Deep Learning–Driven Acceleration of Stochastic Gradient Methods for Well Location Optimization under Uncertainty

Summary We have developed the deep learning-accelerated gradient (DLAG) algorithm, a novel solution for well location optimization (WLO) problems. DLAG accelerates optimization by leveraging data from the explored parameter space to train a deep neural network (NN) that maps well locations to the objective function. The algorithm utilizes the analytical gradient of the NN, resulting in an effective search direction while saving the computational cost associated with stochastic gradient perturbations. Our method introduces a novel NN architecture, the spatial pairwise interaction network (SPINet), composed of independent neural pathways (NPs) to capture primary well characteristics and contextual NPs to capture 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. SPINet structure proves to efficiently model pairwise relationships while maintaining invariance to input permutation. The NP with a weight-sharing mechanism has superior performance in terms of mean square error and gradient accuracy while also demonstrating more consistent and reliable training outcomes. For the test problem, DLAG dramatically improved computational efficiency, reducing function evaluations by one to two orders of magnitude. Following this validation, we successfully applied our method to optimize trajectories of injection and production wells in a modified version of the Egg reservoir model. To alleviate random artifacts and the inherent possibility of encountering local minima, we executed 20 distinct instances of the WLO problem, comparing performance with and without DLAG. On average, our DLAG optimization method proved significantly more efficient than the traditional approach. This efficiency gain is particularly impactful for real-world applications where project timelines are tightly constrained.