用神经网络求解三维磁流体平衡，精度优于传统方法。
Improving ideal MHD equilibrium accuracy with physics-informed neural networks
- 用神经网络参数化傅里叶模态，直接优化真实空间的力残差。
- 计算成本相当下达到与传统代码相同的残差最小值，更高成本时更优。
- 适用于单个平衡或连续分布平衡的通用建模，潜力大。
我们提出一种新方法，通过人工神经网络参数化傅里叶模态来计算三维磁流体（MHD）平衡，并与传统求解器结果对比。在真实空间中最小化全非线性全局力残差，使用一阶优化器进行优化。现有代码可达到的最小残差水平已可通过相近计算成本实现；进一步增加计算开销后，神经网络能获得更低的残差，确立了力残差的新下界。采用结构极简的神经网络，未来有望显著提升单个平衡求解及覆盖连续平衡分布的神经网络模型性能。
原文摘要 · Abstract (English)
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.
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