南方基地知识库

提出了用深度神经网络代替快速傅里叶变换法求解无碰撞引力N体数值模拟方法PM-Tree（Partical Mesh Tree）中的势能，以提升PM-Tree方法的效率，验证深度学习方法加速无碰撞引力N体数值模拟的可行性。无碰撞引力N体数值模拟对研究星系、暗物质晕以及宇宙大尺度结构的形成和演化有重要意义。无碰撞引力N体数值模拟的传统方法在大规模问题上的模拟计算非常耗时，其中PM-Tree方法的主要耗时部分是求解势能。使用深度神经网络代替传统方法加速求解泊松（Poisson）方程，多次调整并训练和测试深度神经网络模型结构，最终选用辅以残差网络局部结构的编码-解码器（Encoder-Decoder）整体结构。验证了深度神经网络解泊松方程的计算时间复杂度为O（N）。同样数据下进行测试，速度高于快速傅里叶变换法和有限差分法求解；在同等采样率的情况下，精度优于快速傅里叶变换法求解，并且具有可扩展性。无碰撞引力N体数值模拟中，用深度神经网络可以提高PM-Tree方法中求解势能的速度，从而有效提高整体模拟速度。

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 Nbody 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 Nbody 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.