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DOE OSTI2023

Variational Monte Carlo calculations of n + H 3 scattering

A paramount goal in nuclear physics is to unify ab initio treatments of bound and unbound states. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound-state calculations in light systems but have seen minimal implementation in unbound systems. Here, we introduce a numerical method to improve the efficiency and accuracy of unbound-state calculations in QMC. As an initial application, we compute scattering observables for the smallest system available to probe three-body forces, the neutron-triton system, using variational Monte Carlo (VMC) wave functions. The method involves inferring long-range amplitudes in the wave function from integrals over the short-range region where all the particles interact. This approach using integral relations is well established in the literature; here, we develop it for the QMC framework. We validate our approach with a consistency check between short-range spectroscopic overlap functions computed from direct evaluation and from the integral relations; scattering amplitudes are long-range asymptotics of those overlaps. Comparison against published benchmark calculations using the same potential demonstrates that when applied to the current VMC wave functions, the integral method produces more accurate scattering observables than direct evaluation from the same variational wave function. However, it still differs noticeably from the exact results. Using additional interactions, we then present phase shifts and mixing parameters for the n + 3 H system. In particular, we present one of the first applications of the Norfolk family of local coordinate-space chiral potentials in unbound systems of A > 2. The Norfolk results accurately describe s-wave scattering but predict p-wave cross sections too large. Compared with previous QMC scattering calculations, the integral method avoids difficulties associated with the precise computation of energy differences and with convergence outside the interaction region, which is particularly severe in the variational calculation. Application of the integral method here paves the way for its use in Green's function Monte Carlo (GFMC) calculations. In GFMC, the wave functions are more accurate, but the high-precision convergence of their tails is slow, and there are additional difficulties in reading out amplitudes. Here, the integral methods will address both of those remaining problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Risk Assessment of Rare Events in Probabilistic Power Flow via Hybrid Multi-Surrogate Method

The risks associated with rare events threatening the security of power system operation are of paramount importance to power system planners and operators. To analyze the risks caused by high-impact, low-frequency rare events, an immensely large number of samples are typically required for the Monte-Carlo (MC) method on the high-fidelity power system model to achieve a sufficient accuracy, thereby rendering this approach computationally prohibitive. To handle this problem efficiently, it is desirable to construct a surrogate model for the power system response. However, the straightforward MC sampling of the low-fidelity surrogate can lead to biased results in the low-probability tail regions that are vital to risk assessment. Moreover, a single surrogate is unable to handle the topology uncertainties caused by random branch outages. To overcome these issues, we propose a hybrid multi-surrogate (HMS) method based on the polynomial chaos expansion (PCE) with low-probability tail events reevaluated by the high-fidelity model through a probabilistic analysis. This method improves the computational efficiency of the MC method for rare-event risk assessment by leveraging multi-fidelity models while retaining the desired accuracy. Simulations conducted in three test systems verify the excellent performances of the HMS method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Field Measurement and Analysis of Frequency and RoCoF for Low-Inertia Power Systems

The frequency measurement and rate of change of frequency (RoCoF) calculations are important for active power, frequency control, and frequency-related protection in power system operations. With the rapid decrease in inertia under modern power systems, however, multiple power variations introduced by variable renewable energy bring large RoCoF and introduce oscillations in frequency measurements. To shed light on this issue, this article proposes a frequency measurement and RoCoF analysis technology, as well as the sensitivity analysis for the real low-inertia power grid. First, a real-world event in an island power grid is analyzed as an example, and an event numerical model is estimated considering four uncertainties, including event RoCoF, oscillation magnitude, oscillation frequency, and underfrequency load-shedding threshold. Then, a sensitivity analysis is performed using the Sobol indices method and quasi-Monte Carlo simulations to identify the dominant uncertainties based on the event model. Here, the dominant uncertainties are compared to provide a guideline for the frequency estimation algorithm selection under different event cases. This algorithm is compared with an enhanced zero-crossing algorithm and gives a 3.41% better RoCoF error rate. Finally, an experiment is conducted using universal grid analyzers to validate the simulation results and the theoretical analysis.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Superconductivity, charge density waves, and bipolarons in the Holstein model

