History matching, a highly non-unique inverse problem, is critical to calibrate model parameters in many scientific applications. A typical approach to history matching is to start with a uniform sampling of the high-dimensional parameter space and employ a surrogate modeling based black-box optimization to perform sequential sampling. Though this general workflow has been well studied, the problem of choosing an appropriate merit function to compare time-varying simulation outputs has been overlooked. Instead, convenient metrics such as the L2 or the LI-norm are employed. In this paper, we show that choosing an appropriate metric can significantly improve the solutions of sequential sampling. To this end, we propose a metric learning technique, develop a sequential sampling pipleline with the metric, and demonstrate its superiority to the conventional L2-norm metric.

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