Deep learning-based surrogate models have been a promising way of dealing with the computational effort of data assimilation. Although the surrogate can reduce the computational cost, the results are influenced by the approximation error of the surrogate. Online learning methods refit surrogates to improve the accuracy using newly generated samples during iterations. However, it is still a challenge to determine which samples should be selected to refit the surrogate. In this work, we develop a Bayesian surrogate model and an online learning method to enhance the feasibility of surrogate models and the efficiency of data assimilation. First, the Bayesian surrogate model is constructed with a deep learning-based surrogate architecture and a dropout mechanism. After the training of the surrogate, the uncertainty of samples can be obtained by multiple forward inferences of the surrogate, in which the dropout is kept active. Second, the Bayesian surrogate model is combined with the ensemble smoother with multiple data assimilation (ES-MDA) algorithm to update uncertain parameters. In each iteration, an adaptive online learning method, based on the prediction uncertainty of the surrogate model, is designed to select samples for simulation and retrain the surrogate. This work provides an efficient framework to quantify the uncertainty of deep-learning surrogate models and determine the samples to retrain the surrogate. It is suitable for most deep-learning surrogate architectures and can be easily integrated into data assimilation problems. The proposed method was verified on a complex three-dimensional three-phase reservoir. The results indicated that, compared with simulation-based methods, the proposed method can achieve similar inversion results while reducing the computational cost by over 45%; compared with other surrogate-based methods, the proposed method makes the surrogate model more robust and yields the closest results to those based on numerical simulation.

中文翻译：

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具有自适应在线采样的 Deep Bayesian 代理模型，用于基于集成的数据同化


基于深度学习的代理模型一直是处理数据同化计算工作的一种很有前途的方法。尽管代理项可以降低计算成本，但结果会受到代理项的近似误差的影响。在线学习方法在迭代期间使用新生成的样本重新调整代理项以提高准确性。但是，确定应选择哪些样本来重新安装替代项仍然是一个挑战。在这项工作中，我们开发了一个贝叶斯代理模型和一种在线学习方法，以提高代理模型的可行性和数据同化的效率。首先，贝叶斯代理模型采用基于深度学习的代理架构和退出机制构建。在代理项训练之后，可以通过代理项的多个前向推理来获得样本的不确定性，其中 dropout 保持活动状态。其次，将贝叶斯代理模型与具有多重数据同化的集成平滑器 （ES-MDA） 算法相结合，以更新不确定参数。在每次迭代中，设计了一种基于代理模型预测不确定性的自适应在线学习方法，以选择样本进行仿真并重新训练代理。这项工作提供了一个有效的框架来量化深度学习代理模型的不确定性，并确定重新训练代理模型的样本。它适用于大多数深度学习代理架构，并且可以轻松集成到数据同化问题中。在复杂三维三相储层上验证了所提方法。 结果表明，与基于仿真的方法相比，所提方法可以获得相似的反演结果，同时将计算成本降低45%以上;与其他基于代理的方法相比，所提出的方法使代理模型更加稳健，并产生最接近基于数值模拟的结果。