论文标题
快速神经庞加莱图
Fast neural Poincaré maps for toroidal magnetic fields
论文作者
论文摘要
通常采用用于含有热等离子体的设备的设备中，通常使用用于环形磁场的Poincaré地图研究总限制性能。在大多数实际应用中，评估庞加莱地图需要磁场线的数值集成，这一过程可能会很慢，并且不能使用并行计算轻松地加速。我们表明，一种新型的神经网络架构TheHénonnet能够从对传统遵循算法的观察结果准确地学习逼真的庞加莱地图。训练后，这种学识渊博的庞加莱地图的评估速度比现场线集成方法快得多。此外，Hénonnet体系结构恰好重现了对现场线庞加莱地图施加的主要物理限制：磁通保存。这种具有结构的属性是Hénonnet中每一层的结果是符号映射。我们从经验上证明，Hénonnet可以通过使用盘绕的双曲线不变歧管在所需的岛屿位置产生一个粘性的混乱区域来学会模拟大型磁岛的限制特性。这表明了一种具有良好限制特性的磁场设计的新方法，该磁场比确保使用KAM Tori限制更灵活。
Poincaré maps for toroidal magnetic fields are routinely employed to study gross confinement properties in devices built to contain hot plasmas. In most practical applications, evaluating a Poincaré map requires numerical integration of a magnetic field line, a process that can be slow and that cannot be easily accelerated using parallel computations. We show that a novel neural network architecture, the HénonNet, is capable of accurately learning realistic Poincaré maps from observations of a conventional field-line-following algorithm. After training, such learned Poincaré maps evaluate much faster than the field-line integration method. Moreover, the HénonNet architecture exactly reproduces the primary physics constraint imposed on field-line Poincaré maps: flux preservation. This structure-preserving property is the consequence of each layer in a HénonNet being a symplectic map. We demonstrate empirically that a HénonNet can learn to mock the confinement properties of a large magnetic island by using coiled hyperbolic invariant manifolds to produce a sticky chaotic region at the desired island location. This suggests a novel approach to designing magnetic fields with good confinement properties that may be more flexible than ensuring confinement using KAM tori.
