球面上频谱整形无序结构的快速生成
Fast generation of spectrally-shaped disorder, on the sphere
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中文总结 AI 辅助
本文提出FaSHIoNPOp算法，可快速生成球面上具有指定对关联的无序点模式，时间复杂度为O(N log N)，并可结合多种全局与局部约束，应用于超均匀结构、旋向体等设计，为弯曲流形相关研究奠定基础。
中文摘要 AI 辅助
具有理想特性的无序点模式设计是一项令人兴奋且持续推进的研究工作，其应用范围涵盖材料科学至计算机科学领域。近年来，一种成功的方法是通过损失函数优化点模式，该损失函数在傅里叶空间表示中强制实现所需特性。然而，这些方法迄今为止严格局限于平直欧几里得空间，无法应用于光子学中曲面涂层或弯曲流形采样等场景。我们提出FaSHIoNPOp算法，该算法依赖快速非均匀球谐变换，可在球面上的点模式中强制实现对关联，其时间复杂度为O(N log N)，其中N为点的数量。在验证其性能后，我们展示了FaSHIoNPOp的应用，包括生成球面上用于采样和物理应用的超均匀结构，以及设计球面上的旋向体（在给定频率下具有最大散射能力的无序结构）。此外，我们还证明FaSHIoNPOp可与全局约束（如中心对称性，应用于设计更具各向同性的三维旋向体）和局部实空间约束（如对排斥）相结合。我们的工作为弯曲流形上的最优采样和涂层设计铺平了道路，在物理学、材料科学和计算机科学领域具有诸多应用。
英文摘要
The design of disordered point patterns with desirable properties is an exciting and ongoing research endeavor, with applications ranging from materials to computer science. A successful approach in recent years has been the optimization of point patterns through a loss function that enforces properties in their Fourier-space representation. Yet, these methods have so far strictly been limited to flat Euclidean space, precluding their use in the contexts of coatings of curved surfaces for photonics, or of sampling of curved manifolds for instance. We introduce FaSHIoNPOp, an algorithm that relies on fast non-uniform spherical harmonics transforms, to enforce pair correlations in point patterns on the sphere with an $O(N \log N)$ complexity in $N$ the number of points. Having demonstrated its performance, we showcase applications of FaSHIoNPOp, ranging from the generation of hyperuniform structures on the sphere for sampling and physical applications, to the design of gyromorphs (disordered structures with maximal scattering power at a given frequency) on the sphere. We additionally show that FaSHIoNPOp can be combined to both global constraints like centrosymmetry, with applications to the design of more isotropic $3d$ gyromorphs, and local real-space constraints like pair repulsion. Our work paves the way for optimal sampling and coating design on curved manifolds, with many applications across physics, materials and computer science.
