Identification of Nonlinear Spatiotemporal Dynamical Systems With Nonuniform Observations Using...

Area of Science:

• Dynamical Systems and Control
• Computational Mathematics
• Scientific Computing

Background:

• Identifying nonlinear spatiotemporal systems governed by partial differential equations is crucial but challenging.
• Existing methods often require small, uniform sampling intervals, limiting practical applications.
• There is a need for robust identification techniques that accommodate nonuniform data.

Purpose of the Study:

• To propose a novel, robust method for identifying nonlinear spatiotemporal dynamical systems.
• To overcome the limitations of existing methods regarding sampling regularity.
• To enable accurate system identification from pointwise nonuniform observations.

Main Methods:

• Integral Least Square Regularization Regression (ILSRR) for accurate time-domain derivative estimation.
• Inverse meshless collocation for spatiotemporal system dimensional reduction.
• A multistep identification strategy combining ILSRR and multiple-kernel learning.

Main Results:

• The proposed method accurately identifies nonlinear spatiotemporal systems.
• It effectively handles pointwise nonuniform observations, a significant improvement over existing techniques.
• Numerical studies demonstrate the method's effectiveness and advantages on benchmark systems.

Conclusions:

• The developed multistep identification method offers a powerful solution for complex spatiotemporal system identification.
• ILSRR and inverse meshless collocation provide robust tools for handling practical, nonuniformly sampled data.
• This work advances the field of system identification for nonlinear dynamical systems.