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DOI | 10.1029/2019WR026731 |
Physics-Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems | |
Tartakovsky, A. M.1; Marrero, C. Ortiz1; Perdikaris, Paris2; Tartakovsky, G. D.1; Barajas-Solano, D.1 | |
2020-05-01 | |
发表期刊 | WATER RESOURCES RESEARCH |
ISSN | 0043-1397 |
EISSN | 1944-7973 |
出版年 | 2020 |
卷号 | 56期号:5 |
文章类型 | Article |
语种 | 英语 |
国家 | USA |
英文摘要 | We present a physics-informed deep neural network (DNN) method for estimating hydraulic conductivity in saturated and unsaturated flows governed by Darcy's law. For saturated flow, we approximate hydraulic conductivity and head with two DNNs and use Darcy's law in addition to measurements of hydraulic conductivity and head to train these DNNs. For unsaturated flow, we approximate unsaturated conductivity function and capillary pressure with DNNs and train these DNNs using measurements of capillary pressure and the Richards equation. Because it is difficult to measure unsaturated conductivity in the field, we assume that no measurements of unsaturated conductivity are available. The proposed approach enforces the partial differential equation (PDE) (Darcy or Richards equation) constraints by minimizing the PDE residual at select points in the simulation domain. We demonstrate that physics constraints increase the accuracy of DNN approximations of sparsely observed functions and allow for training DNNs when no direct measurements of the functions of interest are available. For the saturated conductivity estimation problem, we show that the physics-informed DNN method is more accurate than the state-of-the-art maximum a posteriori probability method. For the unsaturated flow in homogeneous porous media, we find that the proposed method can accurately estimate the pressure-conductivity relationship based on the capillary pressure measurements only, even in the presence of measurement noise. |
英文关键词 | deep neural networks physics-informed machine learning parameter estimation learning constitutive relationships unsaturated flow MAP |
领域 | 资源环境 |
收录类别 | SCI-E |
WOS记录号 | WOS:000537736400036 |
WOS关键词 | ENCODER-DECODER NETWORKS ; UNCERTAINTY QUANTIFICATION ; INVERSE PROBLEMS ; SYSTEMS |
WOS类目 | Environmental Sciences ; Limnology ; Water Resources |
WOS研究方向 | Environmental Sciences & Ecology ; Marine & Freshwater Biology ; Water Resources |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://119.78.100.173/C666/handle/2XK7JSWQ/280662 |
专题 | 资源环境科学 |
作者单位 | 1.Pacific Northwest Natl Lab, Richland, WA 99352 USA; 2.Univ Penn, Mech Engn & Appl Mech, Philadelphia, PA 19104 USA |
推荐引用方式 GB/T 7714 | Tartakovsky, A. M.,Marrero, C. Ortiz,Perdikaris, Paris,et al. Physics-Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems[J]. WATER RESOURCES RESEARCH,2020,56(5). |
APA | Tartakovsky, A. M.,Marrero, C. Ortiz,Perdikaris, Paris,Tartakovsky, G. D.,&Barajas-Solano, D..(2020).Physics-Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems.WATER RESOURCES RESEARCH,56(5). |
MLA | Tartakovsky, A. M.,et al."Physics-Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems".WATER RESOURCES RESEARCH 56.5(2020). |
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