Enterprise AI Analysis

A dynamic mixed-precision framework is introduced for FFTMatvec, allowing algorithms to selectively use single (FP32) or double (FP64) precision based on desired error tolerance. This strategy capitalizes on the higher throughput of GPUs for lower-precision workloads, achieving significant speedups while maintaining accuracy. A Pareto front analysis guides the optimal precision configuration, identifying that FFT and SBGEMV in single precision yield the best balance of speedup and error.

Key performance optimizations for AMD GPUs were integrated directly into the open-source rocBLAS library. Specifically, an optimized strided batched GEMV (SBGEMV) kernel addresses performance reductions in conjugate transpose matvecs for short, wide matrices (Nd << Nm). This custom kernel, utilizing tiling, 2D thread blocks, vectorized data loads, and pipelining, achieved significantly higher memory bandwidth, resolving a critical bottleneck for F* matvecs.

The performance-portable, mixed-precision FFTMatvec application was successfully scaled to 4,096 GPUs on the OLCF Frontier supercomputer. Communication-aware partitioning was used to optimize the 2D processor grid shape. At this scale, the application computed a matvec with over 20 billion parameters in approximately 0.11 seconds, demonstrating its capability for extreme-scale scientific computing for problems like Bayesian inverse problems and optimal sensor placement.