Latent-space inversion (LSI): a deep learning framework for inverse mapping of subsurface flow data

This paper presents Latent-Space Inversion (LSI) as a new data-informed inversion and parameterization framework where dimensionality reduction is tailored to flow physics that governs the behavior of subsurface systems. Inverse modeling in hydrogeology and petroleum engineering involves minimizing...

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Published in:	Computational geosciences Vol. 26; no. 1; pp. 71 - 99
Main Authors:	Razak, Syamil Mohd, Jiang, Anyue, Jafarpour, Behnam
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.02.2022 Springer Nature B.V
Subjects:	Calibration Contamination Data integration Deep learning Earth and Environmental Science Earth Sciences Feature extraction Flow mapping Flow simulation Geology Geotechnical Engineering & Applied Earth Sciences Hydrogeology Inverse problems Kalman filters Large scale integration Learning algorithms Learning behaviour Machine learning Mapping Mathematical Modeling and Industrial Mathematics Mathematical models Original Paper Parameterization Parameters Petroleum engineering Physics Redundancy Soil Science & Conservation Training Wavelet transforms Deep learning Subsurface flow Model calibration Parameterization Latent space inversion
ISSN:	1420-0597, 1573-1499
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Abstract	This paper presents Latent-Space Inversion (LSI) as a new data-informed inversion and parameterization framework where dimensionality reduction is tailored to flow physics that governs the behavior of subsurface systems. Inverse modeling in hydrogeology and petroleum engineering involves minimizing the mismatch between observed and simulated data from a set of prior models. A myriad of approaches has been developed to accomplish this goal over the years, and their performance is dependent on the effectiveness of parameterization and the capability of data conditioning technique. We demonstrate LSI as a more robust and efficient approach for calibration of subsurface model over traditional approaches where dimensionality reduction of model parameters is done independently (decoupled) of flow data integration. LSI provides a compact description of the parameters in a latent space that does not only exploit the redundancy of large-scale geologic features but also retain features that are sensitive to flow data. Motivated by recent advances in machine learning research, LSI architecture involves a pair of deep convolutional autoencoders that are coupled to jointly extract spatial geologic features in subsurface models and temporal trends in flow data. The LSI architecture is trained offline using prior model realizations and their corresponding simulated flow responses (as training data) to effectively represent the model and data and to learn the complex nonlinear inverse mapping between data and model. Once field data becomes available, calibrated models can be rapidly obtained using the trained LSI architecture. The resulting data-informed model latent space can be explored to allow the generation of an ensemble of calibrated model realizations around the inversion solution. This is especially useful when observed data is noisy and multiple inversion solutions can be accepted within the noise range. We present several inversion examples to illustrate the performance of LSI and to discuss the advantages and limitations of data-driven inversion approaches compared to the conventional inverse modelling formulations.
AbstractList	This paper presents Latent-Space Inversion (LSI) as a new data-informed inversion and parameterization framework where dimensionality reduction is tailored to flow physics that governs the behavior of subsurface systems. Inverse modeling in hydrogeology and petroleum engineering involves minimizing the mismatch between observed and simulated data from a set of prior models. A myriad of approaches has been developed to accomplish this goal over the years, and their performance is dependent on the effectiveness of parameterization and the capability of data conditioning technique. We demonstrate LSI as a more robust and efficient approach for calibration of subsurface model over traditional approaches where dimensionality reduction of model parameters is done independently (decoupled) of flow data integration. LSI provides a compact description of the parameters in a latent space that does not only exploit the redundancy of large-scale geologic features but also retain features that are sensitive to flow data. Motivated by recent advances in machine learning research, LSI architecture involves a pair of deep convolutional autoencoders that are coupled to jointly extract spatial geologic features in subsurface models and temporal trends in flow data. The LSI architecture is trained offline using prior model realizations and their corresponding simulated flow responses (as training data) to effectively represent the model and data and to learn the complex nonlinear inverse mapping between data and model. Once field data becomes available, calibrated models can be rapidly obtained using the trained LSI architecture. The resulting data-informed model latent space can be explored to allow the generation of an ensemble of calibrated model realizations around the inversion solution. This is especially useful when observed data is noisy and multiple inversion solutions can be accepted within the noise range. We present several inversion examples to illustrate the performance of LSI and to discuss the advantages and limitations of data-driven inversion approaches compared to the conventional inverse modelling formulations.
Author	Jafarpour, Behnam Jiang, Anyue Razak, Syamil Mohd
Author_xml	– sequence: 1 givenname: Syamil Mohd surname: Razak fullname: Razak, Syamil Mohd organization: Mork Family Department of Chemical Engineering and Materials Science, University of Southern California – sequence: 2 givenname: Anyue surname: Jiang fullname: Jiang, Anyue organization: Mork Family Department of Chemical Engineering and Materials Science, University of Southern California – sequence: 3 givenname: Behnam orcidid: 0000-0003-1071-5299 surname: Jafarpour fullname: Jafarpour, Behnam email: jafarpou@usc.edu organization: Mork Family Department of Chemical Engineering and Materials Science, University of Southern California
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Copyright	The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021.
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SubjectTerms	Calibration Contamination Data integration Deep learning Earth and Environmental Science Earth Sciences Feature extraction Flow mapping Flow simulation Geology Geotechnical Engineering & Applied Earth Sciences Hydrogeology Inverse problems Kalman filters Large scale integration Learning algorithms Learning behaviour Machine learning Mapping Mathematical Modeling and Industrial Mathematics Mathematical models Original Paper Parameterization Parameters Petroleum engineering Physics Redundancy Soil Science & Conservation Training Wavelet transforms
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Title	Latent-space inversion (LSI): a deep learning framework for inverse mapping of subsurface flow data
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