Faculty Profiles - ENDO Tomohiro

MISC - ENDO Tomohiro

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Subcriticality: from basics to applications; (3) The ABC's of Subcriticality Measurements Reviewed

T. Endo, S. Atsushi

ATOMOΣ: Journal of the Atomic Energy Society of Japan Vol. 61 ( 12 ) page： 857 - 862 2019.12

Subcriticality Estimation without Point Kinetics Parameters Based on Autocovariance of Reactor Noise Using Delayed Neutron Components Reviewed International journal

Tomohiro Endo, Ryoga Hirota, Akio Yamamoto, Kenichi Watanabe, Genichiro Wakabayashi, Kengo Oda, Junichi H. Kaneko

Proc. M&C2025 page： 2028 - 2037 2025.4

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The reactor noise analysis method is useful as a passive measurement technique for a steady-state target subcritical system. When detailed information is not available in the target system, there are large uncertainties in the point kinetics parameters, such as the effective delayed neutron fraction and the neutron generation time. In this case, if the subcriticality measurement techniques using the point kinetics parameters (e.g., indirect conversion method from the measured prompt neutron decay constant to the subcriticality) are applied, the measured subcriticality will inevitably have a large uncertainty. To address this problem, the present study aims to investigate the absolute measurement of subcriticality without the point kinetics parameters by focusing on the delayed neutron components in the zero-power reactor noise. For this purpose, an analytical formula for the lag-1 autocovariance of the reactor noise is derived via the pair detection probability based on the fundamental mode approximation using the forward and adjoint eff-eigenfunctions. The proposed method utilizes the nonlinear least squares fitting method for the measured autocovariance to determine the following three fitting parameters: the subcriticality in the dollar units; the ratio of eff ⁄Λ; and a proportional factor related to the Diven factor, the detection efficiency, and so on. Preliminary experimental analysis using the proposed method is demonstrated through the reactor noise measurement at UTR-KINKI (University Teaching and Research Reactor of Kindai University) under a shutdown state.

DOI： 10.13182/MC25-46579

A Simple Resonance Calculation Method for Flexible Geometry Using Equivalence Relation and Point-wise Cross Sections (ERPX) Reviewed International journal

A. Yamamoto, T. Endo

Proc. M&C2025 page： 544 - 553 2025.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

ERPX, a simple resonance calculation method that can incorporate space-dependent shelf-shielding is proposed. ERPX calculates space-dependent escape cross sections using the ultra-fine group (UFG) calculation in heterogeneous and homogeneous geometries with the narrow resonance (NR) approximation. Then the space-dependent escape cross sections and the explicit slowing down calculation in homogeneous geometry are then used to estimate the space-dependent effective cross section to mitigate the error caused by the NR approximation. The reduce-order model is developed and used in the UFG calculation in heterogeneous geometry to achieve short computation time. Verification calculation is carried out in 3x3 pin-cell geometry containing a large water region. The fuel pellet in focus is azimuthally and annularly divided. The calculation results indicated that the ERPX method can provide reasonable accuracy with practical computation time that can be used for the design calculations.

DOI： 10.13182/MC25-47330

Correction Method of Few-Group Cross Sections for Core Analysis of High-Temperature Gas-Cooled Reactors Reviewed International journal

Amane Haga, Tomohiro Endo, Akio Yamamoto, Go Chiba

Proc. M&C2025 page： 472 - 481 2025.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

To reduce the discretization error associated with the energy group collapsing, a correction method for few-group cross sections used in a core calculation of High-Temperature Gas-cooled Reactors (HTGRs) was investigated. It was confirmed that the correction of the removal scattering cross section as a function of the spectral index, which is the ratio of the fast and thermal group neutron fluxes, improves the calculation accuracy of the k-effective and the fuel compact-wise relative power distribution in the two-dimensional heterogeneous full core model of the High Temperature engineering Test Reactor (HTTR). The method of correcting the total scattering cross section, including the self-group scattering cross section, did not improve the accuracy. The method using the removal scattering cross section may be a candidate for a core design method of HTGRs.

