A Koopman operator-based prediction algorithm and its application to COVID-19 pandemic and influenza cases

Area of Science:

• Dynamical Systems Theory
• Data-Driven Modeling
• Predictive Analytics

Background:

• Classical prediction models struggle with nonlinear dynamics, chaotic systems, and sudden process changes.
• Existing methods often rely on long observation sequences and stationarity assumptions.
• Predicting 'Black Swan' events remains a significant challenge in time series analysis.

Purpose of the Study:

• To develop a robust prediction algorithm for nonlinear dynamical systems capable of handling abrupt changes.
• To introduce a method for dynamically switching between global and local prediction strategies.
• To create a retouching mechanism for adapting predictions when system dynamics revert.

Main Methods:

• The methodology is grounded in Koopman operator theory.
• A model-free, purely data-driven approach is employed.
• Algorithms integrate global and local prediction with a dynamic switching and retouching mechanism.

Main Results:

• The developed algorithms successfully predict future states in systems with changing dynamics.
• The approach demonstrates adaptability to unforeseen events and chaotic behaviors.
• Validated on COVID-19 and influenza case predictions, showing broad applicability.

Conclusions:

• This data-driven, model-free methodology offers a significant advancement in predicting complex dynamical systems.
• The approach is versatile, extending beyond epidemiology to various scientific and engineering fields.
• The Koopman operator theory-based method provides a powerful tool for adaptive forecasting.