The electron-phonon ( e-ph ) interaction remains of great interest in condensed matter physics and plays a vital role in realizing superconductors, charge density waves (CDW), and polarons. We study the two-dimensional Holstein model for e-ph coupling using determinant quantum Monte Carlo across a wide range of its phase diagram as a function of temperature, electron density, dimensionless e-ph coupling strength, and the adiabatic ratio of the phonon frequency to the Fermi energy. We describe the behavior of the CDW correlations, the competition between superconducting and CDW orders and polaron formation, the optimal conditions for superconductivity, and the transition from the weak-coupling regime to the strong-coupling regime. Superconductivity is optimized at intermediate e-ph coupling strength and intermediate electron density, and the superconducting correlations increase monotonically with phonon frequency. The global maximum for superconductivity in the Holstein model occurs at large phonon frequency, the limit where an attractive Hubbard model effectively describes the physics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Autoregressive neural quantum states of Fermi Hubbard models

Neural quantum states (NQSs) have emerged as a powerful ansatz for variational quantum Monte Carlo studies of strongly correlated systems. Here, we apply recurrent neural networks (RNNs) and autoregressive transformer neural networks to the Fermi-Hubbard and the (non-Hermitian) Hatano-Nelson-Hubbard models in one and two dimensions. In both cases, we observe that the convergence of the RNN ansatz is challenged when increasing the interaction strength. We present a physically motivated and easy-to-implement strategy for improving the optimization, namely, by ramping of the model parameters. Furthermore, we investigate the advantages and disadvantages of the autoregressive sampling property of both network architectures. For the Hatano-Nelson-Hubbard model, we identify convergence issues that stem from the autoregressive sampling scheme in combination with the non-Hermitian nature of the model. Our findings provide insights into the challenges of the NQS approach and make the first step towards exploring strongly correlated electrons using this ansatz. Published by the American Physical Society 2025

Ibarra-García-Padilla, Eduardo (ORCID:000000019165↗
DOE OSTI2019

Deep Direct-Use Feasibility Study Temperature-Depth Estimates for West Virginia University, Morgantown, WV

This dataset contains data spreadsheets and figures that summarize the results of a stochastic analysis of temperatures at depth below the West Virginia University campus in Morgantown, WV. These results are extracted from a study by Smith (2019), whose results are included in a GDR submission that provides rasters and shapefiles for the Appalachian Basin states of New York, Pennsylvania, and West Virginia (GDR submission #1182). Uncertainties considered included geologic properties, thermal properties, and uncertainty from geostatistical interpolation of the surface heat flow. A Monte Carlo analysis of these uncertain properties was used to predict temperatures at depth using a 1-D heat conduction model. For the pixel corresponding to West Virginia University, a .csv file containing the 10,000 temperature-depth profiles estimated from a Monte Carlo analysis is provided. Temperatures are provided for depths from 1-5 km in 0.5 km increments. These data are summarized in a figure containing violin plots that illustrates the probability of obtaining certain temperatures at depth for Morgantown.

15 GEOTHERMAL ENERGY↗
DOE OSTI2023

High-Performance Accelerator Modeling: Toward Improving Controls and Diagnostics for High-Brightness Beams in Experiment

One of the main charges of beam physics is to improve the overall beam quality delivered to experiments and applications, which is generally quantified by the beam brightness. High brightness beams have numerous applications, including x-ray free electron lasers and ultrafast electron diffraction (UED). To these ends, this thesis details efforts to use high-performance models --- high-fidelity models that execute quickly --- for controls and diagnostics. To demonstrate the generality of these techniques, this thesis focuses on three of the most successful photoinjector designs currently used worldwide: the UCLA/SLAC/BNL-type high-gradient S-band gun, the continuous-wave high-repetition rate VHF APEX gun and the L-band DESY-PITZ-type gun. Work will be shown from Pegasus (UCLA), HiRES (LBNL) and FAST (FNAL).Specifically, data-driven models for online virtual diagnostics are presented, in this case, in the context of UED at HiRES, leading to a temporal resolution improvement. Methods for improving the fidelity of physics-based models are discussed, with examples at HiRES, Pegasus and FAST. Markov-chain Monte Carlo analysis is applied to match simulations, in the context of photocathode studies at HiRES and Pegasus. Lastly, the augmentation of online model-based predictions with model-independent optimization is explored in a fluctuating environment at Pegasus and HiRES. A central theme of this dissertation is working with parameter fluctuations when modeling an accelerator beamline. Long-term drifts and shot-to-shot jitter exist in every accelerator to a varying degree and therefore play an important role in every chapter of this dissertation. This thesis attempts to address the issues associated with these fluctuations when trying to develop faithful model representations of the system.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Prognostic model and failure mechanisms of steam generators in Sodium-Cooled fast reactors

