ReBA: A Hybrid Sparse Reconfigurable Butterfly Accelerator for Solving Partial Differential Equations via Hardware and Algorithm Co-Design

Partial differential equations (PDEs) are widely used in many scientific and engineering fields. Traditional numerical methods for solving PDEs often struggle with complex equations and require extensive computation. Recent advances in neural operators, particularly the Galerkin Transformer (GT-FNO), offer faster solutions but present unique challenges for hardware due to complex neural network operations such as attention, Fourier transforms, and convolution. To address these challenges, we propose ReBA, a dedicated hardware and algorithm co-design framework specified for GT-FNO. Our design implements hybrid sparsity schemes for efficient workload balance, significantly reducing hardware overhead while maintaining high accuracy. ReBA introduces a reconfigurable dual-engine architecture, featuring an adaptable butterfly processing element (BPE), which efficiently supports FFT and other DNN operations through flexible BPE allocation, offering high parallelism and low-latency computation. Experiments validate that ReBA delivers significant speedups of 34.57×, 2.70×, and 1.82 51.26× over conventional CPUs, GPUs, and prior state-of-the-art accelerators in solving PDEs.