An observer for an occluded reaction-diffusion system with spatially varying parameters.

Area of Science:

• Ecological modeling
• Oceanography
• Dynamical systems theory

Background:

• Ocean ecology models often use partial differential equations (PDEs) to describe complex interactions.
• Remote sensing data provides valuable but often incomplete or noisy observations of marine ecosystems.
• Cloud cover frequently obstructs satellite-based oceanic observations, creating data gaps.

Purpose of the Study:

• To develop a method for estimating spatially dependent parameters in a two-component chaotic reaction-diffusion PDE model of ocean ecology.
• To infer the dynamics of unobserved species and model parameters from partially observed data of a single species.
• To analyze the stability of the learned spatio-temporal dynamics using a network approach.

Main Methods:

• Utilizing autosynchronization to evolve model quantities based on the misfit between model predictions and partially observed data.
• Applying the method to a chaotic reaction-diffusion PDE model relevant to ocean ecology.
• Employing a network approach to analyze the stability of the learned synchronizing system.

Main Results:

• Successfully estimated model parameters and unobserved species dynamics from partially observed, noisy data.
• Demonstrated the ability to learn large-scale coupled synchronizing systems representing spatio-temporal dynamics.
• Applied network analysis to assess the stability of the learned ecological system.

Conclusions:

• Autosynchronization is an effective technique for parameter estimation and system identification in complex ecological models with limited observational data.
• The developed method can handle noisy and occluded data, such as that encountered in remote sensing of ocean ecosystems.
• Network analysis provides insights into the stability of learned ecological dynamics, crucial for understanding ecosystem resilience.