Deeppipe: A two-stage physics-informed neural network for predicting mixed oil concentration distribution

Owing to the oil diffusion, a mixed oil segment would inevitably form between two adjacent oil products, leading to economic loss and a reduction of oil product quality. Current works have inherent drawbacks, including computational inapplicability for long-distance pipelines by using numerical methods and unreasonable physical results by using conventional machine learning models. This work proposes a two-stage physics-informed neural network (TS-PINN) method, aiming to provide a highly efficient and precise predictive tool for the mixed oil concentration distribution of multi-product pipelines. In the TS-PINN, the scientific theory and engineering control knowledge of mixed oil diffusion are incorporated into the neural network, which allows the developed neural network model to be capable of exploring the potential physical information of mixed oil and constraining the training process. Subsequently, a two-stage modelling approach is proposed to improve the convergence effect and prediction accuracy of the proposed TS-PINN model. Results from numerical case studies suggest the higher accuracy and robustness achieved by the proposed model compared to the deep neural network, while the root mean square error and mean absolute percentage error gotten by TS-PINN are reduced by 79.5% and 80.5%. Further, the test results on sparse data prove that the TS-PINN achieves a reduction in dependency on available data when training the neural network. Compared with the numerical methods, the TS-PINN reduces the calculation time from several days to hundreds of seconds, it is practicable to predict the mixed oil migration in long-distance pipelines rapidly and accurately using the proposed model.