This paper presents a prognostic model for sodium-cooled fast reactor (SFR) steam generators (SGs). Here, the purpose of the model is to estimate the remaining useful life of SFR SGs and thus to support the decision-making of autonomous control. SFR SGs are of great interest for plant integrity due to their harsh operation environment. They operate at higher temperatures and higher coolant-to-steam pressure differences than those of current light water reactors (LWR). The severity of the SFR SG failure consequences, which include water-sodium contact, is another reason. Understanding its failure mechanisms is important for the development of its prognostic model. Based on our literature review and physics-based analysis, we concluded that creep would be a dominant degradation mode of SFR SGs due to SFR’s high-temperature and high-pressure environment. Thus, creep is the focus of the prognostic model. Various other failure modes were also investigated in this study. The mechanical fatigue due to flow-induced vibration is usually observed in early developmental phases and would not be an important issue during normal operation. The thermal fatigue due to thermal stripping is occasionally observed in other components in SFRs but does not affect SG integrity. Pure water stress corrosive crack, fretting, and so on are commonly observed in LWR SGs but are significantly less important in SFR SGs because of the high temperatures, high pressure differences, and chemical properties of liquid sodium. Based on these investigations, a prognostic model focusing on creep failures was developed. It estimates the failure probability profile by sampling the Larson-Miller parameter (LMP) and temperature and associated uncertainties through Monte Carlo methods. Two case studies were presented. The first one demonstrated the model’s capability to calculate the failure probability for a new specimen within a given time. If the tube is working under temperatures of 500C ± 3 and pressures of 15.2 MPa, which leads to LMP of 20,100 ± 50, the failure probabilities within 50, 70, and 90 years are approximately 0.1 %, 3.2 %, and 17.5 %. The second demonstrated how adjusting the workload can help to protect the integrity of the component. For an old tube reaching 99 % of its lifespan, continuing to run at temperatures of 500C ± 3 and LMP of 20,100 ± 50 leads to a failure probability of about 29.0 % within a year. If the temperature is reduced by 5C, the failure probability can be reduced to 2.5 %, and, if the pressure is also reduced such that the LMP is increased by 100, the failure probability can further be reduced to 0.12 %.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Machine learning predictions for local electronic properties of disordered correlated electron systems

We present a scalable machine learning (ML) model to predict local electronic properties such as on-site electron number and double occupation for disordered correlated electron systems. Our approach is based on the locality principle, or the nearsightedness nature, of many-electron systems, which means local electronic properties depend mainly on the immediate environment. A ML model is developed to encode this complex dependence of local quantities on the neighborhood. We demonstrate our approach using the square-lattice Anderson-Hubbard model, which is a paradigmatic system for studying the interplay between Mott transition and Anderson localization. We develop a lattice descriptor based on the group-theoretical method to represent the on-site random potentials within a finite region. The resultant feature variables are used as input to a multilayer fully connected neural network, which is trained from data sets of variational Monte Carlo (VMC) simulations on small systems. We show that the ML predictions agree reasonably well with the VMC data. Our work underscores the promising potential of ML methods for multiscale modeling of correlated electron systems.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Applying Constrained Bayesian Optimization to the Design of Critical Experiments

Often when planning a criticality experiment, many design configurations are iteratively investigated with a Monte Carlo transport code. The goal is that the experiment will be optimal with respect to some variable, like the fraction of fissions occurring at a certain energy range, while simultaneously being critical. Unfortunately, the Monte Carlo transport simulations are expensive, which can ultimately limit the number of configurations that can be explored. In this work, we present how Gaussian processes (GPs) can be used as a reduced-order model in a constrained Bayesian optimization (CBO) algorithm to design a criticality experiment. The GPs replace the Monte Carlo transport simulations that explore the design space. The CBO algorithm efficiently identifies new points in the design space to run the Monte Carlo transport code while respecting the criticality constraint. It does so in a manner that both improves the accuracy of the GP and finds the approximate global optimum. We demonstrate the performance of CBO with the design of a Thermal Epithermal eXperiment (TEX) for the criticality safety validation of nuclear waste models of the Hanford Tank Farm.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

A Hydro-based MCMC Analysis of SNR 0509–67.5: Revealing the Explosion Properties from Fluid Discontinuities Alone

