Transfer learning based multi-fidelity physics informed deep neural network
Transfer learning based multi-fidelity physics informed deep neural network
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DOI：
10.1016/j.jcp.2020.109942
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发表时间：
2021-01-05
影响因子：
4.1
通讯作者：
Chakraborty, Souvik
中科院分区：
文献类型：
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作者：
Chakraborty, Souvik
对于科学和工程中的许多系统，控制微分方程要么是未知的，要么是近似已知的。此类系统的分析和设计取决于从现场和/或实验室实验中收集的数据。当数据收集既昂贵又耗时时，这种具有挑战性的情况会进一步恶化。针对这一问题，提出了一种新的多保真物理信息深度神经网络(MF-PIDNN)。所提出的框架特别适用于在近似意义上已知问题的物理(低保真物理)并且只有少数高保真数据可用的情况。MF-PIDNN通过使用迁移学习的概念，融合了物理知识和数据驱动的深度学习技术。该近似控制方程首次用于训练低保真物理信息的深度神经网络。然后是转移学习，其中通过使用可用的高保真数据来更新低保真模型。MF-PIDNN能够从近似控制微分方程中编码关于问题物理的有用信息，因此，即使在没有数据的区域也能提供准确的预测。此外，训练该模型不需要低保真数据。给出了两个涉及线性和非线性相关函数逼近的例子，说明了转移学习在解决多保真度问题中的有效性。以四个基准可靠性分析问题为例，说明了MF-PIDNN的适用性和实用性。所提供的案例研究说明了拟议方法的有趣特征。(C)2020 Elsevier Inc.保留所有权利。
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 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. Two examples involving function approximations with linear and nonlinear correlation are presented to illustrate the effectiveness of transfer learning in solving multi-fidelity problems. Applicability and utility of MF-PIDNN are illustrated in solving four benchmark reliability analysis problems. Case studies presented illustrate interesting features of the proposed approach. (C) 2020 Elsevier Inc. All rights reserved.