Wavelet Techniques for Solving Complex Physical Models : A Hybrid Approach to Science and Engineering Challenges

The increasing complexity of modern scientific and engineering challenges necessitates advanced computational techniques for modeling and problem-solving. Wavelet techniques, known for their ability to analyze data across multiple scales and resolutions, have emerged as powerful tools for addressing these challenges. Their applications span diverse fields. This study presents a novel hybrid LSTM-XGBoost model enhanced with wavelet techniques, focusing on the COVID-19 pandemic as a case study for modeling irregular fluctuations in energy demand. The proposed model employs wavelet decomposition to extract frequency components from the data, isolating both short-term variations and long-term trends. These components are integrated as features to enhance the model's sensitivity to anomalies and improve forecasting accuracy over extended periods without frequent retraining. The hybrid approach leverages LSTM’s strength in capturing temporal dependencies and employs XGBoost to correct residual errors. Experimental evaluations demonstrate that the model delivers high-precision forecasts on regular weekdays and maintains robustness during unpredictable anomalies. This methodology highlights the potential of wavelet-enhanced hybrid models in improving the reliability of energy forecasting systems. The findings suggest significant implications for smart grid management, sustainable energy planning, and handling challenges posed by unexpected events in energy systems.