Characterizing the multidimensional structure of hadrons in terms of quarks and gluons is one of the major objectives of hadronic physics today. This is not only the central theme of many experimental facilities worldwide, but also one of the main reasons for the construction of future colliders in the USA and China. It is also one of the key areas of research for intensive numerical simulations of the strong interaction. However, in both cases, the connection between measured and simulated data on the one hand, and the multidimensional structure of hadrons on the other, is not direct. The data are linked to the hadron structure via mathematically ill-posed multidimensional inverse problems. It has been shown that these inverse problems lead to a significant increase in uncertainties, to the point of becoming the dominant source of uncertainty in some cases. The aim of this thesis is to use machine learning tools to assess, reduce and correctly propagate uncertainties from experimental or simulation data to the multidimensional structure of hadrons. The strategy for achieving this is to develop an original neural network architecture capable of taking into account the full range of theoretical properties arising from quantum chromodynamics, and then to adapt it to inverse problems linking experimental and simulation data to the 3D structure of hadrons.