An efficient transformer-based surrogate model with end-to-end training strategies for automatic history matching

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In recent years, surrogate models have gained popularity as a tool to tackle the challenges presented by time-consuming numerical simulations in automatic history matching (AHM). Although there are many different surrogate models designed to alleviate this issue, it is still challenging for most of them to handle the high dimensionality and strong non-linearity in reservoir models and dynamic production data. Inspired by the rapid development of Transformer, we propose a novel hybrid hierarchical Vision Transformer (HHVT) approach for history matching, which utilizes a unified architecture to predict production data for specific physical fields with an end-to-end strategy. For predicting the production data of wells, the Transformer supports parallelism computation among multiple timesteps, which shows more superiority than traditional recurrent neural networks. Specifically, our approach constructs a novel encoder-decoder Transformer architecture to learn the implicit features of high-level spatial parameters to match the features of time-series production data. With this architecture, HHVT achieves fast training and inference, which is suitable for large-scale datasets and high-dimensional features. The proposed HHVT model is integrated with a multimodal optimization algorithm to find history-matching solutions. We first validated the effect of hyperparameters of HHVT on a simple 2D reservoir. Moreover, the proposed method was verified on the complex 3D Brugge model. The results demonstrate that the training speed of the Transformer-based model is approximately twice as fast as the surrogates based on convolutional and recurrent neural networks. The proposed HHVT also shows better prediction accuracy in two cases, compared with other surrogate models, which enhances the applicability of surrogate-based history-matching methods in large-scale complex reservoir scenarios.