Data-space inversion (DSI) and related procedures represent a family of methods applicable for data assimilation in subsurface flow settings. These methods differ from usual 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 (O(500–1000)) of flow simulations to first be performed on prior geological realizations. Given observed data, posterior predictions for time series of interest, such as well injection or production rates, 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 is useful in DSI as it 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) recurrent neural network architecture to represent flow-rate time series. The RAE-based parameterization is combined with an ensemble smoother with multiple data assimilation (ESMDA) for posterior data sample generation. Results are presented for two- and three-phase flows in a 2D channelized system and a 3D multi-Gaussian model. The new DSI RAE procedure, along with several existing DSI treatments, is assessed through detailed comparison to reference rejection sampling (RS) results. The new DSI methodology is shown to consistently outperform existing approaches, in terms of statistical (P₁₀–P₉₀ interval and Mahalanobis distance) 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.

数据空间反演（DSI）和相关过程代表了适用于地下流量设置中数据同化的一系列方法。这些方法与通常的基于模型的技术的不同之处在于，它们仅提供感兴趣量（时间序列）的后验预测，而不提供具有已校准参数的后验模型。DSI方法需要大量（O（500–1000））的流动模拟首先要在先前的地质实现上进行。在给定观测数据的情况下，可以直接生成感兴趣的时间序列的后验预测，例如井注或产量。DSI在贝叶斯设置下运行，并提供数据向量的后采样。在这项工作中，我们开发和评估了DSI中数据参数化的新方法。参数化在DSI中很有用，因为它减少了要在反演中确定的变量数量，并且保持了数据变量的物理特性。新的参数化使用递归自动编码器（RAE）来减少尺寸，并使用长短期记忆（LSTM）递归神经网络体系结构来表示流速时间序列。基于RAE的参数化与具有多个数据同化（ESMDA）的整体平滑器相结合，用于生成后验数据样本。给出了2D通道化系统和3D多高斯模型中两相和三相流的结果。通过与参考拒绝采样（RS）结果进行详细比较，评估了新的DSI RAE程序以及几种现有的DSI处理方法。新的DSI方法论在统计数据（P₁₀ –P ₉₀间隔和马氏距离）与RS结果一致。还显示了该方法可以准确捕获派生的数量，这些数量是根据直接在DSI中考虑的变量计算得出的。这要求正确捕获变量之间的相关性和协方差，并证明这些关系的准确性。此处开发的基于RAE的参数化在DSI中显然非常有用，并且可能还会在其他地下流动问题中找到应用。