标题： 理想MHD平衡的神经网络求解器 显示英文标题

标题： Neural-Network solver of ideal MHD equilibria

摘要： 我们提出了一种新方法，通过用人工神经网络参数化傅里叶模式来计算三维磁流体动力学平衡，并将其与传统求解器计算的平衡进行比较。 然后在实空间中对整个体积的非线性全局力残差进行一阶优化器最小化。 我们已经观察到，计算成本与现有代码计算相同最小残差具有竞争力。 随着计算成本的增加，神经网络实现了更低的残差最小值，确立了力残差的新下限。 我们使用了最小复杂度的神经网络，并预计在不仅解决单个平衡问题，而且在计算适用于连续平衡分布的神经网络模型方面，将有显著改进。 显示英文摘要

摘要： We present a novel approach to compute three-dimensional Magnetohydrodynamic equilibria by parametrizing Fourier modes with artificial neural networks and compare it to equilibria computed by conventional solvers. The full nonlinear global force residual across the volume in real space is then minimized with first order optimizers. Already,we observe competitive computational cost to arrive at the same minimum residuals computed by existing codes. With increased computational cost,lower minima of the residual are achieved by the neural networks,establishing a new lower bound for the force residual. We use minimally complex neural networks,and we expect significant improvements for solving not only single equilibria with neural networks,but also for computing neural network models valid over continuous distributions of equilibria.