Donglin Liu presents his PhD dissertation on "System Identification and Data-Driven Modeling"

This thesis explores the integration of machine learning techniques with classical numerical methods to develop more robust approaches for data-driven modeling. Motivated by challenges such as noise, partial observability, and data scarcity, it proposes hybrid frameworks that combine domain knowledge with learning-based methods. The research focuses on three key areas: parameter estimation, identification of complex dynamical systems from observational data, and synthetic data generation.
The first two studies apply neural ordinary differential equations and Bayesian optimization to enable robust parameter estimation and dynamic reconstruction, with applications such as epidemic modeling. The third study advances sparse identification of nonlinear dynamics by incorporating group similarity and Earth Mover’s Distance to improve robustness and generalization.
The final two studies focus on high-dimensional data settings, developing a graph-enhanced diffusion model for spatiotemporal imputation and employing generative diffusion models to synthesize realistic biometric data, such as fingerprints. These contributions demonstrate the value of generative and hybrid modeling in domains with limited or noisy data and strict privacy constraints.

Supervisor: Alexandros Sopasakis