标题： cuHPX：HEALPix网格上的GPU加速可微分球谐变换 显示英文标题

标题： cuHPX: GPU-Accelerated Differentiable Spherical Harmonic Transforms on HEALPix Grids

摘要： HEALPix（分层等面积等纬度像素化）是在天体物理学、宇宙学和地球科学中广泛采用的球面网格系统。 其等面积、等纬度的结构使其特别适合球面上的大规模数据分析。 然而，由于像素几何不规则、纬度依赖的对齐方式以及在大规模情况下对高分辨率变换的需求，实现在HEALPix网格上的高性能球谐变换（SHTs）仍然具有挑战性。 在本工作中，我们提出了cuHPX，这是一个优化的CUDA库，可在HEALPix网格上提供球谐分析及相关功能。 除了显著的性能提升，cuHPX确保了高数值精度，为与深度学习框架集成提供了解析梯度，实现了内存高效的外存优化，并支持HEALPix、等角和其他常见球面网格格式之间的灵活重采样。 通过评估，我们展示了cuHPX实现了快速谱收敛，并相比现有库提高了20倍以上的速度，同时保持数值一致性。 通过结合精度、可扩展性和可微性，cuHPX在气候科学、天体物理学和机器学习领域实现了广泛的应用，有效地将优化的GPU内核与科学工作流结合起来。 显示英文摘要

摘要： HEALPix (Hierarchical Equal Area isoLatitude Pixelization) is a widely adopted spherical grid system in astrophysics, cosmology, and Earth sciences. Its equal-area, iso-latitude structure makes it particularly well-suited for large-scale data analysis on the sphere. However, implementing high-performance spherical harmonic transforms (SHTs) on HEALPix grids remains challenging due to irregular pixel geometry, latitude-dependent alignments, and the demands for high-resolution transforms at scale. In this work, we present cuHPX, an optimized CUDA library that provides functionality for spherical harmonic analysis and related utilities on HEALPix grids. Beyond delivering substantial performance improvements, cuHPX ensures high numerical accuracy, analytic gradients for integration with deep learning frameworks, out-of-core memory-efficient optimization, and flexible regridding between HEALPix, equiangular, and other common spherical grid formats. Through evaluation, we show that cuHPX achieves rapid spectral convergence and delivers over 20 times speedup compared to existing libraries, while maintaining numerical consistency. By combining accuracy, scalability, and differentiability, cuHPX enables a broad range of applications in climate science, astrophysics, and machine learning, effectively bridging optimized GPU kernels with scientific workflows.