Deep Learning for Simultaneous Inference of Hydraulic and Transport Properties

Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this invers...

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Published in:	Water resources research Vol. 58; no. 10
Main Authors:	Zhou, Zitong, Zabaras, Nicholas, Tartakovsky, Daniel M.
Format:	Journal Article
Language:	English
Published:	Washington John Wiley & Sons, Inc 01.10.2022 American Geophysical Union (AGU)
Subjects:	adversarial Algorithms Bayesian analysis Bayesian theory Coders Computational efficiency Computer applications Computing costs Conductivity Contaminants Data assimilation Data collection Deep learning History Hydraulics Identification inverse problem Inverse problems Machine learning Mathematical models neural network Parameters Piezometric head Probability theory Reconstruction Remediation Simulators Simultaneous discrimination learning source indentification subsurface Transport Transport properties water
ISSN:	0043-1397, 1944-7973
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Abstract	Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this inverse problem is notoriously difficult due to, in part, high dimensionality of the parameter space and high computational cost of repeated forward solves. We use a convolutional adversarial autoencoder (CAAE) to parameterize a heterogeneous non‐Gaussian conductivity field via a low‐dimensional latent representation. A three‐dimensional dense convolutional encoder‐decoder (DenseED) network serves as a forward surrogate of the flow and transport model. The CAAE‐DenseED surrogate is fed into the ensemble smoother with multiple data assimilation (ESMDA) algorithm to sample from the Bayesian posterior distribution of the unknown parameters, forming a CAAE‐DenseED‐ESMDA inversion framework. The resulting CAAE‐DenseED‐ESMDA inversion strategy is used to identify a three‐dimensional contaminant source and conductivity field. A comparison of the inversion results from CAAE‐ESMDA with physical flow and transport simulator and from CAAE‐DenseED‐ESMDA shows that the latter yields accurate reconstruction results at the fraction of the computational cost of the former. Plain Language Summary Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this inverse problem is notoriously difficult due to, in part, high dimensionality of the parameter space and high computational cost of repeated forward solves. We develop a deep‐learning strategy to identify a three‐dimensional contaminant source and conductivity field from sparse observations. Key Points Our deep‐learning strategy reconstructs three‐dimensional conductivity field and contaminant release history Conductivity parameterization with convolutional adversarial autoencoder reduces the inverse problem's dimensionality Convolutional encoder‐decoder acts as a surrogate of forward models; ensemble smoother approximates parameters' posterior distribution
AbstractList	Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this inverse problem is notoriously difficult due to, in part, high dimensionality of the parameter space and high computational cost of repeated forward solves. We use a convolutional adversarial autoencoder (CAAE) to parameterize a heterogeneous non‐Gaussian conductivity field via a low‐dimensional latent representation. A three‐dimensional dense convolutional encoder‐decoder (DenseED) network serves as a forward surrogate of the flow and transport model. The CAAE‐DenseED surrogate is fed into the ensemble smoother with multiple data assimilation (ESMDA) algorithm to sample from the Bayesian posterior distribution of the unknown parameters, forming a CAAE‐DenseED‐ESMDA inversion framework. The resulting CAAE‐DenseED‐ESMDA inversion strategy is used to identify a three‐dimensional contaminant source and conductivity field. A comparison of the inversion results from CAAE‐ESMDA with physical flow and transport simulator and from CAAE‐DenseED‐ESMDA shows that the latter yields accurate reconstruction results at the fraction of the computational cost of the former. Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this inverse problem is notoriously difficult due to, in part, high dimensionality of the parameter space and high computational cost of repeated forward solves. We use a convolutional adversarial autoencoder (CAAE) to parameterize a heterogeneous non‐Gaussian conductivity field via a low‐dimensional latent representation. A three‐dimensional dense convolutional encoder‐decoder (DenseED) network serves as a forward surrogate of the flow and transport model. The CAAE‐DenseED surrogate is fed into the ensemble smoother with multiple data assimilation (ESMDA) algorithm to sample from the Bayesian posterior distribution of the unknown parameters, forming a CAAE‐DenseED‐ESMDA inversion framework. The resulting CAAE‐DenseED‐ESMDA inversion strategy is used to identify a three‐dimensional contaminant source and conductivity field. A comparison of the inversion results from CAAE‐ESMDA with physical flow and transport simulator and from CAAE‐DenseED‐ESMDA shows that the latter yields accurate reconstruction results at the fraction