Intelligent element: Coupling Green function approach and artificial intelligence to reduce discretization effort

Abstract

This research work presents a method that modifies a classical numerical method using artificial intelligence (AI) and takes advantage of an analytical method to minimize the usual need for increasing discretization. Its formulation is based on the integration of two main concepts: the reciprocity theorem and the generalization capability of artificial neural networks (ANNs). The reciprocity theorem is used to formulate the mathematical expression governing the geomechanical problem, which is then discretized in space into intelligent elements. The behavior of the strain field inside these new elements is predicted using an ANN. To make these predictions, the neural network uses displacement boundary conditions, material properties, and the geometric shape of the element as input data. The comparison was performed for two examples, in which the first had a uniform depletion of the reservoir, while the second had a non-uniform variation of the pore pressure. For the same level of accuracy, the proposed method was 10 times faster than the traditional method for the first example and five times faster for the second example on a computer with 12 threads of 2.6 GHz and 32 GB RAM.

Non‐iterative Green's function approach for 2D unbounded heterogeneous fluid‐saturated media

“…The Green's function approach (GFA) proposed by Peres et al, [28][29][30] uses the classical Green's functions for point load as an auxiliary solution that together with the reciprocity theorem to capture the variation in the stress state of a geological formation subjected to processes of injection or extraction of fluids. This approach has no limitations in terms of geometry, number of layers, and heterogeneity of the geological profile and can be applied to materials with linear or non-linear behavior.…”