Data-driven stochastic model for cross-interacting processes with different time scales

Area of Science:

• Complex Systems Modeling
• Data-Driven Science
• Time Series Analysis

Background:

• Modeling interacting processes with different time scales is challenging.
• Existing methods often struggle with asynchronous time series data.
• Generalizing nonlinear stochastic models to accommodate varied sampling steps is needed.

Purpose of the Study:

• To propose a novel data-driven method for modeling cross-interacting processes with different time scales.
• To generalize nonlinear stochastic evolution operator models for time series with varying sampling steps.
• To develop a multi-scale stochastic model that accounts for asymmetric, bidirectional nonlinear connections.

Main Methods:

• Developed a generalized nonlinear stochastic model using neural networks.
• Incorporated individual stochastic evolution operators for each process and its time step.
• Parameterized asymmetric, bidirectional nonlinear connections between processes.
• Utilized a Bayesian framework for training and optimizing model components.
• Constructed a multi-scale stochastic model.

Main Results:

• Demonstrated the model's performance on coupled oscillators, correctly reproducing coupling effects.
• Applied the model to spatially distributed climate data, capturing inter-process coupling missed by single-scale models.
• Showcased the model's ability to handle nonlinear connections and different time scales effectively.

Conclusions:

• The proposed multi-scale stochastic model accurately captures cross-interactions in systems with different time scales.
• The data-driven approach offers a significant improvement over independent, single-scale models.
• This method has broad applicability in fields dealing with complex, multi-scale data.