Abstract: Fragment productions in spallation reactions and projectile fragmentation reactions are important topics in nuclear reaction both theoretically and experimentally, which find important applications in fundamental nuclear physics, radioactive ion beam facilities, nuclear waste disposal, medical isotopes production, etc. Besides the many models to predict the fragment productions, such as the transport model, empirical parametrizations or formula, machine learning models have been constructed to predict fragment cross-sections in proton induced spallation reactions and projectile fragmentation reactions. In this paper, the recently proposed models using Bayesian neural network (BNN) models were introduced for precise prediction of fragments, especially for extreme rare isotopes with large isospins in nuclear spallation and projectile fragmentation reactions. Two types of models were introduced, i.e., the BNN models which were constructed based on massive learning to experimental data, and the physical model guided BNN+ models which were constructed based on massive learning to the differences between measured data and physical model predictions. The simplified EPAX (sEPAX) formula and the FRACS formulas were adopted as the physical model to guide the BNN+ model for spallation reaction (BNN+sEPAX) and projectile fragmentation reaction (BNN+FRACS), respectively. The BNN and BNN+ models have the structure of one input layer with key parameters related to the reaction, one hidden layer with optimized numbers of neural nodes and one output layer. For the numbers of learning data set, it was 15 370 measured fragments in the proton induced nuclear spallation reactions and 6 393 measured fragments in the projectile fragmentation reactions. It is found that the machine learning models provide new type of predictive models for nuclear reactions besides the physical models. The BNN model needs sufficient information to achieve good prediction ability, while the BNN+ model can inherit the advantage of the physical model and make up for the defects of the physical model, which makes it achieve good predictive ability when known data are insufficient. The predicted results show that the BNN and BNN+ models have high predictions to fragments cross-sections in spallation reactions smaller than 136Xe within an incident energy range from tens of MeV/u to a few GeV/u, and projectile fragmentation reactions for projectile from ⁴⁰Ar to ²⁰⁸Pb within the range of incident energy from tens of MeV/u to 1 GeV/u. Particularly, the BNN model for projectile fragmentation reaction predicts a 0.46 fb compared to the experimental estimation 0.5 fb for ³⁹Na isotope in the 345 MeV/u ⁴⁸Ca+⁹Be reaction, indicating it is capable for high quality prediction to near drip-line isotopes.