Hydrodynamic numerical simulations based on residual cooperative neural network

As a gridless computational method, physics-informed neural networks (PINNs) have been widely applied and are a research hotspot in the field of numerical simulation due to their potential to provide approximations that are infinitely close to the analytical solutions. To address the complex hydrodynamic simulation scenarios with a large solution domain, where the conventional PINNs are not fully applicable, we propose a residual cooperative neural network (RCNN) embedded with hard constraints and optimized by the automatic mixed-precision (AMP) computational technique. To perform extreme condition hydrodynamic simulations, we provide smooth surro-gate functions for each of the point-source and step conditions. The applicability and advantages of the RCNN model are verified with a total of four typical hydrodynamic cases. The results show that the RCNN performs better than the conventional PINN in terms of convergence, applicability, and fitting accuracy, with an overall goodness-of-fit of over 0.99. The computational cost of the RCNN model can be significantly reduced by the AMP technique, with the average computation time and occupied GPU memory reduced by 45.77% and 43.16%, respectively. The RCNN can effectively address the gradient explosion and gradient disappearance problems in complex hydrodynamic simulations with a large solution domain.