Time-Varying Biological Time-Series Prediction and Pattern Recognition Using Koopman Theory and Large Language Models

Biologically related time-series data characterize the dynamic evolution of biological systems, including genetic inheritance, disease diagnosis, and the biological microenvironment. However, accurate prediction of these data remains challenging due to their pronounced time-varying, non-stationary, and noisy characteristics. Existing approaches often fail to capture latent shifts of biologically related time series, limiting both predictive performance and time-varying pattern recognition capability. Thus, in this study, we first propose a time-varying neural network (TVNN) model that combines frequency-domain information with Koopman 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 classify the extracted time-varying patterns, enabling the identification of potential pattern categories. Thirdly, we have developed a biology-related time-series predictive platform that can offer visualization, data analysis, and predictive services. Experimental results demonstrate that the TVNN model outperforms existing mainstream methods in predicting biology-related time-varying time series, and that it achieves competitive forecasting performance, though its behavior depends strongly on the design of the frequency-domain decomposition. Additional robustness analyses reveal that the choice of Fourier masking strategy can materially affect both RMSE and long-horizon stability. We further show that Koopman-derived time-varying representations are highly discriminative for dynamic state recognition.