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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

MPACT Verification With Magnox Reactor Neutronics Progression Problems

MPACT is a state-of-the-art core simulator designed to perform high-fidelity analysis using whole-core, three-dimensional, pin-resolved neutron transport calculations on modern parallel computing hardware. MPACT was originally developed to model light water reactors, and its capabilities are being extended to simulate gas-cooled, graphite-moderated cores such as Magnox reactors. To verify MPACT’s performance in this new application, the code is being formally benchmarked using representative problems. Progression problems are a series of example models that increase in complexity designed to test a code’s performance. The progression problems include both beginning-of-cycle and depletion calculations. Reference solutions for each progression problem have been generated using Serpent 2, a continuous-energy Monte Carlo reactor physics burnup calculation code.Using the neutron multiplication eigenvalue ke as a metric, MPACT’s performance is assessed on each of the progression problems. Initial results showed that MPACT’s multi-group cross section libraries, originally developed for pressurized water reactor problems, were not sufficient to accurately solve Magnox problems. MPACT’s improved performance on the progression problems is demonstrated using this new optimized cross section library.

Luciano, Nicholas↗
DOE OSTI2022

Modeling of the TRIGA IPR-R1 research reactor with the Serpent2/RINNOVO Nodal core analysis package

The Serpent2/RINNOVO nodal core analysis code system, a dedicated tool for modeling research reactors, has the capability to accurately predict important core physics parameters involved in the safety of reactor operation, such as various reactivity coefficients, control rod and bank worths including the shutdown margin, power distributions as well as local neutron flux predictions at various core locations of high importance, e.g., at irradiation rigs. In this work, a hexagonal model of the unrodded initial core of the Brazilian IPR-R1 Mark I type TRIGA nuclear reactor has been created using the Serpent2/RINNOVO code system. The choice of employing a hexagonal core geometry representation has mainly been made to facilitate subsequent fuel shuffling operations and core follow calculations of this reactor. Numerical results in terms of the core eigenvalue and the assembly power distribution have then been compared against corresponding full core Serpent2 results to prove feasibility of using the Serpent2/RINNOVO code system for modeling small and highly heterogeneous TRIGA reactors. Overall, RINNOVO predicts the power distribution very accurately but the eigenvalue error still remains quite large. In light of being the very first evaluation of a TRIGA reactor with the RINNOVO nodal core simulator, these results are also considered to be very preliminary. Improved accuracy is expected by incorporating a proper methodology in the current code system for computing discontinuity factors for multi-assembly configurations. Furthermore, improved results are expected by increasing the number of energy groups used by RINNOVO in these core calculations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Towards a NEAMS-based high-fidelity model of the MARVEL reactor

