The high computational costs associated with reservoir simulation create a major barrier in history matching problems. Within the past decades, several efforts have been made to reduce CPU-time by metamodeling (proxy-modeling) techniques in which the original fitness function (OF) is partially or completely substituted by an approximation-function (AF), often called metamodel or surrogate. In order to build a high-fidelity surrogate, usually a large number of training samples is required. This can make the traditional surrogate-assisted algorithms, inefficient. In recent years, it has been shown that to approximate the global optimum using a surrogate-assisted algorithm, the AF does not necessarily need to be of high-fidelity, if it is applied in conjunction with the OF and retrained online, during the optimization process.

In order to use the OF effectively and minimally, a model-management strategy is required. In this study, a new adaptive model-management strategy is proposed, in which a second surrogate is required. The first surrogate approximates the original fitness function landscape, and the second one estimates the fidelity of the first surrogate over the search-space. On the basis of the estimated fidelity, a probability for employing the OF is calculated, and then according to the calculated probability, the algorithm stochastically decides to use the OF or the AF. A heuristic fuzzy rule is also applied to adjust the possible range of probability values in each evolution-cycle, based on the average fidelity of the second surrogate.

The robustness of the proposed algorithm is analyzed using different analytical benchmarking functions, and a semi-synthetic history matching problem, IC-fault model. To deliver a comparative study, the optimization is also carried out using three other algorithms, without metamodeling (OF-only), offline-learning (AF-only), and online metamodeling with a predefined and constant probability. The outcomes of all four algorithms are compared with each other. The assessment shows that the proposed method can reduce the computational costs significantly.

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