# An Observer for an Occluded Reaction-Diffusion System With Spatially Varying Parameters

## TL;DR

This paper develops an observer method for a reaction-diffusion system with spatially varying parameters, enabling parameter estimation and synchronization from partial, noisy, and occluded data, inspired by ocean ecology remote sensing.

## Contribution

It introduces an autosynchronization approach for estimating parameters and states in a spatially varying reaction-diffusion PDE with occlusions, applicable to ocean ecology modeling.

## Key findings

- Successfully estimates parameters from partial data
- Handles noisy and occluded observations effectively
- Analyzes stability using a network approach

## Abstract

Spatially dependent parameters of a two-component chaotic reaction-diffusion PDE model describing ocean ecology are observed by sampling a single species. We estimate model parameters and the other species in the system by autosynchronization, where quantities of interest are evolved according to misfit between model and observations, to only partially observed data. Our motivating example comes from oceanic ecology as viewed by remote sensing data, but where noisy occluded data are realized in the form of cloud cover. We demonstrate a method to learn a large-scale coupled synchronizing system that represents spatio-temporal dynamics and apply a network approach to analyze manifold stability.