Supervised Machine-Learning for History Matching: Learning the Inverse Mapping from Low-Rank Data and Model Representations

History matching refers to calibration of geologic models so that they can reproduce historical production data. Automatic history matching is performed by solving inverse problems, in which production data mismatch is minimized by iteratively updating reservoir parameters in the direction of decreasing loss function. Conventional algorithms involve many reservoir simulation runs that must be performed online (during history matching), which make the process time-consuming. We have developed a novel machine learning-based approach to history matching where the goal is to learn the mapping from model input and response data during the training phase and use the trained model to generate calibrated reservoir models for a given production data. The advantage of this approach is that the time-consuming training step is performed off-line, enabling a more real-time history matching workflow with the trained model. A challenging aspect in history matching is that historical production data support only coarse-scale geologic features. Hence, without proper parameterization and regularization, the resulting inverse problems are ill-posed. Similarly, the computational efficiency is significantly improved by learning the mapping between low-dimensional representations of geologic realizations and the associated simulated production data. We demonstrate the new approach using a 2D Gaussian field and a complex 3D channelized reservoir.