Data-assisted reduced-order modeling of extreme events in complex dynamical systems

Area of Science:

• Complex Systems Science
• Dynamical Systems Theory
• Computational Science

Background:

• Extreme events (avalanches, droughts, epidemics) arise from complex dynamical systems with high dimensionality.
• Classical order-reduction methods struggle with the complexity and high dimensionality of these systems, especially during rare transitions.
• Data-driven methods face limitations in data-sparse regions, crucial for predicting extreme events.

Purpose of the Study:

• To develop a novel hybrid framework for predicting extreme events.
• To integrate imperfect reduced-order models with data-driven recurrent neural network (RNN) architectures.
• To enhance prediction accuracy in data-sparse regions characteristic of extreme events.

Main Methods:

• Developed a hybrid framework combining a reduced-order model (projected equations) with a long short-term memory (LSTM) recurrent neural network (RNN).
• Trained the LSTM-RNN by analyzing the mismatch between the imperfect model and data streams projected into the reduced-order space.
• Assessed the framework on two prototype systems exhibiting extreme events.

Main Results:

• The hybrid framework demonstrated improved performance over methods using only data streams or the imperfect model alone.
• Significant performance gains were observed in regions associated with extreme events, where data is typically sparse.
• The data-driven component assists the imperfect model where data is available, while the imperfect model provides a baseline in sparse regions.

Conclusions:

• The developed hybrid framework effectively enhances the prediction of extreme events by leveraging both model-based and data-driven approaches.
• This blended approach offers a robust solution for complex dynamical systems where data availability is uneven.
• The framework shows particular promise for improving forecasts of rare and high-impact phenomena.