Deep Learning-Driven Acceleration of Stochastic Gradient Methods for Well Location Optimization Under Uncertainty

Abstract We have developed the deep-learning-accelerated-gradient (DLAG) algorithm, a novel solution for well location optimization (WLO) problems that leverages data collected from the explored parameter space to accelerate optimization. During optimization, we collect data to train a deep neural network (NN), creating a map from well-location parameters to the objective function. We utilize the analytical gradient of the NN, resulting in an effective search direction while saving the computational cost associated with stochastic-gradient perturbations. Our method features a novel NN architecture, the Spatial Pairwise Interaction Network (SPINet) with independent and contextual neural pathways (NPs), designed to capture the primary well characteristics, and its complex interactions with the neighboring wells. For the contextual NP, we explore using the popular Attention mechanism and simpler mechanism with weight-sharing Multilayer Perceptron (MLP) layers. To evaluate the architectures, we designed the Bird Ensemble (BE) test problem which resembles the structure of the WLO problem. The comparison between DL architectures reveals that the NP with a weight-sharing mechanism has superior performance in terms of MSE error and gradient accuracy. The weight-sharing structure allows the model to efficiently model relationships with shared parameters while maintaining invariance to input permutations. For the test function, utilizing DLAG drastically improves computational efficiency, reducing the number of function evaluations required to achieve the same level of optimization by one to two orders of magnitude. Following validation of this test problem, we successfully applied our method to optimizing locations of injection and production wells in the Egg reservoir model. To alleviate random artifacts and the inevitable possibility of encountering local minima, we conducted 20 iterations of the WLO problems both with and without DLAG. The results reveal that, on average, our DLAG optimization method is more efficient than the traditional approach. This efficiency gain is particularly impactful for real-world applications where project timelines are tightly constrained.