Ⅱ-3. Nuclear Data
RIKEN
Accel. Prog. Rep. 56 (2023)

RIKEN Accel. Prog. Rep. 56 (2023)

Generating scattering data using Gaussian process regression†
S. Watanabe,∗1 F. Minato,∗2,∗3 M. Kimura,∗4 N. Iwamoto,∗2 and S. Yoshida∗5
Recently, several studies1,2) have employed machinelearning algorithms to improve the accuracy of nuclear data evaluation and reduce the production cost.
Herein, we introduce a framework which combines
Gaussian process regression (GPR) with a nuclear reaction model code, i.e., ‘CCONE’.3,4) The frameworkdetermines model parameters required by CCONE toreproduce and predict nuclear reaction data.
Figures 1 and 2 demonstrate how the proposed
framework works. In this example, we used the experimental data of neutron elastic scattering on 54 Fe
at incident energies of E = 6, 10, 15, and 17 MeV as
input.5) In the ﬁrst step, by combining CCONE andBayesian optimization with the Gaussian process (BOGP), we optimize the depth of the real part of the opti0(E), to reproduce
cal potential, which is denoted by vR0these data. The obtained optimal values of vR(E) ateach energy is plotted by open circles in Fig. 1.

Expt.

103

Prediction
Prediction updated byadditional input

d/d [mb/sr]

102
101

7MeV

100

10-1

12MeV

10-2
10-3
10-4
026MeV
54Fe(n,n)30×10-2×10-4

60
90
120
150
scattering angle [degrees]

180Fig. 2. Predicted and observed angular distributions of54Fe(n, n) at the incident energies of E = 7, 12, and26 MeV.

52.5
50.0

0Then, using CCONE and the predicted value of vR(E),our framework predicts unknown cross sections. Figure 2 shows the comparison of the prediction resultsfor E = 7, 12, and 26 MeV with the actual experimental data. The framework works quite eﬀectively
to predict data at E = 7 and 12 MeV, which correspond to the interpolation of the known data. Even in
the case of the extrapolation of the known data, i.e.,
E = 26 MeV, it can perform a plausible prediction.
This framework can investigate how new experimental data improve prediction. Herein, we add a newdata set at E = 20 MeV, and calculate the optimal
0vR(E) at this energy, as denoted by the ﬁlled circle inFig. 1. With this additional input, GPR can enhance0(E), as denoted by the dashed line
the prediction of vR0(E), thewith a shadowed area. With this enhanced vRcross section at E = 26 MeV is calculated as plotted
as a dotted line in Fig. 2, where we see considerable
improvement in backward angles.
The development of this framework is in progress,
and we expect that it will generate accurate nuclear
reaction databases enhanced with a large amount ofexperimental data produced at RIBF.

(MeV)

47.5
45.0
Input
42.5

Additional input

40.0

Prediction

37.5

Prediction updated byadditional input

35.00102030

Energy (MeV)
0Fig. 1. Open circles show the optimal values of vR(E) atE = 6, 10, 15 and 17 MeV obtained by BO-GP. With0
these input, GPR predicts vR(E) as shown by solidline with shadowed area. With additional input at
E = 20 MeV denoted by ﬁlled circle, GPR updates
the prediction as shown by dotted line with shadowedarea.

In the second step, using optimal values as inputs,0(E) as a function of E is predicted by GPR, as devR
noted by the solid line with a shadowed area in Fig. 1.
†∗1
∗2
∗3
∗4
∗5References
1) A. E. Lovell et al., J. Phys. G 47, 114001 (2020).
2) H. Iwamoto et al., J. Nucl. Sci. Technol. 57, 932 (2020).
3) S. Watanabe et al., J. Nucl. Sci. Technol. 59, 1399(2022).
4) S. Watanabe et al., Eur. Phys. J. Conf. Ser. (in press).
5) All experimental data are collected from EXFORdatabase.

Condensed from the articles in J. Nucl. Sci. Technol. 59,
1399 (2022)
Department of Physics, Hokkaido University
Nuclear Data Center, Japan Atomic Energy Agency
Department of Physics, Kyushu University
RIKEN Nishina Center
Institute for Promotion of Higher Academic Education, Utsunomiya University- 45 -