This report outlines the progress of Idaho National Laboratory in developing a high-fidelity and high-resolution model of the Microreactor Applications Research Validation and Evaluation reactor. The model was developed under the Nuclear Energy Advanced Modeling and Simulation microreactor application driver at Idaho National Laboratory. The overarching objective of this activity is the development of a high-fidelity multiphysics MARVEL model using NEAMS tools, and to verify and validate NEAMS tools against MARVEL reference simulation and experimental data, respectively. This is a unique opportunity to conduct multiphysics analysis on a soon-to-be-deployed microreactor. This multiphysics model developed under the NEAMS-funded INL microreactor application driver leverages three single-physics models coupled via the MOOSE’s MultiApp and Transfer systems. The latter systems enable in-memory data transfer between MOOSE-based and MOOSE-wrapped applications. The first single-physics model, that functions as main application, leverages Griffin to model the neutron transport in the core through the discontinuous finite element (DFEM) discrete ordinates solver (SN). Several optimization flags that were developed by the Griffin developer team were beta-tested to enhance the solver’s performance. These include the combined use of using_average_xs and update_averaged_xs_on that enable to avoid expensive on-the-fly cross sections evaluations at each linear iterations in favor of evaluations of the macroscopic cross sections at each Picard iteration. The second single-physics model uses BISON to handle solid heat transfer and asymptotic hydrogen redistribution analysis in the fuel. While the model returns consistent results for the temperature and hydrogen distribution in the fuel, a mismatch was noticed in the calculated temperature in the reflector due to the value of the gap conductance used in our model. Ongoing investigations are being performed to assess the origin of this discrepancy. Finally, the System Analysis Module (SAM) was used to model the flow of the sodium-potassium eutectic in the primary loop. A first verification was also performed showing good agreement in terms of mass flow rate and inlet temperature. All mesh files were generated using the MOOSE Reactor module, removing the need for external meshing tools. Notably, this workscope represents one of the initial applications of the MOOSE Reactor module for modeling highly irregular geometries. The use of the reactor module significantly streamlined the mesh generation process. The full multiphysics mode, that combines all the single physics models, was leveraged to conduct initial steady-state multiphysics simulations to compute power, and temperature distribution in the reactor. Initial testing was performed for transient simulations as well. In this case, the new checkpoint restart capability for eigenvalue calculations was tested showing the capability for streamlined restart of transient calculations. Future work will focus on improving the fidelity of the model by performing comprehensive code-to-code comparisons. For instance, the full-core Griffin neutronics model will be benchmarked against MCNP reference results, that were provided by the MARVEL design team. Additionally, the SAM T/H model will be verified against reference RELAP-5 results for selected accident scenarios. Besides code-to-code verification exercises, the model fidelity will be improved by replacing the single-channel SAM model with a more complex SAM-Pronghorn coupled model, in which the sub-channel capability is deployed to obtain radial temperature resolution in the coolant. This model will be developed in synergy with the NEAMS thermal hydraulics team.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Efficient phase-factor evaluation in quantum signal processing

Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in principle be obtained for a range of tasks, such as Hamiltonian simulation and the quantum linear system problem. A further benefit of QSP is that it uses a minimal number of ancilla qubits, which facilitates its implementation on near-to-intermediate term quantum architectures. However, there is so far no classically stable algorithm allowing computation of the phase factors that are needed to build QSP circuits. Existing methods require the use of variable precision arithmetic and can only be applied to polynomials of a relatively low degree. We present here an optimization-based method that can accurately compute the phase factors using standard double precision arithmetic operations. We demonstrate the performance of this approach with applications to Hamiltonian simulation, eigenvalue filtering, and quantum linear system problems. Furthermore, our numerical results show that the optimization algorithm can find phase factors to accurately approximate polynomials of a degree larger than 10000 with errors below 10 -12 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Interpretable, extensible linear and symbolic regression models for charge density prediction using a hierarchy of many-body correlation descriptors

Here, density functional theory (DFT) is routinely used to make electronic structure predictions for high-throughput screening of materials and molecules for technologically relevant areas, like the identification of better catalysts, electronic materials, and drug discovery. However, the DFT formalism is limited by (a) its poor (quadratic-to-quartic) scaling, and (b) the need to perform repeated eigenvalue computations of the electronic Hamiltonian as part of its self-consistent field (SCF) iteration procedure to obtain the converged ground state electron density, ρ (r). Approaches that directly predict ρ (r) of a structure with high accuracy can accelerate conventional SCF calculations and can also be used in linearly scaling methods such as orbital-free DFT. To this end, we present a procedure to predict the ground state electron density of molecular and periodic three-dimensional systems directly from the atomic structure with a particular emphasis on physical interpretability. In our framework, ρ (r) is modeled using many-body correlation descriptors that accurately capture the effects of local atomic arrangements in the neighborhood of a grid point. Our use of a linear regression scheme to fit to charge density data enables transparent analysis of the relative contributions of various types of local atomic correlations. By systematically including increasingly complex correlations, our model is shown to accurately predict ρ (r) for a variety of chemically and electronically diverse systems — amorphous Ge, Al(001) slab, crystalline Ga 2 O 3 , molecular benzene, and polyethylene. We then demonstrate a symbolic regression-based protocol to construct easily computable, interpretable features from lower-order correlations that significantly improves our electron density predictions with effectively no increase in the computational cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Importance of 3-D S{sub N} depletion in non-proliferation using BSOLVE

