用AI寻找球面上的Z/2特征函数，发现三类解。
Search for Z/2 eigenfunctions on the sphere using machine learning
- 构建多值前馈神经网络，用JAX实现
- 固定分支点于正四面体和立方体顶点时找到解
- 自动优化分支点位置，收敛到压扁四面体构型
我们使用机器学习搜索球面（2-球面）上的Z/2特征函数。为此，我们构建了一个多值前馈深度神经网络，并通过JAX库实现。在三个案例中找到了Z/2特征函数：前两个案例分别将分支点固定在正四面体和立方体的顶点；第三个案例允许人工智能自由移动分支点，最终其将分支点定位在压扁四面体的顶点上。
原文摘要 · Abstract (English)
We use machine learning to search for examples of Z/2 eigenfunctions on the 2-sphere. For this we created a multivalued version of a feedforward deep neural network, and we implemented it using the JAX library. We found Z/2 eigenfunctions for three cases: In the first two cases we fixed the branch points at the vertices of a tetrahedron and at a cube respectively. In a third case, we allowed the AI to move the branch points around and, in the end, it positioned the branch points at the vertices of a squashed tetrahedron.
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