Fig. 1. (color online) A schematic diagram of a neural network with a single hidden layer, three hidden neurons (H = 3) and two input variables (I = 2).

Fig. 2. (color online) BNN predictions for selected residue fragments with Z=60 to 65 in the 800 MeV/u ¹⁹⁷Au + p spallation reaction. Three different numbers of hidden nodes are tested, H = 34 (circles), 35 (triangles), 36 (triangles). The measured results are shown as black squares.

Fig. 3. (color online) Similar as Fig. 2, but for Z=66 to 73.

Fig. 4. (color online) Similar as Fig. 2, but for Z=75 to 80.

Fig. 5. (color online) BNN predictions for the 500 MeV/u ⁵⁶Fe + p reaction with H = 34, 35 and 36. The results for the selected residues Z=10 to 15 are compared to the measured residue fragments [41]. The symbols are the same as in Fig. 2.

Fig. 6. (color online) Similar as Fig. 5, but for Z = 16 to 21.

Fig. 7. (color online) Similar as Fig. 5, but for Z = 22 to 27.

Fig. 8. (color online) BNN predictions (with TS1 and H = 35) (circles) for selected fragments with Z = 3 to 22 in the 1000 MeV/u ¹³⁶Xe + p spallation reaction, compared to the experimental data (squares, from [44]) and the SPACS results (triangles, from [25]. The experimental and BNN error bars are smaller than the symbols.

Fig. 9. (color online) Similar as Fig. 8, but for Z = 36 to 54.

Fig. 10. (color online) Predictions of isotopic distributions by BNN (squares) and SPACS (circles) for the 1000 MeV/u ²³⁸U + p spallation reaction for Z = 54 to 70 [48]. Experimental distributions are not available for . The BNN error bars are smaller than the symbol size.

Fig. 11. (color online) Similar as Fig. 8, but for 1000 MeV/u ²³⁸U + p and for Z = 74 to 92.

Fig. 12. (color online) Similar as Fig. 8, but for the 763 MeV/u ⁴⁰Ca + p spallation reaction [9]. Experimental data are not available for fragments with .

Fig. 13. (color online) Similar as Fig. 8, but for the 361 MeV/u ³⁶Ar + p reaction with Z = 3 to 17 [8].

Fig. 14. (color online) Correlation between the isotopic cross-sections and the average binding energy B'. The squares, triangles, and circles denote the measured data, BNN predictions, and SPACS predictions, respectively. The lines denote the linear fit of the correlation between and B'.

Table 1. The number of measured fragments in 19 measured + p spallation reactions.

Table 2. The number of fragments in spallation reactions predicted using the SPACS parametrization.