资源环境科技发展态势分析平台

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.