p-Kernel Stein Variational Gradient Descent for Data Assimilation and History Matching

Abstract

A Bayesian method of inference known as “Stein variational gradient descent” was recently implemented for data assimilation problems, under the heading of “mapping particle filter”. In this manuscript, the algorithm is applied to another type of geoscientific inversion problems, namely history matching of petroleum reservoirs. In order to combat the curse of dimensionality, the commonly used Gaussian kernel, which defines the solution space, is replaced by a p-kernel. In addition, the ensemble gradient approximation used in the mapping particle filter is rectified, and the data assimilation experiments are re-run with more relevant settings and comparisons. Our experimental results in data assimilation are rather disappointing. However, the results from the subsurface inverse problem show more promise, especially as regards the use of p-kernels.