New approach of the solution of physical fields of fluid dynamics: Physics-informed long short-term memory network

Abstract

The essence of fluid dynamics problems is to solve the nonlinear partial differential equations (PDEs) of the system. Physics-informed neural networks (PINN) have shown significant advantages in solving nonlinear PDEs using a small number of samples. However, they have inherent limitations in capturing long-term dependencies in time series data, which limits the improvement of their predictive performance. To overcome those problems, this study proposes a novel hybrid model − physics-informed long short-term memory (PI-LSTM), which combines PINN with long short-term memory (LSTM) networks, significantly improving the prediction accuracy and model generalization ability of complex dynamic system behavior. The computational fluid dynamics (CFD) is used to obtain multiple physical field datasets at different time points under different operating conditions. PINN is employed to encode the physical constraints in depth, and obtain the internal physical laws of complex dynamic systems in high dimensions. LSTM is used to dynamically adjust the information flow through its dynamic memory controller, the collaborative update mechanism of memory encoder and state representation vector are used to deeply model the correlation across time steps. To enhance the physical consistency of the model, the control equations are embedded in the loss function in the form of a function as a regularization constraint term. Through the iterative learning process of Deep Neural Network (DNN), the network weight parameters are continuously optimized. The results of three numerical cases, i.e., the flow around the cylinder, Sandia flame D, and ethylene cracking furnace, show that the proposed PI-LSTM model improves the prediction accuracy by 57.27% and 56.22%, 55.88% and 58.23%, 56.56% and 65.39% compared to PINN and BI-LSTM, respectively. Compared with CFD methods, PI-LSTM has increased computational efficiency by 1440 times, while reducing storage space requirements by 99.62%. The proposed PI-LSTM model provides a solid technical support for the design and optimization of complex turbulent reaction coupling processes.