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Abstract

Real-time prediction of complex dynamical systems is critical in many scientific and engineering domains, where traditional numerical solvers can be computationally expensive and limited in generalization across changing environments. This dissertation presents a physics-guided deep learning framework for reduced-order modeling, generalization, and uncertainty quantification in nonlinear dynamical systems, with particular focus on underwater acoustics as a representative application. The dissertation is structured around five core contributions. First, we develop a reduced-order model based on deep learning that combines convolutional encoders with an attention-based recurrent neural network to learn latent dynamics from high-fidelity simulations. Second, we introduce a multistep integration-inspired attention mechanism that connects to and generalizes linear multistep methods for learning latent space dynamics, improving numerical stability and interpretability. Third, we propose a space-time coupled deep learning model based on 3D convolutional neural networks, enabling simultaneous learning of spatial and temporal correlations in unsteady flow data. Fourth, we address the challenge of domain generalization by developing a range-dependent conditional convolutional neural network with a continual learning framework. This allows adaptation across varying underwater ocean environments without performance degradation. Finally, we present a sparse variational Gaussian process model for uncertainty-aware three-dimensional acoustic field prediction in real time. These methods are applied to benchmark dynamical systems as well as realistic underwater acoustic scenarios, including transmission loss prediction over range-dependent ocean bathymetry. The results demonstrate high predictive accuracy, generalizability and computational efficiency, which support the deployment of digital twins in marine applications. This dissertation advances the development of physics-guided learning architectures for dynamical systems, offering new tools for real-time prediction, interpretability, and domain adaptation. The underwater acoustics is considered as a representative use case, highlighting the broader potential of these methods in science and engineering.