Bagging, optimized dynamic mode decomposition for robust, stable forecasting with spatial and temporal uncertainty...

Area of Science:

• * Data-driven science
• * Dynamical systems theory
• * Machine learning for scientific modeling

Background:

• * Dynamic Mode Decomposition (DMD) offers a regression framework for learning linear dynamics from temporal or spatio-temporal data.
• * Standard DMD algorithms often suffer from bias errors due to noisy measurements, leading to inaccurate models and unstable forecasting.
• * Optimized DMD (oDMD) minimizes bias using variable projection optimization for improved forecasting stability.

Purpose of the Study:

• * To enhance the optimized DMD algorithm by incorporating statistical bagging methods.
• * To develop a robust and stable model for probabilistic forecasting with uncertainty quantification.
• * To introduce Bagging Optimized DMD (BOP-DMD) for improved performance in dynamical systems analysis.

Main Methods:

• * Application of statistical bagging to create an ensemble of optimized DMD models from a single dataset.
• * Averaging outputs from the ensemble of oDMD models to produce the final BOP-DMD model.
• * Implementation of ensemble techniques for model stabilization, cross-validation, and robustness.

Main Results:

• * BOP-DMD significantly improves model stability and forecasting capabilities compared to standard DMD algorithms.
• * The ensembling approach robustifies the model against noise and measurement errors.
• * BOP-DMD provides comprehensive spatial and temporal uncertainty quantification (UQ) metrics.

Conclusions:

• * BOP-DMD offers a stable and robust framework for probabilistic (Bayesian) forecasting in dynamical systems.
• * The method provides superior uncertainty quantification, enabling more reliable predictions.
• * BOP-DMD represents a significant advancement for data-driven prediction in dynamical systems.