Featurizing Koopman mode decomposition for robust forecasting.

Area of Science:

• Dynamical Systems and Control Theory
• Machine Learning for Scientific Discovery
• Computational Biology and Bioinformatics

Background:

• High-dimensional dynamical systems present significant challenges for analysis and prediction.
• Traditional Koopman Mode Decomposition (KMD) requires prior knowledge of system features for optimal performance.
• Accurate modeling of complex systems like cell signaling is crucial for scientific advancement.

Purpose of the Study:

• To introduce Featurized Koopman Mode Decomposition (FKMD), an advanced KMD technique.
• To enhance the analysis and prediction capabilities for high-dimensional dynamical systems.
• To demonstrate FKMD's effectiveness in scenarios lacking a priori feature information.

Main Methods:

• Utilizing delay embedding to expand the observation space and capture manifold structures.
• Incorporating a learned Mahalanobis distance to dynamically adjust observations based on system dynamics.
• Applying FKMD to diverse high-dimensional systems, including a linear oscillator, a partially observed Lorenz attractor, and a cancer-related cell signaling model.

Main Results:

• FKMD demonstrated improved predictive accuracy compared to standard methods.
• The technique effectively handled systems where relevant features were not initially known.
• Successful application to a complex biological system highlights its potential in cancer research.

Conclusions:

• Featurized Koopman Mode Decomposition (FKMD) offers a powerful new approach for analyzing and predicting high-dimensional dynamical systems.
• The combination of delay embedding and learned Mahalanobis distance overcomes limitations of traditional KMD.
• FKMD shows significant promise for applications in various scientific fields, including computational biology and complex systems modeling.