Physics-informed neural networks for multiphysics data assimilation with application to subsurface transport
Physics-informed neural networks for multiphysics data assimilation with application to subsurface transport
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DOI：
10.1016/j.advwatres.2020.103610
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发表时间：
2020-07-01
影响因子：
4.7
通讯作者：
Tartakovsky, Alexandre M.
中科院分区：
文献类型：
--
作者：
He, QiZhi;Barajas-Solano, David;Tartakovsky, Alexandre M.
地下输运问题中参数和状态估计的数据同化仍然是一个重大的挑战，因为测量的稀疏性，多孔介质的非均匀性，以及正演数值模型的高计算成本。我们提出了一种多物理信息的深度神经网络机器学习方法，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。在这种方法中，我们采用单独的深度神经网络（DNN）来近似未知参数（例如，水力传导性）和状态（例如，水力压头和浓度）。接下来，我们通过最小化损失函数来联合训练这些DNN，该损失函数由控制方程残差以及测量数据的误差组成。我们应用这种方法来同化的电导率，水头和浓度测量的联合反演这些参数和状态在一个稳态的对流扩散问题。我们研究了所提出的数据同化方法相对于数据大小的准确性（即，测量变量的数量和每个变量的测量数量）、DNN大小和参数字段的复杂度。我们证明了物理信息DNN比标准数据驱动DNN更准确，特别是当训练集由稀疏数据组成时。我们还表明，参数估计的准确性增加，因为更多的不同的多物理场变量联合反演。
Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge because of the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward numerical models. We present a multiphysics-informed deep neural network machine learning method for estimating space-dependent hydraulic conductivity, hydraulic head, and concentration fields from sparse measurements. In this approach, we employ individual deep neural networks (DNNs) to approximate the unknown parameters (e.g., hydraulic conductivity) and states (e.g., hydraulic head and concentration) of a physical system. Next, we jointly train these DNNs by minimizing the loss function that consists of the governing equations residuals in addition to the error with respect to measurement data. We apply this approach to assimilate conductivity, hydraulic head, and concentration measurements for the joint inversion of these parameter and states in a steady-state advection-dispersion problem. We study the accuracy of the proposed data assimilation approach with respect to the data size (i.e., the number of measured variables and the number of measurements of each variable), DNN size, and the complexity of the parameter field. We demonstrate that the physics-informed DNNs are significantly more accurate than the standard data-driven DNNs, especially when the training set consists of sparse data. We also show that the accuracy of parameter estimation increases as more different multiphysics variables are inverted jointly.