We present a single Pressurized Water Reactor (PWR) 3-D fuel rod design for depletion analysis using BSOLVE, our newly developed Runge-Kutta-Fehlberg based depletion code. BSOLVE is coupled with the deterministic 3-D S{sub N} particle transport code, PENTRAN, applied here with a 4-neutron energy group comparison to Continuous Energy (C/E) SERPENT2 Monte Carlo results. Differences are expected, as PENTRAN+BSOLVE retains full (multi-group) energy information for reactions, nuclide specific fission contributions, and energy dependent fission yields, using the latest available ENDF-BVIII data, important to retain accurate burned fuel inventories; SERPENT2 collapses burnup reactions to a single energy value. For depletion times up to ∼ 700 days and typical PWR power densities, relative differences between multigroup 3-D S{sub N} with full energy data and Monte Carlo one group burnup for trans-uranium nuclide concentrations and fission products are up to ∼20%. System eigenvalues are consistent, but with differences early and late in the cycle attributed to multigroup vs. C/E Monte Carlo cross sections. This work highlights the importance of low variance transport driven burnup for non-proliferation concerns, since plutonium quality varies significantly along axial lengths, and is more challenging to converge using Monte Carlo; details of depletion steps with spatial/zone dependent plutonium quality are provided. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Improving Estimation of the Koopman Operator with Kolmogorov–Smirnov Indicator Functions

It has become common to perform kinetic analysis using approximate Koopman operators that transform high-dimensional timeseries of observables into ranked dynamical modes. The key to the practical success of the approach is the identification of a set of observables that form a good basis on which to expand the slow relaxation modes. Good observables are, however, difficult to identify a priori and suboptimal choices can lead to significant underestimations of characteristic time scales. Leveraging the representation of slow dynamics in terms of Hidden Markov Models (HMM), we propose a simple and computationally efficient clustering procedure to infer surrogate observables that form a good basis for slow modes. Here, we apply the approach to an analytically solvable model system as well as on three protein systems of different complexities. We consistently demonstrate that the inferred indicator functions can significantly improve the estimation of the leading eigenvalues of Koopman operators and correctly identify key states and transition time scales of stochastic systems, even when good observables are not known a priori.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part I: Flux and Eigenvalue Solutions

Computing in the energy dimension is one of the greatest challenges confronting present-day deterministic neutron transport solvers. Accurately resolving the neutron flux as neutrons downscatter across resonances in the nuclear cross sections currently requires considerable computing power and suffers from approximation errors. Flux uncertainty resulting from the uncertainty of the resonance structure is the single-largest cause of reactivity uncertainty. Any additional reference solution for the critical neutron downscattering problem with resonance phenomena would be a boon to verification and validation of neutronics codes. This paper establishes a benchmark to verify the accuracy of neutron transport criticality solvers along the energy dimension. For the first time, the analytic solution of the flux amplitude is derived in the particular case of an infinite homogeneous medium with isotropic scattering in the center of mass and an arbitrary number of no-threshold, neutral particle reaction resonances (e.g., radiative capture, fission, and resonance scattering). Furthermore, original analytic expressions are established to quantify the discrepancy between the ψ k (E) and ψ α (E) flux amplitudes, respective solutions of the multiplication factor k, or the exponential time-evolution frequency α eigenproblems. The physical study of these relations led to analysis of their first-order relative difference near the criticality condition α=0. Finally, numerical solutions are provided to a benchmark problem constituted of the first resonance of 239 Pu, the 6.67-eV resonance of 238 U, and a scattering isotope with a flat cross section, allowing for the computational verification of the energy resolution of current neutron transport criticality codes. Through these novel results, this analytic benchmark can serve as a reference to verify the energy resolution and sensitivity analysis of neutron transport criticality calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Issue Summary of INL Phase IV Transient Results for IAEA CRP on HTGR UAM Benchmark

