2023/11/24 by Matt A. Price, Price, Matthew A., Jason D. McEwen +1 · 2 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Cosmology and Gravitation Theories #FOS: Computer and information sciences #FOS: Physical sciences #Geophysics and Gravity Measurements #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Machine Learning (cs.LG) #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2311.14670
openalex publication_date 2023/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Many areas of science and engineering encounter data defined on spherical manifolds. Modelling and analysis of spherical data often necessitates spherical harmonic transforms, at high degrees, and increasingly requires efficient computation of gradients for machine learning or other differentiable programming tasks. We develop novel algorithmic structures for accelerated and differentiable computation of generalised Fourier transforms on the sphere \mathbbS2 and rotation group SO(3), i.e. spherical harmonic and Wigner transforms, respectively. We present a recursive algorithm for the calculation of Wigner d-functions that is both stable to high harmonic degrees and extremely parallelisable. By tightly coupling this with separable spherical transforms, we obtain algorithms that exhibit an extremely parallelisable structure that is well-suited for the high throughput computing of modern hardware accelerators (e.g. GPUs). We also develop a hybrid automatic and manual differentiation approach so that gradients can be computed efficiently. Our algorithms are implemented within the JAX differentiable programming framework in the S2FFT software code. Numerous samplings of the sphere are supported, including equiangular and HEALPix sampling. Computational errors are at the order of machine precision for spherical samplings that admit a sampling theorem. When benchmarked against alternative C codes we observe up to a 400-fold acceleration. Furthermore, when distributing over multiple GPUs we achieve very close to optimal linear scaling with increasing number of GPUs due to the highly parallelised and balanced nature of our algorithms. Provided access to sufficiently many GPUs our transforms thus exhibit an unprecedented effective linear time complexity.
cunuSHT: GPU Accelerated Spherical Harmonic Transforms on Arbitrary Pixelizations