MATRIX AND TENSOR-DRIVEN AI FRAMEWORKS FOR SUSTAINABLE DEVELOPMENT SYSTEMS A FRAMEWORK UTILIZING LINEAR ALGEBRA FOR MODELING STRUCTURED SUSTAINABILITY DATA
Keywords:
Sustainable Development, Linear Algebra, Tensor Decomposition, Low-Rank Approximation, Artificial Intelligence, Spectral Stability, Structured Data Modeling,,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
