Digital twins represent a transformative approach for integrating computational models, sensor data, machine learning, and real-time analysis to support engineering decisions for dynamical systems. However, a system -- whether linear or non-linear -- is subject to uncertainties arising from system parameters, environmental conditions, experimental setups, and complex non-linear phenomena (e.g., large deformations, material non-linearities, contact, and multi-physics couplings). It opens many questions on how those uncertainties must be integrated in the context of digital twins. This mini symposium aims to bring together advances in digital twin methodologies, numerical optimisation, inverse problems, and uncertainty quantification for dynamical systems, with a particular focus on non-linear behaviours. Contributions may address theoretical developments, computational methods, or experimental validations, including but not limited to: - Physics-based models combined with machine learning - Real-time model updating and parameter identification - Sensor placement and optimal experimental design - Stochastic modelling in structural dynamics - Multi-scale and multi-fidelity uncertainty propagation - Reliability analysis and robust design under uncertainty - Parametric and structural optimisation in non-linear dynamics - Model calibration and inverse methods under uncertainty - Surrogate modelling for high-dimensional problems We welcome contributions that bridge gaps between digital twin technologies, computational optimisation, and uncertainty modelling for improved prediction and decision-making. Example of applications: structural dynamics, wind turbines, aircraft engines, rotordynamics, automotive/aerospace industry. REFERENCES [1] Wagg, D.J. et al., The philosophical foundations of digital twinning, Data Centric Engineering, 6, e12, 2025. doi:10.1017/dce.2025.4 [2] Ritto, T.G., Rochinha, F.A. Digital twin, physics-based model, and machine learning applied to damage detection in structures. Mechanical Systems and Signal Processing, 155, 107614, 2021 [3] Wagg, D.J., Worden, K., Barthorpe, R.J., Gardner, P. ASCE ASME Journal of Risk and Uncertainty in Engineering Systems Part B Mechanical Engineering, 6(3), 030901, 2020