DOI： 10.13182/MC25-47343

Reactivity Estimation in Dollar Units Based on Bayesian Monte Carlo Using Autocovariance of Reactor Noise Measurement Reviewed International journal

Ryoga Hirota, Tomohiro Endo, Akio Yamamoto, Kenichi Watanabe, Genichiro Wakabayash, Kengo Oda, Junichi H. Kaneko

Proc. M&C2025 page： 2038 - 2047 2025.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The reactor noise analysis method can measure the prompt neutron decay constant using only time series data of neutron counts measured in a steady-state subcritical system. However, the point kinetics parameters such as the neutron generation time Λ and the effective delayed neutron fraction eff are needed to estimate the reactivity in dollar units by conversion from the measured value. To address the above-mentioned problem, this study aims to develop the estimation technique of the reactivity in dollar units eff , by utilizing the delayed neutron component of reactor noise. To extract the delayed neutron components, this study focused on the lag-1 autocovariance for reactor noise. In addition, the Bayesian Monte Carlo (BMC) with merging particle filter (MPF) was applied as the data assimilation technique to estimate eff from the measured variation of the autocovariance with respect to the counting gate width. As a result, the proposed method was validated through the reactor noise measurement at UTR-KINKI (University Teaching and Research Reactor of Kindai University).

2D Cylindrical SP3 Transport Calculation Using Finite Volume Method with Cross-Diffusion Treatment for Unstructured Meshes Reviewed International journal

Tomohiro Endo, Akio Yamamoto

Transactions of the American Nuclear Society Vol. 131 ( 1 ) page： 1053 - 1056 2024.11

Authorship：Lead author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

This study presents a prototype of an in-house code to numerically solve the simplified P3 (SP3) neutron transport equation for a 2D cylindrical (r-z) geometry using unstructured meshes for spatial discretization. In the developed SP3 calculation code, the cross-diffusion effect due to the unstructured meshes can be treated by a variant of the Green-Gauss reconstruction technique.

DOI： 10.13182/T131-46095

Study on Fusion Safety Concept Based on Nuclear Safety (2) Defense in Depth in Fusion Safety Reviewed International journal

Yoshiki Yamashita, Tomohiro Endo, Akio Yamamoto, Takashi Ino

Transactions of the American Nuclear Society Vol. 131 ( 1 ) page： 299 - 302 2024.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The concept of fusion safety is studied with reference to nuclear safety. Risk profiles of fusion reactor facilities are reviewed and organized and implementation of defense in
depth (DID) in fusion safety is developed based on the risk profiles.

DOI： 10.13182/T131-46140

Study on Fusion Safety Concept Based on Nuclear Safety (1) Fusion Safety Objective and Principles Reviewed International journal

Yoshiki Yamashita, Tomohiro Endo, Akio Yamamoto, Takashi Ino

Transactions of the American Nuclear Society Vol. 131 ( 1 ) page： 292 - 295 2024.11

A Simple Resonance Calculation Approach for Space-Dependent Self-Shielding Reviewed International journal

Akio Yamamoto, Tomohiro Endo

Transactions of the American Nuclear Society Vol. 131 ( 1 ) page： 1038 - 1041 2024.11

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

A simple resonance calculation method for space-dependent self-shielding treatment is proposed. The present method is based on three calculations: 1) ultra-fine group (UFG) calculation with the narrow resonance (NR) approximation in a homogeneous medium, 2) UFG calculation with explicit slowing down (SLD) calculation in a homogeneous medium, and 3) UFG calculation with the NR approximation in a heterogeneous system. The space-dependent effective cross sections are generated by the synthesis of these three calculations.

