Efficient generation of grids and traversal graphs in compositional spaces towards exploration and path planning

Journal Article · 05 November 2024 · npj Unconventional Computing

DOI: https://doi.org/10.1038/s44335-024-00012-2 · OSTI ID:2476575

Krajewski, Adam M. ; Beese, Allison M. ; Reinhart, Wesley F. ; Liu, Zi-Kui

Abstract Diverse disciplines across science and engineering deal with problems related to compositions, which exist in non-Euclidean simplex spaces, rendering many standard tools inaccurate or inefficient. This work explores such spaces conceptually in the context of materials discovery, quantifies their computational feasibility, and implements several essential methods specific to simplex spaces through a new high-performance open-source library . Most significantly, we derive and implement an algorithm for constructing a novel n-dimensional simplex graph data structure, containing all discretized compositions and possible neighbor-to-neighbor transitions. Critically, no distance or neighborhood calculations are performed, instead leveraging pure combinatorics and order in procedurally generated simplex grids, keeping the algorithm $$$${\mathcal{O}}(N)$$$$ $O\left(N\right)$ , with minimal memory, enabling rapid construction of graphs with billions of transitions in seconds. Additionally, we demonstrate how such graph representations can be combined to homogeneously express complex path-planning problems, while facilitating efficient deployment of existing high-performance gradient descent, graph traversal, and other optimization algorithms.

• Sponsoring Organization: USDOE Advanced Research Projects Agency - Energy (ARPA-E)
• Grant/Contract Number: AR0001435
• OSTI ID: 2476575
• Journal Information: npj Unconventional Computing, Journal Name: npj Unconventional Computing Journal Issue: 1 Vol. 1; ISSN 3004-8672
• Publisher: Nature Publishing GroupCopyright Statement
• Country of Publication: Country unknown/Code not available
• Language: English