Topological feature engineering and persistent homology hybrid deep learning model for time-series prediction

The integration of persistent homology with time-series forecasting remains largely unexplored, despite its potential for capturing topological structures in dynamic data. This is partly due to the prevailing belief that persistent homology is better suited for quantifying and extracting hidden structural information for classification or clustering tasks, rather than for predictive modeling. Additionally, there is no well-established framework for incorporating persistent homology into time-series forecasting models. In this study, we propose a novel hybrid approach that leverages persistent homology as a feature extraction technique for deep learning models. Our framework places persistent homology at the core of a structured pipeline, engineering topological features that capture temporal dependencies. These features are then used as model inputs, while a topological consistency loss is introduced alongside the prediction loss to guide learning. Based on this framework, we develop PH-RNN-based models for univariate time-series forecasting and PH-transformer-based and PH-CNN-based models for multivariate time-series prediction. Experimental results demonstrate the effectiveness of our approach, consistently outperforming baseline methods across multiple benchmark datasets. This work bridges the gap between topological data analysis and deep learning for time-series forecasting, providing a new perspective on feature engineering in predictive modeling.