AOT–KSE Data Assimilation

This repository provides MATLAB scripts for simulating the Azouani–Olson–Titi (AOT) nudging data assimilation algorithm applied to the one-dimensional Kuramoto–Sivashinsky Equation (KSE).
The implementation is designed to study synchronization, convergence, and reconstruction of the true system state using conventional (e.g., Lagrangian and pseudo-Lagrangian) and optimal sensor placement/movement.

Usage

Running a Simulation

The entry point for running simulations is

KSE_inter.m

Modifying System Parameters

To change:

• KSE parameters (e.g., viscosity, domain length)
• Simulation settings
• Plotting options (solution, error, sensors)
  edit the following file:

default_config/initDefaultEnv.m

Selecting Sensor Types

To use various sensor types (e.g., Lagrangian, pseudo-Lagrangian, and/or Directed sensors), open

default_config/DataAssimilationVariables_KSE.m

and uncomment the desired sensor configuration.

References

• Azouani, A., Olson, E., & Titi, E. S.
  Continuous Data Assimilation Using General Interpolant Observables

• Ning, Ning, and Collin Victor. An Assessment of Ensemble Kalman Filter and Azouani–Olson–Titi Algorithms for Data Assimilation: A Comparative Study

Credits

• Original author of the code and contributor - Collin Victor
• Supervisor - Zhao Pan