UCLA

Fluid flows are high-dimensional, nonlinear dynamical systems governed by partial differential equations, making their direct simulation computationally expensive for many practical applications. Nevertheless, many flows evolve on low-dimensional manifolds, motivating reduced-order models that capture the essential dynamics while significantly reducing computational complexity. Recent advances in machine learning provide powerful nonlinear dimensionality reduction techniques capable of learning such representations directly from data. This thesis investigates data-driven latent representations for reduced-order modeling in fluid mechanics, with an emphasis on aerodynamic applications. Rather than treating latent spaces solely as compact embeddings optimized for reconstruction, this work explores representations that incorporate physical and mathematical structure to improve interpretability, robustness, and predictive capability. First, an autoencoder-based framework is developed for aerodynamic design optimization of industrial automobile geometries. The learned latent representation efficiently captures geometric variations, enabling accelerated design exploration while achieving an 11% reduction in drag coefficient. The framework predicts aerodynamic performance within 2% of experimentally validated large-eddy simulations, demonstrating sufficient fidelity for practical design optimization.Second, a physically structured latent space based on optimal transport distances is introduced for flow control analysis. Applied to separated flow over a NACA 0012 airfoil with leading-edge thermal actuation, the approach identifies distinct control regimes associated with changes in separation bubble size and the onset of partial and global laminarization, providing an interpretable representation of the underlying flow dynamics.Finally, a probabilistic state estimation framework combining latent diffusion models with particle filtering is developed for reconstructing and predicting transient aerodynamic states from limited observations. Applied to a high-incidence airfoil subjected to gust disturbances, the framework enables uncertainty-aware estimation of complex unsteady flows.Collectively, these studies demonstrate that physically informed latent representations provide efficient and interpretable reduced-order models for aerodynamic design optimization, flow control assessment, and probabilistic state estimation. The results highlight the importance of incorporating physical structure into representation learning, illustrating the potential of hybrid machine learning and physics-based approaches for reliable modeling and analysis of complex fluid systems.