of the computational cost of the former. Plain Language Summary Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this inverse problem is notoriously difficult due to, in part, high dimensionality of the parameter space and high computational cost of repeated forward solves. We develop a deep‐learning strategy to identify a three‐dimensional contaminant source and conductivity field from sparse observations. Key Points Our deep‐learning strategy reconstructs three‐dimensional conductivity field and contaminant release history Conductivity parameterization with convolutional adversarial autoencoder reduces the inverse problem's dimensionality Convolutional encoder‐decoder acts as a surrogate of forward models; ensemble smoother approximates parameters' posterior distribution Abstract Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this inverse problem is notoriously difficult due to, in part, high dimensionality of the parameter space and high computational cost of repeated forward solves. We use a convolutional adversarial autoencoder (CAAE) to parameterize a heterogeneous non‐Gaussian conductivity field via a low‐dimensional latent representation. A three‐dimensional dense convolutional encoder‐decoder (DenseED) network serves as a forward surrogate of the flow and transport model. The CAAE‐DenseED surrogate is fed into the ensemble smoother with multiple data assimilation (ESMDA) algorithm to sample from the Bayesian posterior distribution of the unknown parameters, forming a CAAE‐DenseED‐ESMDA inversion framework. The resulting CAAE‐DenseED‐ESMDA inversion strategy is used to identify a three‐dimensional contaminant source and conductivity field. A comparison of the inversion results from CAAE‐ESMDA with physical flow and transport simulator and from CAAE‐DenseED‐ESMDA shows that the latter yields accurate reconstruction results at the fraction of the computational cost of the former. Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this inverse problem is notoriously difficult due to, in part, high dimensionality of the parameter space and high computational cost of repeated forward solves. We use a convolutional adversarial autoencoder (CAAE) to parameterize a heterogeneous non‐Gaussian conductivity field via a low‐dimensional latent representation. A three‐dimensional dense convolutional encoder‐decoder (DenseED) network serves as a forward surrogate of the flow and transport model. The CAAE‐DenseED surrogate is fed into the ensemble smoother with multiple data assimilation (ESMDA) algorithm to sample from the Bayesian posterior distribution of the unknown parameters, forming a CAAE‐DenseED‐ESMDA inversion framework. The resulting CAAE‐DenseED‐ESMDA inversion strategy is used to identify a three‐dimensional contaminant source and conductivity field. A comparison of the inversion results from CAAE‐ESMDA with physical flow and transport simulator and from CAAE‐DenseED‐ESMDA shows that the latter yields accurate reconstruction results at the fraction of the computational cost of the former. Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this inverse problem is notoriously difficult due to, in part, high dimensionality of the parameter space and high computational cost of repeated forward solves. We develop a deep‐learning strategy to identify a three‐dimensional contaminant source and conductivity field from sparse observations. Our deep‐learning strategy reconstructs three‐dimensional conductivity field and contaminant release history Conductivity parameterization with convolutional adversarial autoencoder reduces the inverse problem's dimensionality Convolutional encoder‐decoder acts as a surrogate of forward models; ensemble smoother approximates parameters' posterior distribution
Author	Tartakovsky, Daniel M. Zhou, Zitong Zabaras, Nicholas
Author_xml	– sequence: 1 givenname: Zitong surname: Zhou fullname: Zhou, Zitong organization: Stanford University – sequence: 2 givenname: Nicholas orcidid: 0000-0003-3144-8388 surname: Zabaras fullname: Zabaras, Nicholas organization: University of Notre Dame – sequence: 3 givenname: Daniel M. orcidid: 0000-0001-9019-8935 surname: Tartakovsky fullname: Tartakovsky, Daniel M. email: tartakovsky@stanford.edu organization: Stanford University
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Snippet	Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two... Abstract Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation....
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SubjectTerms	adversarial Algorithms Bayesian analysis Bayesian theory Coders Computational efficiency Computer applications Computing costs Conductivity Contaminants Data assimilation Data collection Deep learning History Hydraulics Identification inverse problem Inverse problems Machine learning Mathematical models neural network Parameters Piezometric head Probability theory Reconstruction Remediation Simulators Simultaneous discrimination learning source indentification subsurface Transport Transport properties water
Title	Deep Learning for Simultaneous Inference of Hydraulic and Transport Properties
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