DeepPipe: A multi-stage knowledge-enhanced physics-informed neural network for hydraulic transient simulation of multi-product pipeline

In the chemical pipelining industry, owing to the high-pressure transportation process, an accurate hydraulic transient simulation tool plays a central role in preventing the slack line flow and overpressure from causing pipeline operation treacherous. Nevertheless, the current model-driven method often faces challenges in balancing computational efficiency with accuracy, and the existing data-driven models struggle to produce explainable results from the physics perspectives since insufficient theoretical principles are incorporated into the model training. Additionally, the existing physics-informed learning architecture fails to achieve a gradient-balanced training, resulting from the significant magnitude difference in outputs and multiple loss terms. Consequently, a Multi-Stage Knowledge-Enhanced Physics-Informed Neural Network (MS-KE-PINN) is proposed for the hydraulic transient simulation of multi-product pipelines. To enforce the neural network producing simulation results with high consistency to physical laws, the governing equations, boundary, and initial condition are incorporated into the training process for an efficient mesh-free simulation. Then, considering that the significant magnitude difference between outputs can easily lead to deficient performance in the gradient descent, the magnitude conversion on the outputs and the equivalent conversion of the governing equations are implemented to enhance the training effect of the neural network. Subsequently, to tackle the imbalanced gradient of multiple loss terms with fixed weights, a multi-stage hierarchical training strategy is designed to improve the approximation capacity of the neural network. Numerical simulation cases demonstrate a better approximation function of the proposed model than the state-of-art models, while the mean absolute percentage errors yielded by MS-KE-PINN are reduced by 77.4 %, 88.7 %, and 87.8 % in three simulation operation conditions for pressure prediction. Furthermore, experimental investigations from a real-world multi-product pipeline suggest that the proposed model can still draw accurate simulation results even under complex and dynamic hydraulic transient scenarios in practice, with root mean squared errors reduced by 94.8 % and 80 % than that of the physics-informed neural network. To this end, the proposed model can conduct accurate and effective hydraulic transient analysis, thus ensuring the safe operation of the pipeline.