This report details the Parallel and Highly Innovative Simulation for Idaho National Laboratory (INL) Code System (PHISICS)/Reactor Excursions and Leak Analysis Program (RELAP5)-3D results obtained for the transient core exercises defined for Phase IV of the International Atomic Energy Agency (IAEA) Coordinated Research Project (CRP) on high-temperature gas cooled reactor (HTGR) uncertainty analysis in modeling (UAM). The Phase III models and results are linked to the earlier Standardized Computer Analyses for Licensing Evaluation (SCALE)/Sampler/New ESC-based Weighting Transport (NEWT) data generated for the lattice physics (lattice) stage Phase I of the CRP. The focus of this report is the Uncertainty/Sensitivity Assessment (U/SA) of the prismatic modular high-temperature gas cooled reactor (MHTGR)-350 design, and specifically for Exercises IV-1 and IV-2 of the benchmark: the Control Rod Withdrawal (CRW) and Pressurised Loss of Cooling (PLOFC) events. The statistical U/SA methodology is implemented and demonstrated using the RAVEN code, based on perturbed cross-section libraries obtained from the SCALE/Sampler sequence. Uncertainties in nuclear data (cross-sections and the average number of neutrons produced per fission, 235U[¯v ]) lead to standard deviations (uncertainties of one s) of approximately 0.5% in the core eigenvalues of the MHTGR-350 and core models. For the coupled neutronics/thermal fluid model, local power density uncertainties up to 3.6% were observed in the colder regions of the core, while the local maximum fuel temperature uncertainties reached 1.5% for the models that included thermal fluid uncertainties. The addition of thermal fluid uncertainties dominated the impacts of nuclear data uncertainties in all cases. The main contributors to uncertainties in the power density and fuel temperatures during the transients were uncertainties in the reactor operating conditions (total power, inlet mass flow rate and inlet gas temperature). Variations in the bypass flows did not have significant impact on any of the output variables. For the nuclear data uncertainties it was found that the 235U(¯v ) / 235U(¯v ) covariance produced the largest sensitivities in terms of its impact on the eigenvalue and peak reactor power. It was also observed that the impact of any nuclear data uncertainties on the maximum fuel temperature was much less significant that the impact on eigenvalue and power. Another important finding was that although the use of eight or more energy groups is recommended for best-estimate HTGR simulation, two-group models produced acceptable uncertainty and sensitivity results for most FOMs. Since the statistical U/SA methodology is computationally expensive, and most transient solver requirements will scale directly with the number of energy groups, two energy groups could be used by HTGR developers during the early stages of design when larger uncertainty margins can be tolerated.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Modeling of the Molten Salt Reactor Experiment with SCALE

A SCALE model was developed for the Molten Salt Reactor Experiment (MSRE) benchmark that was recently added to the International Handbook of Evaluated Reactor Physics Benchmark Experiments. This SCALE model served as a basis for criticality calculations and nuclear data sensitivity and uncertainty analyses with the Monte Carlo code Shift and the TSUNAMI computational capabilities in the SCALE code system. The focus of this work is the assessment of the impact of nuclear data on the calculated eigenvalue results in support of the discussion of differences between the calculated and the experimental eigenvalue result. The differences in the eigenvalues obtained using the ENDF/B-VII.0, ENDF/B-VII.1, and ENDF/B-VIII.0 nuclear data libraries cover a relatively small range of ~230 pcm. Since eigenvalue sensitivity of the MSRE is dominated by the neutron multiplicity and neutron capture of 235 U and elastic scattering in graphite, relevant changes in the ENDF/B libraries for nuclear reactions (such as carbon capture) that caused large differences in other graphite-moderated systems did not have a significant impact. Propagation of nuclear data uncertainty results in an eigenvalue uncertainty of ~700 pcm with the major contributors being 235 U neutron multiplicity, graphite elastic scattering, and 7Li neutron capture. All calculations resulted in large differences of ~2000 pcm in eigenvalue compared to the benchmark experimental value. Several potential contributors to this difference—including uncertainties and gaps in the knowledge of the material, geometry, and nuclear data—were identified. Simplified models of the full MSRE core were developed, and similarity assessments were conduced with the full MSRE core model. It was found that simplified models can serve as adequate surrogates of the full-core model such that they can be used for performing selected nuclear data performance assessments with a lower computational burden.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Lattice realizations of topological defects in the critical (1+1)-d three-state Potts model

Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and analyzed in the case of the three-state Potts CFT. In particular, lattice versions for all the primitive defects are presented, with the remaining defects obtained from the fusion of the primitive ones. The defects are obtained by introducing modified interactions around two given sites of an otherwise homogeneous spin chain with periodic boundary condition. The various primitive defects are topological on the lattice except for one, which is topological only in the scaling limit. The lattice models are analyzed using a combination of exact diagonalization and density matrix renormalization group techniques. Low-lying energy spectra for different defect Hamiltonians as well as entanglement entropy of blocks located symmetrically around the defects are computed. The latter provides a convenient way to compute the g-function which characterizes various defects. Finally, the eigenvalues of the line operators in the “crossed channel” and fusion of different defect lines are also analyzed. The results are all in agreement with expectations from conformal field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Deployment of neural-network-based neutron microscopic cross sections in the Griffin reactor physics application

The capability to utilize neural networks to predict macroscopic and microscopic cross section parametric spaces has been developed for the Griffin reactor physics application. The LibTorch interface enables Griffin's MOOSE-based materials to interact with LibTorch-trained models, allowing for the evaluation of complex macroscopic or microscopic cross section spaces, which are then used to evaluate the neutronic properties of the Griffin finite element model. This study benchmarks traditional ISOXML-formatted tabulation libraries against neural network-based models for 279 nuclides on 20,160 grid points for zero-dimensional and two-dimensional reactor models. Benchmark metrics include the fundamental mode eigenvalue, fission and absorption rates, and various temperature coefficients of reactivity (isothermal, fuel, and moderator). From the perspective of storage space, the complete set of LibTorch models uses 11 MB on disk, compared to the 10 GB for the ISOXML multigroup library that covers the same grid space. For the two-dimensional performance case considered in Griffin, the Torch model uses 97% less RAM than the reference ISOXML dataset while runtime increases by a factor of 3 when using the LibTorch model compared to the ISOXML dataset with multi-linear interpolation. The LibTorch model consistently yields errors within 0.01% for most analyzed quantities except for the temperature coefficients of reactivity where the maximum discrepancies are up to 0.3 $\frac{pcm}{K}$. Due to the neural network attempting to best predict quantities with no regard for a positive or negative bias for any given quantity, predictions may experience random fluctuations, resulting in both positive and negative errors. Future work will entail both depletion and coupled transient analysis to determine the predictive capabilities of Griffin with neural network-based cross sections.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Improved Fast Reactor Capability of Griffin in FY23

Griffin is a MOOSE based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the DOE-NE NEAMS program. In FY23, we enhanced capabilities required for fast reactor analysis. This effort included primarily updating the cross-section generation workflow using MC2-3 for various reactor configurations, such as homogeneous, duct-heterogeneous, ring-heterogeneous, and fully-heterogeneous geometries. In addition, we initiated the implementation of a multi-cycle depletion and shuffling capability. To support fast reactor simulation capabilities, we significantly improved the performance of the DFEM-SN-based R-Z transport solver to efficiently solve ultrafine group (over 1000 groups) transport problems. Additionally, the performance of HFEM-PN was improved by introducing red-black iteration, the cmfd acceleration technique, and various optimizations. We also completed the pin power reconstruction capability to support multiphysics simulations while identifying and addressing issues associated with SPH equivalence parameter approach. These enhanced capabilities for fast reactor core simulations, specially HFEM-PN and pin power reconstruction features, were applied to benchmark problems involving ABTR and ABR-1000. These applications showcased excellent agreement with Monte Carlo and other code solutions in terms of eigenvalue, control rod worth, and assembly and pin powers.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Small-Signal Stability Impacts of Load and Network Dynamics on Grid-Forming Inverters

