  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.
