Hypergraph modelling of wave scattering to speed-up material design

TL;DR

This paper introduces a hypergraph-based model for wave-matter interactions that accelerates material design by reducing computational complexity and integrating with existing methods for scalable, efficient optimization.

Contribution

The authors develop a hypergraph framework for wave scattering that enables faster material design algorithms with preserved accuracy by hybridizing with traditional methods.

Findings

Hypergraph model describes multiparticle wave interference efficiently.

The proposed evolutionary algorithm achieves O(N^{1/2}) complexity.

Hybrid approach maintains accuracy while significantly speeding up design.

Abstract

Hypergraphs offer a generalized framework for understanding complex systems, covering group interactions of different orders beyond traditional pairwise interactions. This modelling allows for the simplified description of simultaneous interactions among multiple elements in coupled oscillators, graph neural networks, and entangled qubits. Here, we employ this generalized framework to describe wave-matter interactions for material design acceleration. By devising the set operations for multiparticle systems, we develop the hypergraph model, which compactly describes wave interferences among multiparticles in scattering events by hyperedges of different orders. This compactness enables an evolutionary algorithm with O(N1/2) time complexity and approximated accuracy for designing stealthy hyperuniform materials, which is superior to traditional methods of O(N) scaling. By hybridizing our hypergraph evolutions to the conventional collective-coordinate method, we preserve the original accuracy, while achieving substantial speed-up in approaching near the optimum. Our result paves the way toward scalable material design and compact interpretations of large-scale multiparticle systems.