[Paper Review] Data-Space Inversion Using a Recurrent Autoencoder for Time-Series Parameterization

Su Jiang, Louis J. Durlofsky|arXiv (Cornell University)|Apr 30, 2020

Reservoir Engineering and Simulation Methods36 references4 citations

TL;DR

This paper proposes a recurrent autoencoder (RAE)-based data parameterization method for data-space inversion (DSI) in subsurface flow modeling, using LSTM networks to capture temporal correlations in time-series flow data. The RAE-DSI approach significantly improves posterior prediction accuracy—especially for covariance and derived quantities—compared to PCA-based and truncation-based DSI methods, as validated against rejection sampling benchmarks in 2D and 3D reservoir models.

ABSTRACT

Data-space inversion (DSI) and related procedures represent a family of methods applicable for data assimilation in subsurface flow settings. These methods differ from model-based techniques in that they provide only posterior predictions for quantities (time series) of interest, not posterior models with calibrated parameters. DSI methods require a large number of flow simulations to first be performed on prior geological realizations. Given observed data, posterior predictions can then be generated directly. DSI operates in a Bayesian setting and provides posterior samples of the data vector. In this work we develop and evaluate a new approach for data parameterization in DSI. Parameterization reduces the number of variables to determine in the inversion, and it maintains the physical character of the data variables. The new parameterization uses a recurrent autoencoder (RAE) for dimension reduction, and a long-short-term memory (LSTM) network to represent flow-rate time series. The RAE-based parameterization is combined with an ensemble smoother with multiple data assimilation (ESMDA) for posterior generation. Results are presented for two- and three-phase flow in a 2D channelized system and a 3D multi-Gaussian model. The RAE procedure, along with existing DSI treatments, are assessed through comparison to reference rejection sampling (RS) results. The new DSI methodology is shown to consistently outperform existing approaches, in terms of statistical agreement with RS results. The method is also shown to accurately capture derived quantities, which are computed from variables considered directly in DSI. This requires correlation and covariance between variables to be properly captured, and accuracy in these relationships is demonstrated. The RAE-based parameterization developed here is clearly useful in DSI, and it may also find application in other subsurface flow problems.

Motivation & Objective

• To improve data-space inversion (DSI) performance by replacing traditional linear parameterization with a nonlinear deep learning approach.
• To address limitations in PCA-based methods, such as unphysical behavior when combined with histogram transformation (HT), especially in capturing complex correlations.
• To enable accurate posterior prediction of time-series flow rates and derived quantities (e.g., BHP, WPR, OPR) in subsurface flow problems.
• To evaluate the RAE-based DSI framework against reference rejection sampling (RS) results in both 2D channelized and 3D multi-Gaussian reservoir models.
• To assess the method’s robustness under low-data conditions and its ability to preserve covariance structures in data vectors.

Proposed method

• A recurrent autoencoder (RAE) is used to perform nonlinear dimensionality reduction on time-series data vectors from flow simulations, replacing linear PCA.
• The RAE architecture includes an encoder with LSTM layers to learn low-dimensional latent representations and a decoder with stacked LSTM layers to reconstruct the original time-series data.
• The RAE-based latent variables are used as the parameterized data space in DSI, enabling efficient posterior sampling.
• Ensemble Smoother with Multiple Data Assimilation (ESMDA) is applied to generate posterior samples of the data vector conditioned on observed data.
• The method is tested on two-phase and three-phase flow in a 2D channelized system and a 3D multi-Gaussian model with multiple wells.
• Performance is evaluated using statistical metrics such as P10-P90 intervals, Mahalanobis distance, and covariance accuracy compared to reference rejection sampling (RS).

Experimental results

Research questions

• RQ1 Can a recurrent autoencoder (RAE) provide a more accurate and physically consistent parameterization of time-series data in data-space inversion (DSI) than traditional PCA-based methods?
• RQ2 How does the RAE-based DSI method perform in capturing posterior correlations and covariances between time-series data variables, especially under limited observed data?
• RQ3 Does the RAE-DSI framework outperform existing DSI variants—including PCA+HT and standalone ESMDA with truncation—in predicting both primary and derived reservoir variables?
• RQ4 How well does the RAE-DSI method preserve the temporal dynamics and inter-well relationships in flow rate time series across different geological models?
• RQ5 What are the limitations of the current RAE-DSI approach in handling high-dimensional data, noisy time series, or abrupt changes (e.g., well operations)?

Key findings

• The RAE-DSI method consistently outperformed PCA+HT+ESMDA and ESMDA with truncation in predicting P10, P50, and P90 posterior intervals for primary and derived time-series variables in both 2D and 3D models.
• The RAE-based parameterization accurately captured the covariance structure between data variables, such as BHP, WPR, and OPR, which was poorly represented by PCA+HT and truncation methods.
• In the 2D channelized case with two additional 'true' models, the RAE-DSI method achieved the lowest Mahalanobis distance to the reference rejection sampling (RS) results across all three test cases.
• The method demonstrated robustness in low-data scenarios, where accurate covariance modeling is critical for reliable posterior predictions.
• The RAE-based approach mitigated unphysical behavior common in PCA+HT methods, particularly in non-Gaussian and complex flow regimes.
• The framework is compatible with existing DSI workflows and enables efficient posterior sampling using ESMDA without additional flow simulations.