Reconstructing and predicting stochastic dynamical systems using probabilistic deep learning

Stochastic effects introduce significant uncertainty into dynamical systems, making the data-driven reconstruction and prediction of these systems highly complex. This study incorporates uncertainty learning into a deep learning model for time-series prediction, proposing a deep stochastic time-delay embedding model to improve prediction accuracy and robustness. First, this model constructs a deep probabilistic catcher to capture uncertainty information in the reconstructed mappings. These uncertainty representations are then integrated as meta-information into the reconstruction process of time-delay embedding, enabling it to fully capture system stochasticity and predict target variables over multiple time steps. Finally, the model is validated on both the Lorenz system and real-world datasets, demonstrating superior performance compared to existing methods, with robust results under noisy conditions.