A MIXED-METHOD STUDY OF SILICATE NETWORK STRUCTURES USING M-POLYNOMIALS AND GRAPH NEURAL NETWORKS

Abstract

The topological characterization of chemical structures constitutes the theoretical backbone of modern computational materials science, enabling the prediction of macroscopic physicochemical properties from atomic-level connectivity. This study presents a highly rigorous, mixed-method paradigm for analyzing complex silicate network structures by integrating classical algebraic graph theory with state-of-the-art deep learning architectures. We analytically derive the generalized M-polynomials for primary structural classes of silicate networks—specifically linear chains, two-dimensional phyllosilicate sheets, and three-dimensional tectosilicate frameworks. Utilizing differential and integral calculus operators, these closed-form polynomials are mathematically transformed into a suite of distinct, globally aware topological invariants, providing highly expressive numerical descriptors. To bridge the epistemic gap between deterministic mathematical formulations and stochastic machine learning, a novel hybrid Graph Neural Network (GNN) architecture is proposed. This architecture mitigates the pervasive "oversmoothing" phenomenon and the expressive limitations bounded by the 1-Weisfeiler-Lehman (1-WL) isomorphism test inherent in standard message-passing algorithms. By orthogonally fusing mathematically extracted macroscopic topological descriptors with localized, permutation-equivariant node embeddings within the network's dense layers, our proposed model achieves an unprecedented classification accuracy of , significantly outperforming traditional spatial baseline models (). This research validates the sustained utility of chemical graph theory within the AI epoch, establishing a computationally tractable and highly robust pipeline for advanced Quantitative Structure-Property Relationship (QSPR) modeling in solid-state chemistry and materials discovery