Many aspects of physics that spans from the origin of the elements to nuclear technologies rely on a robust description of nuclear reactions. One therefore needs predictive modelling of nuclear quantum many-body dynamics in which the uncertainties are well-understood. The authors use the time-dependent Hartree-Fock approach, and apply uncertainty quantification to the nuclear dynamics, considering a collection of low-energy heavy-ion fusion reactions. They find that the uncertainty in the theoretical results mainly arises from structure properties, such as the skin of neutron-rich nuclei, which are particularly ill-constrained. This work highlights the importance of including reaction data in the construction and constraint of new theoretical models that can treat dynamics and structure on the same footing.