DOI： 10.13182/T131-45885

Implementation of track length estimator for flux distribution tallies using proper orthogonal decomposition in one-dimensional geometry Reviewed International journal

Ryoichi Kondo, Tomohiro Endo, Akio Yamamoto

EPJ Web of Conferences Vol. 302 page： 04002 2024.10

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

In a recent study, we have developed an efficient flux distribution tallying method in the Monte Carlo calculation toward the high-fidelity, large scale multi-physics simulation. In this method, the proper orthogonal decomposition is applied to the flux distribution tallies. While the tallying method was implemented with the collision estimator in the previous study, the track length estimator is implemented in the present study to obtain the tally with lower statistical error. The implementation of the flux distribution tally with the track length estimator is compared with that of the collision estimator and the normal track length estimator in a one-dimensional problem. The numerical results reveal that the distribution tally using the proper orthogonal decomposition with the track length estimator can obtain a more precise solution compared with that with the collision estimator. Therefore, in terms of the statistical error, the relationship between the distribution tally with track length and collision estimators is similar to that between the conventional track length and collision estimators.

DOI： 10.1051/epjconf/202430204002

Data Assimilation Using Deterministic Sampling Method to Selectively Reduce Uncertainty due to Thermal Neutron Scattering Law for Light Water Reviewed International journal

Yoshinari Harada, Hibiki Yamaguchi, Tomohiro Endo, Akio Yamamoto, Kenichi Tada

Transactions of the American Nuclear Society Vol. 130 ( 1 ) page： 758 - 762 2024.6

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

This study presents data assimilation using the prompt neutron decay constant α of the water tank system to selectively reduce the uncertainties due to the thermal neutron scattering law of light water. For efficient uncertainty quantification and data assimilation, the deterministic sampling method was applied in this study. Furthermore, in the data assimilation, the α measurement of the water tank system was utilized to improve the prediction accuracy of keff calculations in a critical experiment involving light water.

DOI： 10.13182/T130-44516

Loading Pattern Optimization with Deep Learning and Monte-Carlo Tree Search Reviewed International journal

Rikuto Kasama, Akio Yamamoto, Tomohiro Endo

Transactions of the American Nuclear Society Vol. 130 ( 1 ) page： 1044 - 1047 2024.6

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

We have developed a new optimization method based on Deep Learning (DL) and Monte-Carlo Tree Search (MCTS) for fuel loading pattern optimization. The fuel loading pattern optimization is redefined as a sequence of fuel loadings to an empty core, and the sequence is optimized by the DL and MCTS approach, which is used in AI for board games such as Go, Chess, and Shogi (Japanese Chess).

DOI： 10.13182/T130-44319

Statistical Error Estimation of Autocorrelation Method Using Circular Block Bootstrap Method Reviewed International journal

Ryoga Hirota, Tomohiro Endo, Akio Yamamoto, Kenichi Watanabe, Junichi H. Kaneko

Proc. PHYSOR2024 page： 78 - 86 2024.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

The autocorrelation method is a subcriticality measurement technique based on the reactor noise analysis method. In this method, the prompt neutron decay constant can be obtained from the exponential decay of the autocorrelation of successively detected neutron counts in a target subcritical system. To simply estimate the statistical error of the prompt neutron decay constant, several measurements of the reactor noise are required, although the total measurement time is inevitably long for typical systems where the reactor noise analysis method is applied. Therefore, the purpose of this study is to investigate the applicability of the circular block bootstrap method in order to estimate the statistical error of the prompt neutron decay constant obtained by the autocorrelation method using a single reactor noise measurement. The bootstrap-based statistical error estimation method is validated using the time series data of reactor noise measurements at UTR-KINKI in a shutdown state with the inherent neutron source in the uranium-aluminum fuel. Consequently, this study demonstrates that the circular block bootstrap method can be also utilized for the autocorrelation method, to estimate the confidence interval of the prompt neutron decay constant as the statistical error. Namely, a single reactor noise measurement can be effectively reused for error estimation instead of multiple measurements.

