Efficient super-resolution of pipeline transient process modeling using the Fourier Neural Operator

The rapid simulation of pipelines significantly facilitates tasks such as pipeline operation scheduling and optimization, while neural networks can offer an efficient alternative modeling approach. Based on the Fourier Neural Operator (FNO), this study proposes a rapid and comprehensive model for computing the transient natural gas pipeline processes. To further enhance the performance of the model, a novel loss function is proposed that integrates the Benedict-Webb-Rubin-Starling (BWRS) equation as a physical constraint. After being trained on finite-dimensional data, the proposed model demonstrates high accuracy, good grid invariance, and significant computational acceleration. Compared with data from existing studies and simulation results of the renowned natural gas pipeline simulation software TGNET, the relative error of the proposed model remains below 2.5 %. The trained model can also predict outcomes beyond the original training data with a root mean squared error value of 2.542 × 10⁻³, demonstrating good grid invariance. Moreover, compared to the traditional numerical algorithm, the model exhibits a significantly high acceleration ratio, typically achieving an order of magnitude of 10² and occasionally up to 10³. In conclusion, the proposed model can serve as a solver for transient natural gas pipeline simulation processes, efficiently providing accurate simulation results.