Implement Multipole Graph Neural Operator (MGNO)

[ChrisRackauckas-Claude]

Summary

Implement MGNO, which uses a hierarchical multi-scale graph structure inspired by the Fast Multipole Method for O(m) complexity.

Reference

• Li et al., "Multipole Graph Neural Operator for Parametric Partial Differential Equations," NeurIPS 2020. arXiv:2006.09535

Description

MGNO builds a multi-level hierarchical graph (coarsening hierarchy) and uses a V-cycle algorithm with downward and upward passes to capture both long-range and short-range interactions. This is inspired by the Fast Multipole Method and achieves linear complexity O(m) in the number of nodes, making it efficient for large-scale problems.

Depends on graph neural network support (GNNLux).