Abstract
Modern healthcare increasingly relies on analyzing biomedical sensor data, yet modeling such data is difficult because many physiological systems exhibit nonlinear, nonstationary behaviors. Classical time- and frequency-domain methods support many applications but assume linearity or stationarity but miss the nonlinear dynamics driving complex physiological processes. Deep learning can capture such patterns, but its dynamic representations are opaque and offer limited interpretability. Recurrence analysis (RA), grounded in nonlinear dynamics, provides an alternative by tracing returns in state-space to reveal periodic, intermittent, and chaotic behaviors. However, existing RA approaches underrepresent heterogeneity across modalities and scales, insufficiently capture within- and cross-dynamic variability, and impose heavy computational burdens due to pairwise state comparisons.
This dissertation advances a recurrence-based framework that addresses these challenges in three parts. (1) Advanced Dynamic System Characterization: heterogeneous recurrence analyses for quantifying nonlinear dynamics in spatial and spatiotemporal systems. (2) Rapid Recurrence Quantification: a deep-learning-aided surrogate that amortizes pairwise comparisons to enable near-real-time RA. (3) Quantification-Guided High-Fidelity Synthesis: a conditional generative model constrained by recurrence structure to produce faithful, controllable signals for augmentation, evaluation, and robustness testing.
Together, these methods capture nonlinear and nonstationary dynamics, account for heterogeneous modalities and scales, and deliver calibrated, interpretable metrics. They support diagnosis and prognosis, enable real-time monitoring, and help reveal disease mechanisms. Recurrence-constrained synthesis enhances robustness and efficiency through data augmentation. Overall, this framework offers a principled, interpretable foundation for modeling complex biomedical systems and bridging nonlinear dynamics with clinical translation.