Grey Model (GM): Mathematical Modeling Using Differential Equations from Grey Theory
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Resource Overview
GM stands for Grey Model, which refers to the differential equation-based model within Grey Theory—G representing Grey and M representing Model. GM(1, N) denotes a first-order differential equation model involving N variables, while GM(1, 1) is a first-order single-variable version. The model is implemented using discrete data sequences and matrix calculations to approximate derivative-based relationships.
Detailed Documentation
GM Science, based on Grey Theory, constructs differential equation models capable of predicting and analyzing interdependencies among multiple variables. These models find broad applications across domains such as economics and environmental science. The GM(1, N) model represents a first-order differential equation with N variables, which can algorithmically incorporate accumulated generating operations (AGO) and least squares parameter estimation. In contrast, GM(1, 1) is a simplified first-order single-variable model, often computed using time-series data whitening through exponential fitting. As an analytical tool, GM Science enables deeper understanding of variable relationships, typically implemented via computational steps including data preprocessing, parameter solving, and model validation.
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