Fast Multipole

Fast Multipole Methods (FMM) are computational techniques designed to efficiently handle long-range interactions in large-scale systems, significantly reducing computational complexity from quadratic to near-linear time. Current research focuses on adapting FMM principles to diverse fields, including developing novel neural network architectures (like FMM-Net) that leverage FMM's hierarchical structure for improved performance and memory efficiency, and applying FMM-inspired approaches to accelerate attention mechanisms in deep learning models for processing long sequences. This work has broad implications, impacting areas such as materials science (modeling non-bonded interactions), astrophysics (analyzing gravitational wave data), and signal processing (beamforming for broadband sources).