Analysis of the generalization ability of neural networks based on the NN-MPS-interpolation model

This paper combines the Moving Particle Semi-implicit (MPS) method with neural networks to construct a data-driven model, which is then applied to solve the Poisson equation, aiming to reduce computational resource consumption. A feedforward fully connected neural network interpolation model (NN-MPS-interpolation model) based on the backpropagation algorithm is developed. This model takes parameters with strong correlations to the pressure Poisson equation as inputs to output the desired pressure values, achieving predictions for high-resolution problems using low-resolution examples. The generalization ability of the model is also explored based on relevant metrics, and a range of parameters that can obtain accurate solutions is provided. By replacing the original particle method’s solution to the Poisson equation with a neural network model based on the interpolation method, the proposed approach not only accelerates pressure computation while ensuring accuracy but also demonstrates certain generalization ability, which can reduce the amount of data and computation required for model training.