Spatiotemporal system identification on nonperiodic domains using Chebyshev spectral operators and system reduction...

Area of Science:

• Applied Mathematics
• Computational Science
• System Identification

Background:

• Data-driven modeling of nonlinear spatiotemporal systems is crucial for scientific discovery.
• Existing methods often struggle with accuracy on nonperiodic domains.
• Developing robust identification techniques for complex systems remains a challenge.

Purpose of the Study:

• To propose a novel system identification methodology for nonlinear spatiotemporal systems.
• To leverage Chebyshev spectral operators for accurate model discretization.
• To develop a parsimonious model through orthogonal system reduction.

Main Methods:

• A continuous model structure accommodating arbitrary derivative orders and nonlinearity degrees was devised.
• Chebyshev spectral operators were applied to discretize the continuous model, achieving spectral accuracy.
• Least squares combined with an orthogonal system reduction algorithm were used for parameter estimation and redundancy elimination.

Main Results:

• The proposed Chebyshev spectral identification method was successfully applied to the Allen-Cahn metastable equation.
• The method demonstrated superior accuracy in identifying the system compared to finite difference methods.
• A parsimonious discrete model was achieved, effectively capturing system dynamics.

Conclusions:

• The developed methodology provides an accurate and efficient approach for data-driven modeling of nonlinear spatiotemporal systems.
• Chebyshev spectral operators offer significant advantages for inverse problems and system identification.
• This work advances the field of system identification, particularly for complex systems on nonperiodic domains.