Signal prediction by anticipatory relaxation dynamics

Area of Science:

• Control Systems Engineering
• Dynamical Systems Theory
• Signal Processing

Background:

• Real-time signal prediction is crucial for control problems and biological systems.
• Existing methods may lack the ability to anticipate signal dynamics accurately.
• A need exists for parsimonious and effective predictive models.

Purpose of the Study:

• To introduce and describe a novel parsimonious prediction approach called anticipatory relaxation dynamics (ARD).
• To demonstrate ARD's capability in predicting future signal values and anticipating signal peaks.
• To characterize ARD's predictive properties, including its frequency-dependent nature and prediction horizon.

Main Methods:

• Coupling a linear relaxation-delay system with a smooth, stationary signal.
• Analyzing the resulting anticipatory relaxation dynamics (ARD) as an input-output system.
• Characterizing ARD using its analytically derived frequency response function.

Main Results:

• ARD functions as a frequency-dependent predictor of future signal values.
• The model demonstrates an ability to approximately predict signals on average.
• ARD successfully anticipates the occurrence of signal peaks, explained by negative group delay.

Conclusions:

• Anticipatory relaxation dynamics (ARD) offers a robust and parsimonious approach to real-time signal prediction.
• The model's ability to anticipate peaks and its frequency-dependent nature are key advantages.
• ARD provides a characterized prediction horizon via its frequency response function, advancing control and biological modeling.