MATRIX AND TENSOR-DRIVEN AI FRAMEWORKS FOR SUSTAINABLE DEVELOPMENT SYSTEMS A FRAMEWORK UTILIZING LINEAR ALGEBRA FOR MODELING STRUCTURED SUSTAINABILITY DATA

Abstract

Sustainable development initiatives generate extensive datasets that combine environmental, 
economic, and social metrics. These datasets are often high-dimensional and typically display 
structured relationships that arise naturally in matrix or tensor formats. Many traditional 
artificial intelligence (AI) methods reduce such data by transforming it into flat vector forms, 
which can result in the loss of significant relationships across spatial, temporal, and sectoral 
dimensions. 
Based on the ideas of applied linear algebra, this paper presents an organised artificial 
intelligence framework for sustainable systems. To create comprehensible and computationally 
effective AI models, the framework integrates methods including spectral stability analysis, 
tensor decomposition, and low-rank matrix approximation. Additionally included are 
mathematical findings pertaining to the convergence behaviour of matrix-based learning 
algorithms and optimal low-rank approximation. 
The proposed framework is demonstrated through two practical applications: renewable energy 
production forecasting and completion of missing Sustainable Development Goal (SDG) 
indicators. The findings demonstrate that organized linear algebraic models enhance 
dimensionality reduction, model robustness, and clarity, all while preserving solid 
mathematical principles. The research underscores the importance of matrix and tensor 
techniques in enhancing AI-based evaluation for sustainable development

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