SPH-PINN: An Improved Physics-Informed Neural Network Integrated with Smoothed Particle Hydrodynamics

In this paper, an integration of the improved smoothed particle hydrodynamics (SPH) method with physics-informed neural networks (PINNs) is presented. The improved SPH method is employed to replace automatic differentiation in computing the differential operators of the loss function within the neural network framework, facilitating accelerated neural network training and reducing computational time. Additionally, tests are conducted on two-dimensional partial differential equations (PDEs) and systems of PDEs, with comparisons made to the results obtained using automatic differentiation-based physics-informed neural network (AD-PINN) and finite difference-based physics-informed neural network (FD-PINN). The findings demonstrate that the proposed method achieves faster computation speeds, particularly when dealing with larger network layer sizes and increased equation complexity. It maintains errors within the same order of magnitude while avoiding nonphysical solutions.