论文标题

用于解决XGC中的非线性fokker-Planck-landau碰撞操作员的编码器decoder神经网络

Encoder-decoder neural network for solving the nonlinear Fokker-Planck-Landau collision operator in XGC

论文作者

Miller, M. A., Churchill, R. M., Dener, A., Chang, C. S., Munson, T., Hager, R.

论文摘要

编码器 - 模型神经网络已用于研究加速部分全差异方程的可能性,即fokker-planck-landau碰撞操作员。这是大规模平行的粒子代码XGC中管理方程的一部分,该方程用于研究融合能量设备中的湍流。神经网络强调物理启发的学习,教导它通过将碰撞操作员与L2损失一起包括在训练损失中,以尊重碰撞操作员的物理保护约束。特别是,用于语义分割的计算机视觉任务的网络体系结构已用于培训。使用惩罚方法来强制系统的“软”约束,并将保护属性中的误差整合到损耗函数中。在训练过程中,在每个配置顶点计算代表系统所有物种的密度,动量和能量的数量,反映了XGC中的过程。这种简单的训练已在10E-04的阶面跨配置空间产生了中位相对损失,如果误差是随机性质的,则足够低,但如果在时间段中具有漂移性质,则不能。操作员的PICARD迭代求解器的运行时间为n平方的顺序,其中n是等离子体物种的数量。随着XGC1代码开始攻击包括大量物种在内的问题,碰撞操作员将在计算上变得昂贵,使神经网络求解器变得更加重要,因为训练仅为n。训练数据中考虑了足够多的碰撞,以确保捕获碰撞物理的完整领域。将讨论一种先进的技术来进一步减少损失,这将是随后报告的主题。最终的工作将包括网络的扩展,包括多个等离子体物种。

An encoder-decoder neural network has been used to examine the possibility for acceleration of a partial integro-differential equation, the Fokker-Planck-Landau collision operator. This is part of the governing equation in the massively parallel particle-in-cell code, XGC, which is used to study turbulence in fusion energy devices. The neural network emphasizes physics-inspired learning, where it is taught to respect physical conservation constraints of the collision operator by including them in the training loss, along with the L2 loss. In particular, network architectures used for the computer vision task of semantic segmentation have been used for training. A penalization method is used to enforce the "soft" constraints of the system and integrate error in the conservation properties into the loss function. During training, quantities representing the density, momentum, and energy for all species of the system is calculated at each configuration vertex, mirroring the procedure in XGC. This simple training has produced a median relative loss, across configuration space, on the order of 10E-04, which is low enough if the error is of random nature, but not if it is of drift nature in timesteps. The run time for the Picard iterative solver of the operator scales as order n squared, where n is the number of plasma species. As the XGC1 code begins to attack problems including a larger number of species, the collision operator will become expensive computationally, making the neural network solver even more important, since the training only scales as n. A wide enough range of collisionality is considered in the training data to ensure the full domain of collision physics is captured. An advanced technique to decrease the losses further will be discussed, which will be subject of a subsequent report. Eventual work will include expansion of the network to include multiple plasma species.

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