Other Link： https://www.ans.org/meetings/physor2024/sessions/attachment/paper-9424/

Investigation of Subcriticality Monitoring Method Using Improved Simplest Reactivity Estimator with Bilateral Filter Reviewed International journal

Taiyo Moribe, Tomohiro Endo, Akio Yamamoto, Junichi H. Kaneko

Proc. PHYSOR2024 page： 97 - 106 2024.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

In the retrieval of fuel debris from the Fukushima Daiichi nuclear power plant, there are the following issues: lack of information needed to inversely estimate the subcriticality; and the limitation of neutron detector size. In order to address these issues, we propose a reactivity estimation method that combines the improved simplest reactivity estimator (SRE) and the least squares inverse kinetics method. This study aims to estimate the reactivity in dollar units in a data driven manner only from the measured neutron count rate without point kinetics parameters. Furthermore, the usefulness of the bilateral filter in combination with the median for the count rate is also investigated to mitigate statistical errors in the reactivity estimation results due to the statistical fluctuation and outlier in the measured count rate data. To verify our proposed method, point kinetics calculation is performed to simulate the time series data of the neutron count rate during a stepwise transient from a deep subcritical state to the shallower state. Here, the magnitude of the count rate at the initial state is parametrically varied to investigate the effect of the statistical count rate fluctuation on the estimated reactivity. As a result, it is observed that the estimated reactivity tends to be overestimated (i.e., closer to critical) as lower count rate data are used in our proposed method. Thus, our proposed method is considered practical from the perspective of criticality control. Moreover, it is clarified that the combinational use of the bilateral filter and the median can effectively reduce the error of the estimated reactivity due to the statistical fluctuation of the count rate. Consequently, this feasibility study demonstrates our proposed method for monitoring the reactivity change even under the low neutron count rate condition.

DOI： 10.13182/PHYSOR24-43487

Loading Pattern Optimization for LWRs Using Monte Carlo Tree Search Reviewed International journal

Rikuto Kasama, Akio Yamamoto, Tomohiro Endo

Proc. PHYSOR2024 page： 2490 - 2499 2024.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

Inspired by recent breakthroughs in AI for games, we transform the fuel loading pattern
optimization problem into a game tree search problem and adopt Monte Carlo Tree Search (MCTS) to solve it. The performance of MCTS is compared with the conventional optimization methods, such as the random search and simulated annealing (SA), for the loading pattern optimization of a typical pressurized water reactor. The results demonstrate the superior efficiency of MCTS over the conventional methods. MCTS consistently produces high-quality patterns and effectively avoids the common problem of falling into local minima. By using techniques rooted in AI, we are
opening up a new way of solving complex problems in nuclear engineering, offering the prospect of more reliable and efficient core designs. This innovative approach will not only benefit the nuclear field, but also serve as a bridge between optimization and artificial intelligence.

DOI： 10.13182/PHYSOR24-43466

Preliminary Study on Two-Dimensional SP3 Calculation Based on POD-Local/Global Iterations Reviewed International journal

Masato Ito, Akio Yamamoto, Tomohiro Endo, Yasuhiro Kodama, Taichi Takeishi, Hiroaki Nagano

Proc. PHYSOR2024 page： 1612 - 1621 2024.4

Authorship：Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

As a preliminary study for an efficient heterogeneous neutron transport calculation, this study newly proposes a reduced order core calculation method by applying proper orthogonal decomposition (POD) to the SP3 calculation with the global/local iterations. The fine mesh SP3 calculation (local calculation) for each single assembly can be efficiently solved using POD, thanks to the matrix form-based SP3 equation and the relatively small scale of the simultaneous equations. By reconstructing the fine mesh distribution of neutron flux and partial neutron currents from the POD bases and the expansion coefficients estimated by the local calculation, the p-CMFD calculation is applied to the coarse mesh calculation (global calculation). These local and global calculations are iterated until convergence. Through the two-dimensional small and large UO2-MOX core calculations, our proposed method is verified by comparing with the reference result by the conventional fine mesh SP3 calculation.

