Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a
significant obstacle in forecasting the weather and other geophysical fluid flows. Data …

Abstract Covariant Lyapunov vectors or CLVs span the expanding and contracting directions
of perturbations along trajectories in a chaotic dynamical system. Due to efficient algorithms …

We introduce a framework for data assimilation (DA) in which the data is split into multiple
sets corresponding to low‐rank projections of the state space. Algorithms are developed that …

How does long-term chaotic behavior respond to small parameter perturbations? Using
detailed models, chaotic systems are frequently simulated across disciplines–from climate …

In applications of system identification where the inputs and outputs are scheduled at
different sampling rates, the traditional gradient-based iterative (GI) identification scheme …

Particle flow methods are effective in resolving the particle degeneracy issue in the standard
particle filtering algorithm. However, flow methods have their own difficulties, such as the …

Growing set of optimization and regression techniques, based upon sparse representations
of signals, to build models from data sets has received widespread attention recently with …

This dissertation addresses theoretical and numerical questions in nonlinear filtering theory
for high dimensional, chaotic, multiple timescale correlated systems. The research is …