EPISODE · Dec 19, 2025 · 13 MIN
Differentiable and accelerated spherical harmonic and Wigner transforms
from Earthly Machine Learning · host Amirpasha
Differentiable and accelerated spherical harmonic and Wigner transformsMatthew A. Price, Jason D. McEwen*Journal of Computational Physics (2024)** This work introduces novel algorithmic structures for the **accelerated and differentiable computation** of generalized Fourier transforms on the sphere ($S^2$) and the rotation group ($SO(3)$), specifically spherical harmonic and Wigner transforms.* A key component is a **recursive algorithm for Wigner d-functions** designed to be stable to high harmonic degrees and extremely parallelizable, making the algorithms well-suited for high throughput computing on modern hardware accelerators such as GPUs.* The transforms support efficient computation of gradients, which is critical for machine learning and other differentiable programming tasks, achieved through a **hybrid automatic and manual differentiation approach** to avoid the memory overhead associated with full automatic differentiation.* Implemented in the open-source **S2FFT** software code (within the JAX differentiable programming framework), the algorithms support various sampling schemes, including equiangular samplings that admit exact spherical harmonic transforms.* Benchmarking results demonstrate **up to a 400-fold acceleration** compared to alternative C codes, and the transforms exhibit **very close to optimal linear scaling** when distributed over multiple GPUs, yielding an unprecedented effective linear time complexity (O(L)) given sufficient computational resources.
What this episode covers
Differentiable and accelerated spherical harmonic and Wigner transformsMatthew A. Price, Jason D. McEwen*Journal of Computational Physics (2024)** This work introduces novel algorithmic structures for the **accelerated and differentiable computation** of generalized Fourier transforms on the sphere ($S^2$) and the rotation group ($SO(3)$), specifically spherical harmonic and Wigner transforms.* A key component is a **recursive algorithm for Wigner d-functions** designed to be stable to high harmonic degrees and extremely parallelizable, making the algorithms well-suited for high throughput computing on modern hardware accelerators such as GPUs.* The transforms support efficient computation of gradients, which is critical for machine learning and other differentiable programming tasks, achieved through a **hybrid automatic and manual differentiation approach** to avoid the memory overhead associated with full automatic differentiation.* Implemented in the open-source **S2FFT** software code (within the JAX differentiable programming framework), the algorithms support various sampling schemes, including equiangular samplings that admit exact spherical harmonic transforms.* Benchmarking results demonstrate **up to a 400-fold acceleration** compared to alternative C codes, and the transforms exhibit **very close to optimal linear scaling** when distributed over multiple GPUs, yielding an unprecedented effective linear time complexity (O(L)) given sufficient computational resources.
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Differentiable and accelerated spherical harmonic and Wigner transforms
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