Spatiotemporal System Identification With Continuous Spatial Maps and Sparse Estimation.

Area of Science:

• Dynamical Systems Theory
• Computational Neuroscience
• Signal Processing

Background:

• Spatiotemporal dynamical systems are crucial for understanding complex phenomena.
• Existing models often struggle with spatial heterogeneity and large observation sets.
• A need exists for efficient and accurate identification methods.

Purpose of the Study:

• To present a novel framework for identifying spatiotemporal linear dynamical systems.
• To enable decoupled spatial observation locations from model order.
• To facilitate identification with spatial heterogeneity and continuous spatial representation.

Main Methods:

• Decomposition of spatial fields using basis functions and spatial frequency analysis.
• Closed-form initialization of states.
• Sparse regression (Least Absolute Shrinkage and Selection Operator) for parameter initialization.
• Iterative Kalman filter and sparse regression for joint state and parameter estimation.

Main Results:

• The proposed framework successfully identified spatiotemporal linear dynamical systems.
• High accuracy was achieved in predicting spatiotemporal fields using Kuramoto model data.
• Sparse regression resulted in a compact and parsimonious model representation.

Conclusions:

• The developed framework offers an effective approach for identifying complex spatiotemporal dynamics.
• The method handles spatial heterogeneity and decouples observation locations from model order.
• The use of sparse regression ensures model compactness and efficient parameter estimation.