Differentiable and accelerated spherical harmonic and Wigner transforms

About this episode

This episode discusses novel algorithms for accelerated and differentiable computation of spherical harmonic and Wigner transforms.

Differentiable and accelerated spherical harmonic and Wigner transforms Matthew 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. *…

People in this episode

Host: Amirpasha

Topics covered

• spherical harmonic transforms
• Wigner transforms
• differentiable programming
• high throughput computing
• machine learning

Keywords

• spherical harmonics
• Wigner d-functions
• differentiable computation
• high harmonic degrees
• GPU acceleration
• gradient computation
• automatic differentiation

Mentioned in this episode

Organizations: JAX

Products: S2FFT

Books & works: Journal of Computational Physics

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