Reconstructing and predicting stochastic dynamical systems using probabilistic deep learning.

Area of Science:

• Dynamical Systems and Time-Series Analysis
• Machine Learning and Artificial Intelligence
• Uncertainty Quantification

Background:

• Stochastic effects in dynamical systems introduce significant complexity for data-driven reconstruction and prediction.
• Existing methods often struggle to adequately address uncertainty, limiting prediction accuracy and robustness.
• Accurate modeling of stochasticity is crucial for understanding and forecasting complex systems.

Purpose of the Study:

• To develop a deep learning model that incorporates uncertainty learning for improved time-series prediction.
• To propose a novel deep stochastic time-delay embedding model capable of capturing and utilizing system uncertainty.
• To enhance the robustness and accuracy of predictions in the presence of stochastic effects.

Main Methods:

• Construction of a deep probabilistic catcher to capture uncertainty information in reconstructed mappings.
• Integration of uncertainty representations as meta-information into time-delay embedding.
• Development of a deep stochastic time-delay embedding model for multi-step time-series prediction.

Main Results:

• The proposed model demonstrates superior performance compared to existing methods on both the Lorenz system and real-world datasets.
• The model exhibits robust prediction capabilities under noisy conditions.
• Effective capture of system stochasticity and improved prediction accuracy were achieved.

Conclusions:

• The deep stochastic time-delay embedding model offers a powerful approach for handling uncertainty in time-series prediction.
• Incorporating uncertainty learning significantly enhances the accuracy and robustness of dynamical system predictions.
• This method provides a valuable tool for the data-driven reconstruction and prediction of complex stochastic systems.