Multiscale Dynamics and Information in Data Collection and Assimilation for Environmental Applications.

摘要

Data assimilation or filtering involves blending information from observations of the actual system states with information from dynamical models to estimate the current system states or certain model parameters. The filtering problem relies on three fundamental ingredients, namely 1) sensor placement: where the sensors are placed in order to obtain the most useful information, 2) sensor fusion: how to combine the measurements from different sensors, and 3) estimation: how to use the measurements to obtain the best possible state estimates. In this project, we considered the data assimilation problem for multi-timescale systems. An understanding of how scales interact with information led to the development of rigorous reduced-order data assimilation techniques for these high-dimensional problems. This project developed new algorithms and tools for the collection, assimilation and harnessing of data by threading together ideas from random dynamical systems, information theory, and statistical learning. Anew particle filtering algorithm based on the theoretical result that combines stochastic homogenization with filtering theory to construct a reduced-dimension nonlinear filter is presented. They are used for approximating the real time filtering of chaotic signals. The main results of the research project are: Rigorous mathematical development of a reduced-order particle filtering method for high-dimensional, multiscale random dynamical systems; Development of a particle filtering method adapted to high- dimensional, multiscale, chaotic systems.