This paper treats comprehensively the construction of problems from nonlinear dynamics
and constrained optimization amenable to parameter continuation techniques and with …

Low-order thermoacoustic models are qualitatively correct, but typically, they are
quantitatively inaccurate. We propose a time-domain bias-aware method to make …

We propose a physics-informed machine learning method to predict the time average of a
chaotic attractor. The method is based on the hybrid echo state network (hESN). We assume …

In this computational paper, we perform sensitivity analysis of long-time (or ensemble)
averages in the chaotic regime using the shadowing algorithm. We introduce automatic …

When they occur, azimuthal thermoacoustic oscillations can detrimentally affect the safe
operation of gas turbines and aeroengines. We develop a real-time digital twin of azimuthal …

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

This paper presents a rigorous framework for the continuation of solutions to nonlinear
constraints and the simultaneous analysis of the sensitivities of test functions to constraint …

This article examines the degree to which optimizing a Rijke tube experiment can improve
the accuracy of thermoacoustic model parameter estimation, thereby facilitating robust …

Ensemble data assimilation algorithms combine experimental data and numerical models to
estimate the state and parameters of a system. If the model is unbiased, the estimation …

The objectives of this dissertation are to develop computational techniques for i) tracking
solutions to multi-segment, delay-coupled boundary-value problems, with particular …