Abstract: Nuclear fission fragment yields are the key infrastructure data in the field of nuclear engineering and nuclear applications. However, it is very difficult to obtain accurate and complete energydependent fission yields by experiments and theories. To supply the application needs, the twodimensional cumulative fission yields of neutroninduced fission of 235U are evaluated for energy dependencies and uncertainty qualifications by crossexperiment data fusion. The data fusion is aim to include more data correlations to produce more consistent and useful information. In this work, the Bayesian machine learning with a doublelayer neural network was adopted, which was particularly suitable for dealing with imperfect data. The conventional evaluation methods were not ideal for uncertainty quantifications. Furthermore, the experimental uncertainties of fission yields were taken into account in this work, which was essential for data fusion. This is reasonable that the yields with larger uncertainties would have smaller weights in the data fusion. Previously, the Bayesian evaluation of one dimensional mass yields in terms of Y(A) or Y(Z) was studied. As a further step, this work evaluated the two dimensional yields in terms of Y(N, Z) or Y(A, Z), which are of practical usefulness for developing novel nuclear reactors. The doublelayer networks with 18×18, 20×20 and 22×22 neutrons were tested and the network structure of 20×20 was chosen. The yieldenergy relations of some key fragments such as 99Mo, 97Zr, 127Sb, 131I, 140Ba, 143Ce and 147Nd were obtained. The full twodimensional cumulative fission yields at neutron incident energies of 2, 6, 8, 10, and 14 MeV were obtained. The resulted twodimensional fission yields can reasonably describe the energy dependencies of evolution of fission modes. The resulted uncertainties are dependent on specific fragments and incident energies. The evaluated uncertainties includes a background noise about 1.35, which is still very large. In the future, it is essential to develop physics-informed machine learning to obtain more reliable evaluations. It is promising that Bayesian machine learning can facilitate the maximum utilization of imperfect raw experience data.