Commutative Algebra Modeling in Materials Science – A Case Study on Metal–Organic Frameworks (MOFs)

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. This publication is licensed under You are free to share (copy and redistribute) this article in any medium or format and to adapt (remix, transform, and build upon) the material for any purpose, even commercially within the parameters below: Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. *Disclaimer This summary highlights only some of the key features and terms of the actual license. It is not a license and has no legal value. Carefully review the actual license before using these materials. You are free to share (copy and redistribute) this article in any medium or format and to adapt (remix, transform, and build upon) the material for any purpose, even commercially within the parameters below: Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. *Disclaimer This summary highlights only some of the key features and terms of the actual license. It is not a license and has no legal value. Carefully review the actual license before using these materials. You are free to share (copy and redistribute) this article in any medium or format and to adapt (remix, transform, and build upon) the material for any purpose, even commercially within the parameters below: Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. *Disclaimer This summary highlights only some of the key features and terms of the actual license. It is not a license and has no legal value. Carefully review the actual license before using these materials.