Using Hubble Space Telescope/ACS Hα images of SNR 0509–67.5 taken ~10 yr apart, we measure the forward shock (FS) proper motions (PMs) at 231 rim locations. The average shock radius and velocity are 3.66 ± 0.036 pc and 6315 ± 310 km s –1 . Hydrodynamic simulations, recast as similarity solutions, provide models for the supernova remnant’s expansion into a uniform ambient medium. These are coupled to a Markov chain Monte Carlo (MCMC) analysis to determine explosion parameters, constrained by the FS measurements. For our baseline model, the MCMC posteriors yield an age of 315.5 ± 1.8 yr, a dynamical explosion center at 5 h 09 m 31. s 16, $-67^\circ 31^{\prime} 17\buildrel{\prime\prime}\over{.} 1$ and ambient medium densities at each azimuth ranging over 3.7–8.0 × 10 –25 g cm –3 . The age uncertainty can be an order of magnitude larger when considering other models, or subsets of the data. We detect stellar PMs corresponding to speeds in the Large Magellanic Cloud ≥ 770 km s –1 . Five stars in the remnant show measurable PMs but none are moving radially from the dynamical center. There are four stars 1."4 from the center, including three faint, previously unidentified ones. Using coronal [Fe XIV ] λ5303 emission as a proxy for the reverse shock location, we constrain the explosion energy (for a compression factor of 4) to a value of E = (1.30 ± 0.41) × 10 51 erg for the first time from shock kinematics alone. Higher compression factors (7 or more) are strongly disfavored based on multiple criteria, arguing for inefficient particle acceleration in the Balmer shocks of SNR 0509–67.5.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Z 2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry

We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z 2 gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first order, in contrast to the conventional Z 2 lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic X X interaction while keeping the local gauge symmetry intact. We find that the Z 2 topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.

2-dimensional systems↗
DOE OSTI2023

Evaluation of the spatial self-shielding impact for TRISO-based nuclear fuel depletion

Reactor physics analyses of nuclear cores with nuclear fuel concepts containing tristructural isotropic (TRISO) particles, such as pebbles or compact fuel elements, rely on various degrees of simplification to keep these highly heterogeneous problems computationally tractable. One such limitation regards the level of spatial discretization employed during burnup calculations, where traditionally only a limited number of spatial zones are modeled at the full core level and assume that the spectrum is constant within the fuel elements and TRISO particles in this depletion zone. This type of assumption neglects the impact of spatial self-shielding effect within the kernels (microscale level) as well as within the compact or pebbles (mesoscale level). Furthermore, the Monte Carlo code Serpent 2 contains many relevant features for efficiently modeling this type of geometry, including a collision-based domain decomposition intended for very large burnup calculations, which we leveraged for this work to quantify the impact of capturing neutron flux variations occurring at the micro- and mesoscale level on a series of high-temperature gas-cooled reactor fuel element depletion problems. While spatial self-shielding is observed at both scales, with differences from a volume-averaged burnup of ±7% within the kernels and ±2% between TRISO particles within the fuel element, the conjugated effect on nuclide inventories and multiplication factor are negligible, hence confirming that assuming a single average spectrum value may be sufficient for most applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

SCALE 6.2 Lattice Physics Performance Assessment

The US Nuclear Regulatory Commission relies on the lattice physics analysis capabilities of the SCALE code system to perform confirmatory licensing analyses. Either SCALE lattice physics code—TRITON/NEWT or Polaris—can be used to generate cross section data used by the PARCS nodal core simulator for full-core neutronics calculations. This report presents an assessment of the accuracy of SCALE lattice physics codes for preparation of lattice physics data that are used to support simulator codes such as the NRC’s PARCS, for UO 2 -mixed oxide (MOX)/Zr fueled light water reactor (LWR) analyses. Due to the nature of lattice physics calculations, critical reactor experiment benchmarks cannot be modeled in explicit detail in a lattice physics code. However, this limitation does not mean that these measurement data are not usable for lattice physics studies. Therefore, either geometry approximations or axial buckling must be implemented to determine the critical water height. These modeling limitations have led to development of a three-phase assessment strategy. In the first phase, selected critical experiment benchmarks are modeled using the SCALE 3D continuous-energy (CE) Monte Carlo (MC) code KENO, which is the most rigorous neutron transport method available in SCALE, with no approximations in the spatial, angle, or energy treatments. Biases and statistical uncertainties in quantities of interest such as k eff and pin power distributions are determined by comparing CE KENO results to experimental data. This first phase in the accuracy assessment is to demonstrate and establish the use of CE KENO as a reference solution for the second phase. In the second phase, 14 numerical test suites are used to compare SCALE lattice physics calculations with CE KENO as a reference solution. In the third phase, SCALE lattice physics depletion calculations are performed, and the spent fuel isotopic results are compared with available radiochemical assay measurements. Isotopic measurement comparisons provide quantitative assessment of isotopic density distribution predictions with the depletion models in SCALE lattice physics codes. This report documents results for all test suites. The assessment was performed using standard production techniques unless otherwise noted. Both TRITON/NEWT and Polaris exhibited acceptable accuracy for most test cases. For the few test cases in which acceptable accuracy criteria were not met, further code and data development are planned. The computer codes used in this assessment are as follows: SCALE 6.2 rev19189 (pre-release of 6.2.1) was used for CE KENO, TRITON/NEWT and Polaris (PWR only) calculations; SCALE 6.2.2 was used for Polaris calculations to address several updates in support of support boiling water reactor (BWR) lattice geometries. For this work, there is no difference between SCALE 6.2.1 and SCALE 6.2.2 beyond the inclusion of the Polaris BWR analysis capability; The ENDF/B-VII.1 continuous energy and 252 group libraries deployed in SCALE 6.2 were generated with AMPX 6.2 that is distributed with SCALE.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Urban Flood Modeling: Uncertainty Quantification and Physics‐Informed Gaussian Processes Regression Forecasting

