The objective of this paper is to verify the feasibility of using deep learning method to accelerate collisionless gravitational N-body numerical simulation.The numerical simulation of collisionless gravitational N-body is of great significance to the study of the formation and evolution of galaxies, dark matter halos and large-scale structures of the universe.However, the traditional method of the collisionless gravitational N-body numerical simulation is very time consuming, which limits the scale of simulated cosmic system.At present, the particle number scale of simulation is mainly between 106-1013, and the simulation task with larger particle number scale is difficult to be completed by the current numerical simulation algorithm (which requires a large number of calculation times) and the latest computer.The PM series method used in the collisionless gravitational N-body numerical simulation to caculate the potential energy(solving Poisson equation) requires a lot of calculation times, which seriously reduces the numerical simulation speed of each time step, and also leads to the difficulty in improving the simulation accuracy.In this paper, a deep neural network is proposed instead of the traditional method to solve the potential energy faster in order to accelerate the time-consuming part in the collisionless gravitational N-body numerical simulation.Using the latest deep learning method, the appropriate deep neural network model and training strategy is explored experimentally.Finally, the overall network model structure of Encoder-Decoder supplemented by residual local structure is found and the loss function and training strategy that are more suitable for solving potential energy task are determined.It is verified that the computational complexity of potential energy for deep neural network is O(N).With the increase of N, the computation time of the deep neural network method is less than that of the fast Fourier transform method or the finite difference method.In the case of the same sampling rate, the accuracy is better than the fast Fourier transform method.And the model trained by small mesh data can be applied to large mesh data which is extensible.An excellent 3D Poisson equation solver can also be obtained by training the model structure designed in this paper with 3D data.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 series method, so as to effectively improve the overall simulation speed,or improving the simulation accuracy with less calculation time cost.It lays a foundation for the future large-scale collisionless gravitational N-body numerical simulation.
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