When modeling predator-prey populations in 2d space, as described by a system of two parabolic partial differential equations, state space information could get corrupted during transmission or collection. This has been a problem in research; regular analysis and modeling are done via satellite images, which have a high probability of having significant errors (either noise or regions covered by clouds) in regions of interest. While that wouldn’t be a problem for systems with minor sensitivity, errors could cause significant divergences from actual state behavior in diffusion population systems, which is the system under study. Principal Component Analysis (PCA) is a mathematical method used to realign high-dimensional data to a different dimensional axis by recognizing major principle components of the data. It is a method used in image and error detection, as images can be represented as points in spaces with very large dimensions. However, due to the sequential nature of dynamical system data, a modified PCA uses windowed time steps as data points to identify the principal components of a predator-prey system modeled using some initial state parameters. Then, the PCA was used to recover data that had been erased from a second model using different initial state parameters using PCA inpainting, and the recovered data was used to drive a system in equilibrium into matching the second system. This setup restored the driving system’s behavior even when the corruption (noise and date erasure) affected 30% of the data used for transmission, indicating PCA can recognize and imprint the nonlinear nature of the dynamical system when extended to the time dimension.
Using a modified Principal Component Analysis to recover state information from a corrupted Dynamical System for modelling
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Student Abstract Submission