Dimensionality reduction methods used in history matching

As discussed in Sect. 3.4, one of the challenges in history matching is the high dimensionality (large number of model parameters) of the reservoir model realizations that raises two challenges: 1- more data assimilation iterations are required to get a satisfactory match, 2- preserving the geologic realism becomes harder as there are an infinite number of solutions that can match the actual production data. These challenges are more prominent when dealing with spatially distributed properties such as the permeability distribution. Thereby, dimensionality reduction (also known as parametrization) methods are required to reduce the number of adjustable parameters while keeping the most salient ones. In the following, some of the dimensionality reduction methods used in the course of history matching are explained. These methods include the conventional methods, such as the pilot points, gradual deformation, principal component analysis, and higher-order singular value decomposition, and deep learning methods, including the autoencoders, variational autoencoders, and convolutional variational autoencoders. Also, a brief introduction to machine learning and deep learning is provided.