Publications

A Cubed Sphere Fast Multipole Method

Published in SIAM Journal on Scientific Computing, 2026

This work describes a new version of the Fast Multipole Method for summing pairwise particle interactions that arise from discretizing integral transforms and convolutions on the sphere. The kernel approximations use barycentric Lagrange interpolation on a quadtree composed of cubed sphere grid cells. The scheme is kernel-independent and requires kernel evaluations only at points on the sphere. Results are presented for the Poisson and biharmonic equations on the sphere, barotropic vorticity equation on a rotating sphere, and self-attraction and loading potential in tidal calculations. A tree code version is also described for comparison, and both schemes are tested in serial and parallel calculations.

Recommended citation: Chen, A., & Krasny, R. (2026). A cubed sphere fast multipole method. SIAM Journal on Scientific Computing, 48(4), B671-B697. https://epubs.siam.org/doi/full/10.1137/25M1789615

Communication bounds for convolutional neural networks

Published in PASC '22: Proceedings of the Platform for Advanced Scientific Computing Conference, 2022

Convolutional neural networks (CNNs) are important in a wide variety of machine learning tasks and applications, so optimizing their performance is essential. Moving words of data between levels of a memory hierarchy or between processors on a network is much more expensive than the cost of arithmetic, so minimizing communication is critical to optimizing performance. In this paper, we present new lower bounds on data movement for mixed precision convolutions in both single-processor and parallel distributed memory models, as well as algorithms that outperform current implementations such as Im2Col. We obtain performance figures using GEMMINI, a machine learning accelerator, where our tiling provides improvements between 13% and 150% over a vendor supplied algorithm.

Recommended citation: Anthony Chen, James Demmel, Grace Dinh, Mason Haberle, and Olga Holtz. 2022. Communication bounds for convolutional neural networks. In Proceedings of the Platform for Advanced Scientific Computing Conference (PASC '22). Association for Computing Machinery, New York, NY, USA, Article 1, 1–10. https://dl.acm.org/doi/10.1145/3539781.3539784