In this dissertation, I consider the problem of model reduction in both oscillatory and networked systems. Previously, the Manifold Boundary Approximation Method (MBAM) has been demonstrated as a data-driven tool for reducing the parametric complexity of so-called sloppy models. To be effective, MBAM requires the model manifold to have low curvature. I show that oscillatory models are characterized by model manifolds with high curvature in one or more directions. I propose methods for transforming the model manifolds of these models into ones with low curvature and demonstrate on a couple of test systems. I demonstrate MBAM as a tool for data-driven network reduction on a small model from power systems. I derive multiple effective networks for the model, each tailored to a specific choice of system observations. I find several important types of parameter reductions, including network reductions, which can be used in large power systems models. Finally, I consider the problem of piecemeal reduction of large systems. When a large system is split into pieces that are to be reduced separately using MBAM, there is no guarantee that the reduced pieces will be compatible for reassembly. I propose a strategy for reducing a system piecemeal while guaranteeing that the reduced pieces will be compatible. I demonstrate the reduction strategy on a small resistor network.

<p>Every engineered system behaves slightly differently because of manufacturing and operational uncertainties. The ability to build system-specific predictive models that adapt to manufactured systems, also known as digital twins, opens up many possibilities for reducing operating and maintenance costs. Nonlinear dynamical systems with unknown governing equations and states characterize many engineered systems. As a result, learning their dynamics from data has become both the current research area and one of the biggest challenges. In this thesis, we do an investigation of different data driven approaches for modeling various engineered systems. Firstly, we develop a model to predict the transient and steady-state behavior of a turbocharger turbine using the Koopman operator which can be helpful for modelling, analysis and control design. Our approach is as follows. We use experimental data from a Cummins heavy-duty diesel engine to develop a turbine model using Extended Dynamic Mode Decomposition (EDMD), which approximates the action of the Koopman operator on a finite-dimensional subspace of the space of observables. The results demonstrate comparable performance with a tuned nonlinear autoregressive network with an exogenous input (NARX) model widely used in the literature. The performance of these two models is analyzed based on their ability to predict turbine transient and steady-state behavior. Furthermore, we assess the ability of liquid time-constant (LTC) networks to learn the dynamics of various oscillatory systems using noisy data. In this study, we analyze and compare the performance of the LTC network with various commonly used recurrent neural network (RNN) architectures like long short-term memory (LSTM) network, and gated recurrent units (GRU). Our approach is as follows. We first systematically generate synthetic data by exciting the system of interest with a band-limited white noise and simulating it using a forward Euler discretization scheme. After the output has been simulated, we then corrupt it with different levels of noise to replicate a practically measured signal and train the RNN architectures with that corrupted output. The model is then tested on various types of forcing excitations to analyze the robustness of these networks in capturing different behaviors exhibited by the system. We also analyze the ability of these networks to capture the resonance effect for various parameter settings. Case studies discussing standard benchmark oscillatory systems (i.e., spring-mass-damper (S-M-D) system, single degree of freedom (DOF) Bouc-Wen oscillator, and forced Van der pol oscillator) are used to test the performance of these methodologies. The results reveal that the LTC network showed better performance in modeling the S-M-D system and 1-DOF Bouc-Wen oscillator as compared to an LSTM network but was outperformed by the GRU network. None of the networks were able to model the forced Van der pol oscillator with a reasonable accuracy. Since the GRU network outperformed other networks in terms of the computational time and the model accuracy for most of the scenarios, we applied it to a real world experimental dataset (i.e. turbocharger turbine dynamics) to compare it against the EDMD and NARX model. The results showed better performance of the GRU network in modeling the transient behaviours of the turbine. However, it failed to predict the turbine outlet temperature with a reasonable accuracy in most of the regions for the steady state dataset. As future work, we plan to consider training the GRU network with a data sampling frequency of 100 Hz for a fair comparison with the NARX and the Koopman approach.</p>