理差分方程在近似意义上是不知道的，要么是不知道的。此类系统的分析和设计受现场和/或实验室实验收集的数据的控制。当数据收集昂贵且耗时时，这种挑战性的情况进一步恶化。为了解决这个问题，本文介绍了一种新型的多保真物理学知识深度神经网络（MF-PIDNN）。当问题的物理学以近似意义（低保真物理学）中知道并且只有少数高保真数据可用时，提出的框架特别适合。 MF-PIDNN通过使用转移学习的概念将物理知情和数据驱动的深度学习技术融合在一起。大概管理方程式首先用于训练低保真物理的知情深度神经网络。接下来是转移学习，其中使用可用的高保真数据更新低保真模型。 MF-PIDNN能够从{\ it近似}管理微分方程的{\ it近似}的物理学编码有用的信息，因此，即使在没有数据的区域中，也可以提供准确的预测。此外，训练该模型不需要低保真数据。 MF-PIDNN的适用性和实用性在解决四个基准可靠性分析问题中说明了。还提出了案例研究以说明所提出方法的有趣特征。
For many systems in science and engineering, the governing differential equation is either not known or known in an approximate sense. Analyses and design of such systems are governed by data collected from the field and/or laboratory experiments. This challenging scenario is further worsened when data-collection is expensive and time-consuming. To address this issue, this paper presents a novel multi-fidelity physics informed deep neural network (MF-PIDNN). The framework proposed is particularly suitable when the physics of the problem is known in an approximate sense (low-fidelity physics) and only a few high-fidelity data are available. MF-PIDNN blends physics informed and data-driven deep learning techniques by using the concept of transfer learning. The approximate governing equation is first used to train a low-fidelity physics informed deep neural network. This is followed by transfer learning where the low-fidelity model is updated by using the available high-fidelity data. MF-PIDNN is able to encode useful information on the physics of the problem from the {\it approximate} governing differential equation and hence, provides accurate prediction even in zones with no data. Additionally, no low-fidelity data is required for training this model. Applicability and utility of MF-PIDNN are illustrated in solving four benchmark reliability analysis problems. Case studies to illustrate interesting features of the proposed approach are also presented.
