Commutative Algebra Modeling in Materials Science – A Case Study on Metal–Organic Frameworks (MOFs)
Year: 2026
Type: article
Abstract: Metal-organic frameworks (MOFs) are a class of important crystalline and highly porous materials whose hierarchical geometry and chemistry hinder interpretable predictions in materials properties. Commutative algebra is a branch of abstract algebra that has been rarely applied in data and material sciences. We introduce the first ever commutative algebra modeling and prediction in materials science. Specifically, category-specific commutative algebra (CSCA) is proposed as a new framework for MOF representation and learning. It integrates element-based categorization with multiscale algebraic invariants to encode both local coordination motifs and global network organization of MOFs. These algebraically consistent, chemically aware representations enable compact, interpretable, and data efficient modeling of MOF properties such as Henry's constants and uptake capacities for common gases. Compared to traditional geometric and graph-based approaches, CSCA achieves comparable or superior predictive accuracy while substantially improving interpretability and stability across data sets. By aligning commutative algebra with the chemical hierarchy, the CSCA establishes a rigorous and generalizable paradigm for understanding structure and property relationships in porous materials and provides a nonlinear algebra-based framework for data-driven material discovery.
Authors: Caleb Simiyu Khaemba, Hongsong Feng, Dong Chen, Chun-Long Chen, Guo-Wei Wei
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,500
Funders: National Science Foundation, U.S. Department of Energy, Battelle, Bristol-Myers Squibb, Michigan State University, Michigan State University Foundation, National Institutes of Health, Defense Threat Reduction Agency, Office of Science, College of Engineering, Michigan State University, National Institute of General Medical Sciences, Basic Energy Sciences, Pacific Northwest National Laboratory
Awards: G1199819875, G125460123, G138090931, G1851334662, G1899721271, G2506945562, G2510423872, G2551507366, G2988778103, G3265316475, G391136020, G402711812, G4934647071, Collaborative Research: Integrating Algebraic Topology, Graph Theory, and Multiscale Analysis for Learning Complex and Diverse Datasets, G5049402221, G5321382714, G5653134238, G5726405315, G6065440738, Discovery-Driven Mathematics and Artificial Intelligence for Biosciences and Drug Discovery, G7560550554, G821644656, G9000094880, G921665476
OpenAlex ID: W7129656245