This paper presents several stability analyses for grid-forming inverters and synchronous generators considering the dynamics of transmission lines and different load models. Load models are usually of secondary importance compared to generation source models, but as the results show, they play a crucial role in stability studies with the introduction of inverter-based resources. Given inverter control time scales, the implications of considering or neglecting electromagnetic transients of the network are very relevant in the stability assessments. In this paper, we perform eigenvalue analyses for inverter-based resources and synchronous machines connected to a load and explore the effects of multiples models under different network representations. We explore maximum loadability of inverter-based resources and synchronous machines, while analyzing the effects of load and network dynamic models on small-signal stability. The results show that the network representation plays a fundamental role in the stability of the system of different load models. The resulting stability regions are significantly different depending on the source and load model considered.

grid forming inverters↗
DOE OSTI2021

Nuclear Data Sensitivity Study for the EBR-II Fast Reactor Benchmark Using SCALE with ENDF/B-VII.1 and ENDF/B-VIII.0

The EBR-II benchmark, which was recently included in the International Handbook of Evaluated Reactor Physics Benchmark Experiments, served as a basis for assessing the performance of the SCALE code system for fast reactor analyses. A reference SCALE model was developed based on the benchmark specifications. Great agreement was observed between the eigenvalue calculated with this SCALE model and the benchmark eigenvalue. To identify potential gaps and uncertainties of nuclear data for the simulation of various quantities of interest in fast spectrum systems, sensitivity and uncertainty analyses were performed for the eigenvalue, reactivity effects, and the radial power profile of EBR-II using the two most recent ENDF/B nuclear data library releases. While the nominal results are consistent between the calculations with the different libraries, the uncertainties due to nuclear data vary significantly. The major driver of observed uncertainties is the uncertainty of the 235 U ( n,γ ) reaction. Since the uncertainty of this reaction is significantly reduced in the ENDF/B-VIII.0 library compared to ENDF/B-VII.1, the obtained output uncertainties tend to be smaller in ENDF/B-VIII.0 calculations, although the decrease is partially compensated by increased uncertainties in 235 U fission and ν ¯ .

42 ENGINEERING↗
DOE OSTI2022

Impact of Increased Latent Generations on Sensitivity Calculations with SCALE

Analyses of cross section sensitivity data from systems with fissile material allow analysts to associate an importance for each material, nuclide, reaction, and neutron energy by simulating real world criticality scenarios. Although criticality safety validation efforts can be guided by the cross-section sensitivity and uncertainty data generated for a particular system, these calculations can often be computationally expensive and sometimes cumbersome without proper guidance. The TSUNAMI suite within the SCALE code package has several methods for generating sensitivity data, including multigroup and continuous energy (CE) capabilities. The release of SCALE 6.3 has three different CE methods for generating cross section sensitivity data: (1) the Iterated Fission Probability (IFP) method with the KENO Monte Carlo transport solver, (2) the IFP method with the Shift Monte Carlo transport solver, and (3) the Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method with the KENO Monte Carlo transport solver. Although the CLUTCH method has additional parameters for generating sensitivity data files relative to the IFP method, all three methods use latent generations, which are the generations between an event (i.e., fission) and the assessment of importance based on the asymptotic population of progeny neutrons. Increasing the number of latent generations in a calculation leads to increased discrimination of the sensitivity coefficients but at the cost of the increased uncertainty associated with those generated values. Analysts must balance the accuracy of the sensitivity calculations and its uncertainty with the associated computational cost involved in generating the values. This paper discusses the impact of adjusting the latent generation parameter for a range of sensitivity values and how these changes compare with the direct perturbation values obtained from a change of ±0.5% Δ k in both benchmark and safety application models. Two benchmarks from the International Handbook of Evaluated Criticality Safety Benchmark Experiments and the MPC-32 dual purpose canister for spent nuclear fuel are used for analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Deep Learning for Multigroup Cross-Section Representation in Two-Step Core Calculations

