Time-Varying Biological Time Series Prediction and Pattern Interpretation via Koopman Theory and Large Language Model

Biological time series data characterizes the dynamic evolution of biological systems and plays a crucial role in genetic inheritance, disease diagnosis, and biological microenvironment. However, accurate prediction for biological time-series data remains challenging due to their pronounced time-varying, non-stationary, and noisy characteristics. Existing approaches often fail to capture latent distribution shifts and the coupled evolution of global and local patterns, limiting both predictive performance and interpretability. Thus, this study firstly proposes a time-varying neural network (TVNN) model that combine frequency-domain information with Koopman embedding theory. TVNN model Koopman transition matrices are used to model global dynamics and local time-varying behaviors for pattern extraction. Secondly, a time-varying pattern recognition large language model (TVPRLLM) is introduced to recognize and interpret the extracted time-varying patterns, enabling the discovery of their potential biological significance. Thirdly, we have developed such a biological time series predictive platform that can offer visualization, data analysis, and predictive services. Experimental results demonstrate that TVNN model outperforms existing mainstream methods in predicting on biological time-varying time series.