4D Seismic History Matching Incorporating Unsupervised Learning

The work discussed and presented in this paper focuses on the history matching of reservoirs by integrating 4D seismic data into the inversion process using machine learning techniques. A new integrated scheme for the reconstruction of petrophysical properties with a modified Ensemble Smoother with Multiple Data Assimilation (ES-MDA) in a synthetic reservoir is proposed. The permeability field inside the reservoir is parametrised with an unsupervised learning approach, namely K-means with Singular Value Decomposition (K-SVD). This is combined with the Orthogonal Matching Pursuit (OMP) technique which is very typical for sparsity promoting regularisation schemes. Moreover, seismic attributes, in particular, acoustic impedance, are parametrised with the Discrete Cosine Transform (DCT). This novel combination of techniques from machine learning, sparsity regularisation, seismic imaging and history matching aims to address the ill-posedness of the inversion of historical production data efficiently using ES-MDA. In the numerical experiments provided, I demonstrate that these sparse representations of the petrophysical properties and the seismic attributes enables to obtain better production data matches to the true production data and to quantify the propagating waterfront better compared to more traditional methods that do not use comparable parametrisation techniques

Ultra-fast Deep Mixtures of Gaussian Process Experts

Mixtures of experts have become an indispensable tool for flexible modelling in a supervised learning context, and sparse Gaussian processes (GP) have shown promise as a leading candidate for the experts in such models. In the present article, we propose to design the gating network for selecting the experts from such mixtures of sparse GPs using a deep neural network (DNN). This combination provides a flexible, robust, and efficient model which is able to significantly outperform competing models. We furthermore consider efficient approaches to computing maximum a posteriori (MAP) estimators of these models by iteratively maximizing the distribution of experts given allocations and allocations given experts. We also show that a recently introduced method called Cluster-Classify-Regress (CCR) is capable of providing a good approximation of the optimal solution extremely quickly. This approximation can then be further refined with the iterative algorithm

Cluster, Classify, Regress: A General Method For Learning Discountinous Functions

This paper presents a method for solving the supervised learning problem in which the output is highly nonlinear and discontinuous. It is proposed to solve this problem in three stages: (i) cluster the pairs of input-output data points, resulting in a label for each point; (ii) classify the data, where the corresponding label is the output; and finally (iii) perform one separate regression for each class, where the training data corresponds to the subset of the original input-output pairs which have that label according to the classifier. It has not yet been proposed to combine these 3 fundamental building blocks of machine learning in this simple and powerful fashion. This can be viewed as a form of deep learning, where any of the intermediate layers can itself be deep. The utility and robustness of the methodology is illustrated on some toy problems, including one example problem arising from simulation of plasma fusion in a tokamak.Comment: 12 files,6 figure