DL-NRS Net: A Physics-Informed Fourier Neural Operator Framework for High-Resolution Reconstruction Without High-Resolution Labels
摘要
High-resolution (HR) time-series pressure and saturation evolution data are crucial for accurate simulation and analysis of subsurface flow. Acquiring this HR data through conventional numerical solvers is computationally expensive, especially for large-scale fine grids. However, traditional deep learning methods for high-resolution reconstruction tasks focus primarily on static images and require a large amount of high-resolution data as labels to train the network. This work presents a novel framework, DL-NRS, that enables the rapid acquisition of high-resolution dynamic evolution results using only low-resolution data as input. This approach integrates advanced deep learning (DL) super-resolution techniques with conventional numerical reservoir simulation (NRS). The DL-NRS framework employs the Fourier neural operator (FNO) as its primary network structure and introduces a loss function based on physical constraints for network training. Specifically, numerical simulators are used to obtain lower-resolution results on coarse grids, and the lower-resolution results are directly upsampled using the nearest neighbor interpolation algorithm. Then, these upsampling results serve as training inputs for the FNO network, integrating the discretized governing equations into the loss function, updating the network weights until convergence to produce high-resolution results. Our results demonstrate that the DL-NRS framework achieves high-resolution reconstruction of time-series pressure and saturation distributions in two-phase flow problems, with a mean relative error below 0.8% for pressure and 0.4% for saturation. This work establishes a physics-informed paradigm for super-resolution in subsurface flow modeling, eliminating the dependence on high-resolution labels and enabling scalable reconstruction of dynamic fields.