DOI： 10.13182/PHYSOR24-43629

Real-Time 3D Fine Spatial Mesh Kinetics Simulator Using POD for Coupled Core Reviewed International journal

Kaito Ito, Kosuke Tsujita, Tomohiro Endo, Akio Yamamoto

Proc. PHYSOR2024 page： 6986 2024.4

Authorship：Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

Toward the development of the digital triplets to effectively educate the reactor physics experiment, the present study develops a real-time 3D fine spatial mesh kinetics simulator based on the proper orthogonal decomposition (POD). Our developed simulator, called Ikaros3D, was specifically designed for a coupled core to promote students’ better understanding of the complicated behavior of the spatial variation of the dynamic reactivity depending on the neutron detector position. Through a verification test, we confirmed that the reduced order model (ROM) using POD was able to accurately and quickly simulate the variation in the total core power due to the operation of two different control rods, thanks to the pre-tabulated compressed coefficient matrices for the POD based kinetics calculation.

DOI： 10.13182/PHYSOR24-43834

Reconstruction of In-Core Power Distribution Based on POD Using Ex-Core Detector Signals Reviewed International journal

Yuki Urase, Tomohiro Endo, Akio Yamamoto

Proc. PHYSOR2024 page： 1642 - 1651 2024.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

A reconstruction method of in-core power distribution using the proper orthogonal decomposition (POD) and the signal from ex-core detectors is developed. In the present method, the neutron flux distribution is expanded in a small number of POD bases and expansion coefficients. Neutron transport calculations were performed with several calculation conditions to perturb the neutron flux distributions in the reactor core and the POD bases were obtained using the multiple neutron flux distributions as the snapshot data. The neutron counts of ex-core detectors were evaluated from the in-core neutron flux distributions and the detector response coefficients. Considering the neutron counts of ex-core detectors as measured signals, the expansion coefficients of POD that represent the in-core neutron flux distributions were determined. Assuming a simple two-dimensional core with nine regions, the reconstruction accuracy of in-core neutron flux distribution was verified for several conditions. The results indicate that the in-core neutron flux distributions can be reconstructed by the ex-core detector signals when the distance between the detectors and the core is appropriately chosen.

DOI： 10.13182/PHYSOR24-43478

Simplified Treatment of Coating Layers in TRISO Fuel in Statistical Geometry Method in Monte Carlo Calculation Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Satoshi Takeda, Kazuya Yamaji, Hiroki Koike, Koji Asano

Proc. PHYSOR2024 page： 1036 - 1047 2024.4

Language：English Publishing type：Research paper, summary (international conference) Publisher：American Nuclear Society

An improved sampling method for flight distance is proposed for Monte Carlo analysis of TRISO fuel particles using the statistical geometry method. The statistically uniform distribution of fuel particles, which is usually assumed as a default sampling method of flight distance of a neutron in graphite matrix, shows considerable bias on neutronics property when coating layers of a TRISO fuel particle are homogenized with graphite matrix. The proposed new sampling method almost resolves the difference between the homogenized coating model and the reference model that explicitly considers coating layers. By adopting the present method, the homogenized coating model can be used without significant loss of accuracy in the statistical geometry method. Computation time for a typical HTTR fuel compact cell with a continuous energy Monte Carlo code is reduced to 1/7 when the homogenized coating model is used.

DOI： 10.13182/PHYSOR24-43318

α-eigenvalue Calculation using the Sn Method with GPU Diffusion Acceleration Reviewed International journal

H. Yamaguchi, T. Endo, A. Yamamoto

Proceedings of the Reactor Physics Asia 2023 (RPHA2023) Conference 2023.10

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