Prediction of Data Using Fusion of GM Gray Model and BP Neural Network

The fusion of GM Gray Model and BP Neural Network represents a predictive technique that combines traditional gray system theory with modern machine learning methods. The GM Gray Model excels at handling uncertain systems with small sample sizes and limited information, revealing inherent data patterns through gray differential equations. Meanwhile, the BP Neural Network possesses strong nonlinear fitting capabilities, automatically adjusting weights through backpropagation to learn complex patterns.

The integration typically employs serial or parallel architectures: In the serial approach, the GM model first extracts data trend components, then feeds the residuals into the BP network for error compensation. The parallel approach allows both models to make independent predictions before weighted integration. This hybrid strategy leverages GM's sensitivity to trends while utilizing the neural network's advantage in handling noise, making it particularly suitable for prediction scenarios with clear time-series characteristics but limited sample sizes (such as energy consumption and economic indicators).

Implementation requires careful coordination between GM's accumulated generating operation and the neural network's input scaling, along with dynamic adjustment of both models' contribution weights. After determining optimal fusion parameters through cross-validation, such hybrid models often demonstrate higher prediction accuracy and robustness compared to single models. Key implementation considerations include proper data preprocessing, setting appropriate network architectures, and tuning hyperparameters for optimal performance.