Here we investigate using deep learning, a type of machine-learning algorithm employing multiple layers of artificial neurons, for the mathematical representation of multigroup cross sections for use in the Griffin reactor multiphysics code for two-step deterministic neutronics calculations. A three-dimensional fuel element typical of a high-temperature gas reactor as well as a two-dimensional sodium-cooled fast reactor lattice are modeled using the Serpent Monte Carlo code, and multigroup macroscopic cross sections are generated for various state parameters to produce a training data set and a separate validation data set. A fully connected, feedforward neural network is trained using the open-source PyTorch machine-learning framework, and its accuracy is compared against the standard piecewise linear interpolation model. Additionally, we provide in this work a generic technique for propagating the cross-section model errors up to the k eff using sensitivity coefficients with the first-order uncertainty propagation rule. Quantifying the eigenvalue error due to the cross-section regression errors is especially practical for appropriately selecting the mathematical representation of the cross sections. We demonstrate that the artificial neural network model produces lower errors and therefore enables better accuracy relative to the piecewise linear model when the cross sections exhibit nonlinear dependencies; especially when a coarse grid is employed, where the errors can be halved by the artificial neural network. However, for linearly dependent multigroup cross sections as found for the sodium-cooled fast reactor case, a simpler linear regression outperforms deeper networks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

MACHINE LEARNING BASED CHEMICAL EXPLOSIVE MODE ANALYSIS (ML-CEMA)

The software consists of a Machine Learning based Chemical Explosive Mode Analysis (ML-CEMA) tool for advanced computational flame diagnostics. CEMA, originally based on eigen-analysis of the local thermochemical system, is capable of identifying reaction fronts and limit phenomena such as auto-ignition and extinction in practical combustion systems, such as internal combustion engines and gas turbine combustors. However, the original CEMA is computationally expensive for large reaction mechanisms that are typically needed to describe fuel chemistry of practical large-hydrocarbon fuels. This novel ML-CEMA tool employs a ML technique to accelerate the eigen-analysis of the basic CEMA approach by orders of magnitude, thus making it suitable for practical fuels. In ML-CEMA,zero-dimensional (0D) reactors and one-dimensional (1D) premixed flames are first used to generate a large number of data points for neural network based ML training. The trained ML model is then used to perform CEMA prediction. This ML-CEMA tool has been demonstrated in canonical 0D and 1D configurations as well as highly-transient three-dimensional spray flames exhibiting multi-mode turbulent combustion, showing promising results. ML-CEMA, as a standalone tool, can be used for computationally-efficient diagnostics of massive datasets generated from both experiments and simulations. For example, based on spatially resolved measurements of a small set of reactive scalars(such as temperature, hydroxyl radical and formaldehyde), ML-CEMA can effectively identify flame fronts and rare events. ML-CEMA also provides a robust online or offline flame feature detection tool. When used for on-the-fly simulations, ML-CEMA further enables zone-adaptive combustion modeling, in which the predicted eigenvalue is used as a robust mode indicator for judicious assignment of locally-valid combustion models. This ML-CEMA based zone-adaptive model can lead to substantial computational cost savings when used for large-scale simulations of multi-mode combustion systems. Third Party Code Web Page to Download Code Web Page Location of Third Party License

Xu, Chao↗