Using Deep Learning to Improve Ensemble Smoother: Applications to Subsurface Characterization

Abstract

Ensemble smoother (ES) has been widely used in various research fields to reduce the uncertainty of the system-of-interest. However, the commonly adopted ES method that employs the Kalman formula, that is, ES (K) , does not perform well when the probability distributions involved are non-Gaussian. To address this issue, we suggest to use deep learning (DL) to derive an alternative analysis scheme for ES in non-Gaussian data assimilation problems. Here we show that the DL-based ES method, that is, ES (DL) , is more general and flexible. In this new scheme, a high volume of training data is generated from a relatively small-sized ensemble of model parameters and simulation outputs, and possible non-Gaussian features can be preserved in the training data and captured by an adequate DL model. This new variant of ES is tested in two subsurface characterization problems with or without the Gaussian assumption. Results indicate that ES (DL) can produce similar (in the Gaussian case) or even better (in the non-Gaussian case) results compared to those from ES (K). The success of ES (DL) comes from the power of DL in extracting complex (including non-Gaussian) features and learning nonlinear relationships from massive amounts of training data. Although in this work we only apply the ES (DL) method in parameter estimation problems, the proposed idea can be conveniently extended to analysis of model structural uncertainty and state estimation in real-time forecasting problems.

Stage‐Wise Stochastic Deep Learning Inversion Framework for Subsurface Sedimentary Structure Identification

“…For example, the inversion framework can be used to optimize the locations of monitoring wells to improve the accuracy of subsurface sedimentary structure identification or parameter estimation (Mo et al, 2019;. The steps of stage-2 are also suitable for the inversion of continuous parameter fields by replacing the training samples of the OCAAE with corresponding training images of continuous parameter distribution (Mo et al, 2020;Zhang et al, 2020). Furthermore, the OCAAE and DOCRN can be widely used in other geophysical domains, which require repeated utilization of the geological and transport models (Kang et al, 2021;Tang et al, 2021).…”

“…Considering the lack of direct facies data (i.e., bodies of sediments and rocks, Soltanian & Ritzi [2014]), inversion or data assimilating methods have been widely adopted to delineate spatial distribution of facies by estimating parameters of the subsurface sedimentary structure model (X. Song et al., 2019; Zhang et al., 2020). The stochastic models (Dai et al., 2019; He et al., 2014; Rajaram, 2016; Soltanian et al., 2020; Tahmasebi, 2017) and the deep‐learning‐based generative models (Bao et al., 2020; Mosser et al., 2017; Tang et al., 2021) are amongst the most commonly used methods to derive subsurface sedimentary structures.…”

“…By changing the value of each dimension of the vector, different structure details can be modified (Laloy et al., 2018; Nesvold & Mukerji, 2021). Therefore, more accurate subsurface sedimentary structures can be obtained by estimating optimized latent vectors (Zhang et al., 2020). However, the requirement of training samples is the main limitation for such methods, as it is practically difficult to obtain sufficient samples with facies distributions similar to that of the target structure.…”

Predicting Thermal Performance of an Enhanced Geothermal System From Tracer Tests in a Data Assimilation Framework

“…On the one hand, PCA is only applicable to random fields that can be fully characterized by two‐point statistics (Liu & Durlofsky, 2020), such as the log‐normal aperture field used in the present study. On the other hand, ES‐MDA requires a Gaussian parameter distribution, otherwise its performance could be severely degraded (Canchumuni et al., 2020; Zhang et al., 2020). In the current study, regardless of the true parameter field distribution, we assume a Gaussian (or log‐normal) aperture field to enable the use of PCA for dimensionality reduction.…”

Learning to Correct Climate Projection Biases

“…The high requirement on the capability of black‐box models is no longer an obstacle. Recent years have witnessed the flourishing of deep learning that successfully solves complex, high‐dimensional problems, including physical system simulations such as electromagnetic and fluid dynamics (Kutz, 2017; Mills et al., 2017), as well as climate applications such as parameterization (Pan, 2019; Rasp et al., 2018), downscaling (Miao et al., 2019; Pan, Hsu, AghaKouchak, & Sorooshian, 2019), analog forecasting (Pan, Anderson, Goncalves, et al., 2020; Weyn et al., 2019), inverse modeling (Zhang et al., 2020), and climate signal identification (Barnes et al., 2019).…”