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深度学习论文:用于多物理场数据同化的物理信息神经网络及其在地下运输中的应用(Physics-Informed Neural Networks for Multi

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sa_group 发表于 2019-12-9 13:43:32 | 显示全部楼层 |阅读模式
sa_group 2019-12-9 13:43:32 199 0 显示全部楼层
深度学习论文:用于多物理场数据同化的物理信息神经网络及其在地下运输中的应用(Physics-Informed Neural Networks for Multiphysics Data Assimilation with  Application to Subsurface Transport)由于测量的稀疏性,多孔介质的非均质性以及前向数值模型的高计算成本,地下传输问题中用于参数和状态估计的数据同化仍然是一项重大挑战。我们提出了一种基于物理学的深度神经网络(DNN)机器学习方法,用于从稀疏测量中估计空间相关的水力传导率,水头和浓度场。在此方法中,我们采用单个DNN近似物理系统的未知参数(例如,水力传导率)和状态(例如,水头和浓度),并通过最小化由控制方程式残差组成的损失函数共同训练这些DNN。关于测量数据的误差。我们采用这种方法来吸收电导率,水力压头和浓度测量值,以便在稳态对流-扩散问题中对电导率,水力压头和浓度场进行联合反演。我们在训练过程中研究了基于数据的DNN方法在数据大小,变量数量(电导率和水头与电导率,水头和浓度),DNNssize和DNN初始化方面的准确性。我们证明,当训练集由稀疏数据组成时,基于物理知识的DNN比标准数据驱动DNN准确得多。我们还表明,参数估计的准确性随着附加变量的反向联合而增加。
Data assimilation for parameter and state estimation in subsurface transportproblems remains a significant challenge due to the sparsity of measurements,the heterogeneity of porous media, and the high computational cost of forwardnumerical models.We present a physics-informed deep neural networks (DNNs)machine learning method for estimating space-dependent hydraulic conductivity,hydraulic head, and concentration fields from sparse measurements.In thisapproach, we employ individual DNNs to approximate the unknown parameters(eg, hydraulic conductivity) and states (eg, hydraulic head andconcentration) of a physical system, and jointly train these DNNs by minimizingthe loss function that consists of the governing equations residuals inaddition tothe error with respect to measurement data.We apply this approachto assimilate conductivity, hydraulic head, and concentration measurements forjoint inversion of the conductivity, hydraulic head, and concentration fieldsin a steady-state advection--dispersion problem.We study the accuracy of thephysics-informed DNN approach with respect to data size, number of variables(conductivity and head versus conductivity, head, and concentration), DNNssize, and DNN initialization during training.We demonstrate that thephysics-informed DNNs are significantly more accurate than standard data-drivenDNNs when the training set consists of sparse data.We also show that theaccuracy of parameter estimation increases as additional variables are invertedjointly.深度学习论文:用于多物理场数据同化的物理信息神经网络及其在地下运输中的应用(Physics-Informed Neural Networks for Multiphysics Data Assimilation with  Application to Subsurface Transport)
URL地址:https://arxiv.org/abs/1912.02968     ----pdf下载地址:https://arxiv.org/pdf/1912.02968    ----深度学习论文:用于多物理场数据同化的物理信息神经网络及其在地下运输中的应用(Physics-Informed Neural Networks for Multiphysics Data Assimilation with  Application to Subsurface Transport)
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