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.

中文翻译：

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DeepPipe：用于多产品管道水力瞬态仿真的多阶段知识增强型物理信息神经网络


在化工管道行业，由于高压输送过程，精确的水力瞬态模拟工具在防止松弛的管线流动和超压导致管道运行危险方面发挥着核心作用。然而，当前的模型驱动方法在平衡计算效率和准确性方面经常面临挑战，并且现有的数据驱动模型难以从物理学角度产生可解释的结果，因为模型训练中没有纳入足够的理论原理。此外，现有的物理信息学习架构无法实现梯度平衡训练，这是由于输出和多个损失项的显著幅度差异造成的。因此，提出了一种多阶段知识增强物理信息神经网络 （MS-KE-PINN） 用于多产品管道的水力瞬态仿真。为了强制神经网络生成与物理定律高度一致的仿真结果，将控制方程、边界和初始条件纳入训练过程，以实现高效的无网格仿真。然后，考虑到输出之间的显著幅度差异容易导致梯度下降性能不足，对输出进行幅度转换和控制方程的等效转换，以增强神经网络的训练效果。随后，为了解决具有固定权重的多个损失项的不平衡梯度，设计了一种多阶段分层训练策略来提高神经网络的逼近能力。 数值模拟实例表明，所提出的模型比最先进的模型具有更好的近似函数，而 MS-KE-PINN 产生的平均绝对百分比误差在三种模拟压力预测操作条件下分别降低了 77.4 %、88.7 % 和 87.8 %。此外，来自真实世界多产品管道的实验研究表明，即使在实际应用中复杂和动态的水力瞬态场景下，所提出的模型仍然可以得出准确的仿真结果，均方根误差比物理信息神经网络减少了 94.8% 和 80%。为此，所提模型可以进行准确有效的水力瞬态分析，从而保证管道的安全运行。