本研究提出了一种基于深度学习（DL）的降阶代理模型，该模型能够在保持高精度数据同化或历史拟合（HM）问题精度的同时，显著降低计算成本。其核心组件是嵌入控制观测（E2CO）深度学习架构。该架构作为一种降阶模型，模拟了轨迹分段线性化（TPWL）结合本征正交分解（POD）的方法，利用由高保真模型或模拟器生成的快照训练的神经网络模块来模拟地下水流。
论文的第一部分概述了支持所提出的E2CO-HM模型的理论、方法和数学方程。这些小节讨论了POD-TPWL公式和E2CO-HM公式。在本概要部分，作者描述了用于应用基于E2CO-HM方法的合成油藏模型SPE10，并讨论了所得结果。
油藏模型。本文提出的E2CO-HM模型采用了SPE10油水基准模型的一部分，网格尺寸为60×60×4。该通道状油藏模型由四层组成，每层的渗透率以mD为单位。
In this study, the authors propose the use of a deep-learning (DL) reduced-order surrogate model that can lower computational costs significantly while maintaining high accuracy for data assimilation or history-matching (HM) problems. The fundamental component is the Embed-to-Control Observe (E2CO) DL architecture. It serves as a reduced-order model mimicking the trajectory piecewise linearization (TPWL) coupled with proper orthogonal decomposition (POD) to simulate subsurface flow by using blocks of neural networks trained with the snapshots generated from a high-fidelity model or simulator.
An initial section of the complete paper outlines the theories, methods, and mathematical equations that support the proposed E2CO-HM. These subsections of the complete paper include discussions of POD-TPWL formulation and E2CO-HM formulation. In this section of the synopsis, the authors describe the synthetic reservoir model, SPE10, used to apply the E2CO-HM-based approach and discuss the results obtained.
Reservoir Model. A section of the oil/water SPE10 benchmark model with grid dimensions 60×60×4 was used in the proposed E2CO-HM. This channelized reservoir model consists of four layers with permeability values measured in mD for each layer.
