FMM-Net: neural network architecture based on the Fast Multipole Method

TL;DR

This paper introduces FMM-Net, a neural network architecture inspired by the H2 matrix and Fast Multipole Method, aiming to enhance performance and scalability while reducing memory usage.

Contribution

The paper presents a novel neural network design based on H2 matrices that improves efficiency and scalability compared to existing H2-inspired networks.

Findings

Outperforms alternative neural networks in numerical tests

Reduces memory costs compared to existing architectures

Demonstrates improved scalability and performance

Abstract

In this paper, we propose a new neural network architecture based on the H2 matrix. Even though networks with H2-inspired architecture already exist, and our approach is designed to reduce memory costs and improve performance by taking into account the sparsity template of the H2 matrix. In numerical comparison with alternative neural networks, including the known H2-based ones, our architecture showed itself as beneficial in terms of performance, memory, and scalability.