Recently, Zhang Kai's team has made significant progress in the field of automatic history matching in reservoirs. Their research results have been published in the journal Journal of Hydrology, in a paper titled "Deep Bayesian surrogate models with adaptive online sampling for ensemble-based data assimilation"。
Innovation：We propose an ensemble data assimilation method based on a deep Bayesian surrogate model with adaptive online sampling to address the computational cost issues in data assimilation. Traditional surrogate-based history matching methods typically involve constructing a dataset, training a surrogate model, and then using the surrogate to replace numerical simulations during automatic history matching. However, these methods are susceptible to the quantity and quality of training samples, leading to poor generalization of the surrogate model and reduced accuracy in history matching. In contrast, our proposed method collects samples online during the iterative process of history matching reservoir model parameters, continuously trains the surrogate model, and employs adaptive sampling based on the prediction uncertainty of the surrogate. This approach enhances model applicability and yields better history matching performance.
Abstract：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.
Journal of Hydrology publishes original research papers and comprehensive reviews in all the subfields of the hydrological sciences, including water based management and policy issues that impact on economics and society. The 2023 impact factor is 5.9, the 2023 CiteScore is 11.0, the 2023 JCR ranking is in Q1, and it is classified as a TOP journal in Category 1 of Earth Sciences by the Chinese Academy of Sciences in 2025.
Paper link:
https://doi.org/10.1016/j.jhydrol.2024.132457
Citation:
Zhang Jinding, Zhang Kai, Liu Piyang, Zhang Liming, Fu Wenhao, Chen Xu, Wang Jian, Liu Chen, Yang Yongfei, Sun Hai, Yao Jun. Deep Bayesian surrogate models with adaptive online sampling for ensemble-based data assimilation[J]. Journal of Hydrology, 2025, 649: 132457.
