Simulation-free reliability analysis with active learning and Physics-Informed Neural Network
Simulation-free reliability analysis with active learning and Physics-Informed Neural Network
复制标题
通过主动学习和物理信息神经网络进行免仿真可靠性分析
DOI：
10.1016/j.ress.2022.108716
复制
发表时间：
2022
影响因子：
8.1
通讯作者：
Shafieezadeh, Abdollah
中科院分区：
文献类型：
--
作者：
Zhang, Chi;Shafieezadeh, Abdollah
物理现象通常由偏微分方程（PDE）描述，传统上使用计算要求高的有限元，差分或体积方法来求解以产生标记数据。由于其多查询的性质，事件概率的表征需要许多这样的模拟，这可能会变得令人望而却步，因为获取标记数据的成本很高。与传统的偏微分方程求解方法不同，物理信息神经网络（PINN）直接使用编码在偏微分方程中的物理知识进行训练，因此无需模拟。在此基础上，我们提出了一种无仿真的不确定性量化方法，称为自适应训练PINN可靠性分析（AT-PINN-RA）。我们引入了一个主动学习的方法，训练PINN求解偏微分方程和表征极限状态的双重目标。该方法从PINN模型的响应中主动学习以识别极限状态，随后自适应地将PINN模型的训练重点转移到故障概率表征的高重要性区域，以提高可靠性估计的准确性和效率。AT-PINN-RA的性能进行了研究，使用不同的复杂性的四个基准问题。在所有示例中，AT-PINN-RA提供了高效率的事件概率的准确估计。
Physical phenomena are often described by partial differential equations (PDEs), which have been traditionally solved using computationally demanding finite element, difference, or volume methods to produce labeled data. Due to its multi-query nature, characterization of event probabilities requires many such simulations, which can become prohibitive given the high costs of acquiring labeled data. As opposed to conventional PDE solution methods, Physics-Informed Neural Network (PINN) is directly trained using the physics knowledge encoded in PDEs, and therefore is simulation free. Building on this capability, we propose a simulation-free uncertainty quantification method called adaptively trained PINN for reliability analysis (AT-PINN-RA). We introduce an active learning approach with the dual objective of training PINN for solving PDEs and characterizing the limit state. The approach actively learns from the responses of the PINN model to identify the limit state and subsequently, adaptively shifts the focus of the training of the PINN model to regions of high importance for failure probability characterization to boost the accuracy and efficiency of reliability estimation. The performance of AT-PINN-RA is investigated using four benchmark problems with varying complexities. In all examples, AT-PINN-RA provides accurate estimates of event probabilities with high efficiency.