Abstract Estimating uncertainty in flood model predictions is important for many applications, including risk assessment and flood forecasting. We focus on uncertainty in physics‐based urban flooding models. We consider the effects of the model's complexity and uncertainty in key input parameters. The effect of rainfall intensity on the uncertainty in water depth predictions is also studied. As a test study, we choose the Interconnected Channel and Pond Routing (ICPR) model of a part of the city of Minneapolis. The uncertainty in the ICPR model's predictions of the floodwater depth is quantified in terms of the ensemble variance using the multilevel Monte Carlo (MC) simulation method. Our results show that uncertainties in the studied domain are highly localized. Model simplifications, such as disregarding the groundwater flow, lead to overly confident predictions, that is, predictions that are both less accurate and uncertain than those of the more complex model. We find that for the same number of uncertain parameters, increasing the model resolution reduces uncertainty in the model predictions (and increases the MC method's computational cost). We employ the multilevel MC method to reduce the cost of estimating uncertainty in a high‐resolution ICPR model. Finally, we use the ensemble estimates of the mean and covariance of the flood depth for real‐time flood depth forecasting using the physics‐informed Gaussian process regression method. We show that even with few measurements, the proposed framework results in a more accurate forecast than that provided by the mean prediction of the ICPR model.

Kohanpur, Amir H.↗
DOE OSTI2021

Pairing correlations in the cuprates: A numerical study of the three-band Hubbard model

We study the three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the pairing correlations in this model using these methods. Specifically, we compute the pair-field susceptibility and study its dependence on temperature, doping, interaction strength, and charge-transfer energy. Using the DCA, we also solve the Bethe-Salpeter equation for the two-particle Green's function in the particle-particle channel to determine the transition temperature to the superconducting phase on smaller clusters. Our calculations reproduce many aspects of the cuprate phase diagram and indicate that there is an “optimal” value of the charge-transfer energy for the model where T c is largest. Finally, these results have implications for our understanding of superconductivity in both the cuprates and other doped charge-transfer insulators.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Improving Detector Systematic Uncertainties Through Data-Driven Machine Learning

Detector simulation in liquid argon time projection chambers (LArTPCs) is a constant challenge. In particular the modeling of electrons response on wires is highly nontrivial. However, new machine learning techniques exist which can be leveraged to ameliorate these concerns. We present a novel methodology to attempt to learn from cosmic muon data in the ICARUS detector how reconstructed wire signals are influenced by features of the hits such as location, particle direction, angle relative to the wire plane, etc. A model can then be generated which can apply the learned mapping to Monte Carlo events to create a more data-like simulation sample. By creating such a sample we expect to reduce the systematic uncertainties at ICARUS due to our detector modeling.

Hausner, Harry [Fermilab] (ORCID:0000000188932280)↗
DOE OSTI2026

Improving Detector Systematic Uncertainties Through Data-Driven Machine Learning

Detector simulation in liquid argon time projection chambers (LArTPCs) is a constant challenge. In particular the modeling of electrons response on wires is highly nontrivial. However, new machine learning techniques exist which can be leveraged to ameliorate these concerns. We present a novel methodology to attempt to learn from cosmic muon data in the ICARUS detector how reconstructed wire signals are influenced by features of the hits such as location, particle direction, angle relative to the wire plane, etc. A model can then be generated which can apply the learned mapping to Monte Carlo events to create a more data-like simulation sample. By creating such a sample we expect to reduce the systematic uncertainties at ICARUS due to our detector modeling.

Hausner, Harry [Fermilab] (ORCID:0000000188932280)↗