# Data-Space Inversion Using a Recurrent Autoencoder for Time-Series Parameterization

arXiv: https://arxiv.org/abs/2005.00061 · HTML: https://mlsanity.com/paper/2005.00061/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2020.

## Built on by (most cited first, 5 of 5)

- [Deep Learning-Accelerated 3D Carbon Storage Reservoir Pressure Forecasting Based on Data Assimilation Using Surface Displacement from InSAR](https://mlsanity.com/paper/2201.08543/) (2022)
- [History Matching for Geological Carbon Storage using Data-Space Inversion with Spatio-Temporal Data Parameterization](https://mlsanity.com/paper/2310.03228/) (2023)
- [Latent diffusion models for parameterization and data assimilation of facies-based geomodels](https://mlsanity.com/paper/2406.14815/) (2024)
- [Deep Learning for Simultaneous Inference of Hydraulic and Transport Properties](https://mlsanity.com/paper/2110.12367/) (2021)
- [Prediction of Fault Slip Tendency in CO2 Storage using Data-space Inversion](https://mlsanity.com/paper/2601.05431/) (2026)

## Abstract (arXiv)

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.