The qualitative and quantitative analysis of dynamical systems is crucial for understanding numerous real-world systems and phenomena, from weather prognosis and biological networks, to medical and engineering applications. However, the ubiquitous presence of uncertainty often renders the analysis of dynamical systems a difficult task. Therefore, methods for uncertainty quantification (UQ) in dynamical systems are evolving rapidly, with a particular emphasis on data-driven and machine learning approaches in recent years. At the same time, numerous challenges remain, particularly in the nonlinear setting. Exemplary challenges include, quantifying uncertainties on bifurcations and limit cycles; computationally managing high-dimensional uncertain states and inputs; deriving suitable sensitivity analysis metrics. This minisymposium aims to cover methodological work in the vast field of UQ in dynamical system analysis with a focus on data driven methods, related (but not limited) to: • UQ for nonlinear dynamics (e.g., bifurcations, limit cycles) • Data-driven forward and inverse UQ for dynamical systems • Combinations of Fourier analysis with UQ methods • Surrogate and reduced order modeling (incl. machine learning) for dynamical systems • Sensitivity analysis for dynamical systems REFERENCES [1] Partovizadeh, A., Schöps, S., and Loukrezis, D. "Fourier-enhanced reduced-order surrogate modeling for uncertainty quantification in electric machine design." Engineering with Computers (2025): 1-21. [2] de Jong, L., Clasen, P., Müller, M., Römer, U. "Uncertainty analysis of limit cycle oscillations in nonlinear dynamical systems with the Fourier generalized Polynomial Chaos expansion." Journal of Sound and Vibration 607 (2025): 119017. [3] Lux, K., Ashwin, P., Wood, R., and Kuehn, C. "Assessing the impact of parametric uncertainty on tipping points of the Atlantic meridional overturning circulation", Environ. Res. Lett. (2022) 17 075002.