Feasibility Study of Collisionless Gravitational N-body Numerical Simulation Based on Deep Learning

In this paper, a Deep Neural Network is proposed to replace the Fast Fourier Transform method to solve the potential energy in the PM-tree method of the collisionless gravitational N-body numerical simulation, so as to improve the efficiency of the PM-tree method and verify the feasibility of the deep learning method to accelerate the collisionless gravitational N-body numerical simulation. Collisionless gravitational N-body numerical simulations are important for the study of galaxies, dark matter halos, and the formation and evolution of the large-scale structure of the universe. The traditional collisionless gravitational N-body numerical simulation method is very time-consuming for large-scale problems, among which the main time-consuming part of the commonly used PM-tree method is solving the potential energy (solving Poisson equation). In this paper, we propose to use deep neural networks instead of traditional methods to accelerate the solving of Poisson equation, adjust and train and test the model structure of deep neural network for many times, and finally select the overall structure of Encoder-Decoder supplemented with the local structure of residual network. We verify that the computational time complexity of deep neural network to solve Poisson equation is O(N). Tested on the same data, the deep neural network is faster than the fast Fourier transform method solution and the finite difference method solution. At the same sampling rate, the accuracy of deep neural network is better than that of the fast Fourier transform method. And it is extensible. Therefore, in the collisionless gravitational N-body numerical simulation, the Deep Neural Network can improve the velocity of solving the potential energy in the PM-Tree method, so as to effectively improve the overall simulation speed.