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DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗

DOE OSTI2021

Geometric Tail Approximation for Reliability and Survivability

A common problem in developing high-reliability systems is estimating the reliability for a population of components that cannot be 100% tested. The radiation survivability of a population of components is often estimated by testing a very small sample to some multiple of the required specification level, known as an overtest. Given a successful test with a sufficient overtest margin, the population of components is assumed to have the required survivability or radiation reliability. However, no mathematical justification for such claims has been crafted without making aggressive assumptions regarding the statistics of the unknown distribution. Here we illustrate a new approach that leverages geometric bounding arguments founded on relatively modest distribution assumptions to produce conservative estimates of component reliability.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

bolt: A GPU-Accelerated Solver for Marginally Collisional Kinetic Physics Using a High- Resolution Constrained Transport Scheme

Collisionless and marginally collisional plasmas are very expensive to simulate due to high dimensionality and large scale separations, especially in global problems with additional length scales. bolt addresses this challenge by achieving high performance on GPUs using the arrayfire performance portability library. We have demonstrated accuracy on a range of test problems, and the bolt code paper is currently in preparation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Correction to “Ruthenium Dye Excitations and Relaxations in Natural Sunlight”

An error in computing the optical rate coefficients for dye RuP was discovered in Table S4 of the Supporting Information Section S8 Model S? for this article, published in J. Phys. Chem. A, 2021, 125, 4365-4372, 10.1021/acs.jpca.1c02386. The optical rate coefficients include absorption, stimulated emission, and ground-state bleach associated with the ground state and the singlet and triplet excited states as well as for the excited-state absorption between the excited states and implicit higher-energy excited states. The optical rate coefficients for continuous solar irradiance were computed using eq 3 of the main text in which the product of the individual signal components and the solar spectrum are integrated and multiplied by the fundamental optical rate coefficient. We determined the incorrect signal components were used for RuP in the published Supporting Information Table S4. The corrected Table S4 column for RuP is presented with the reported values from the original paper in the corrected Supporting Information. New simulations have been performed using the corrected values, and the results were used to update Figures 5 and 6 and also Figure S9 in the corrected Supporting Information. The published conclusions are unchanged. The populations of RuP excited states, Figure 5, are only marginally smaller, which should be expected with minor changes to the optical rate coefficients. There is not a significant change in the results for the number of radiative and nonradiative interactions per dye per second (the optical transitions and nonradiative transitions increased, respectively, by approximately 2% and 10%, Figure 6A). The occurrence of excited-state absorption (ESA) and excited-state emission (ESE) events, Figure 6C, both decreased from the original simulation results by 20% and 33%. The most notable difference is exhibited in Figure 6B; the fraction of population moving from the lowest-energy singlet state (i.e., intersystem crossing or ultrafast nonradiative relaxation) and nonradiative relaxation from the triplet state have decreased from ~0.45 to ~0.4 and increased from ~0.35 to ~0.4, respectively..

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Conjugate Heat Transfer Modeling of Salt-Filled Fuel Pins for Stable Salt Reactor Safety Analysis

The Stable Salt Reactor (SSR) combines the proven structural design of light water reactor fuel assemblies with the inherent safety and fuel-cycle advantages of molten salt technology. In its fast reactor configuration, the SSR utilizes recycled nuclear waste as fuel, sealed within narrow salt-filled fuel pins and cooled by a surrounding liquid salt coolant. Reliable transfer of heat from the molten fuel salt through the cladding to the external coolant is essential for both reactor safety and performance. This work investigates conjugate heat transfer (CHT) in the SSR’s salt-filled fuel pins using NekRS, a high-fidelity spectral element computational fluid dynamics (CFD) solver. The analyses capture internal natural convection within the molten fuel salt and external forced convection in the coolant, under steady-state and transient operating conditions. Parametric studies evaluate how variations in reactor power and coolant flow rate influence heat transfer distributions and system response. The high-fidelity CFD results are time-averaged and post-processed for direct comparison with moderate-fidelity Reynolds-averaged Navier–Stokes (RANS) models, and for the development of reduced-order models within the SAM system code. These validated models support fast-running safety analyses of normal and off-normal transients, improving predictive capability for key safety margins. By integrating advanced CFD with system-level safety tools, this study strengthens the modeling framework for SSR design, reduces uncertainty in molten salt CHT simulations, and accelerates the engineering and licensing of next-generation nuclear reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Lost and Found Opportunities Around the Chlorine Worth Study

Los Alamos National Laboratory performed a series of critical experiments in 2021 to examine the worth of chlorine in plutonium-fueled systems. This series of experiments has been dubbed the “Chlorine Worth Study,” and the evaluation of the experiments was presented to the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Technical Review Group in April, 2023. The primary purpose of these experiments was to enable validation of aqueous solutions crediting neutron absorption in 35 Cl. An external, independent view of the events leading up to the design and execution of these experiments indicates a missed opportunity to leverage sensitivity/uncertainty (S/U) analysis to assert validation without the experiments by taking an additional margin for the lack of direct validation of chlorine. On the other hand, the execution of these experiments also presents a rare opportunity to examine the efficacy of the S/U approach and extract useful information about the evaluated chlorine covariance data. TSUNAMI-1D models of representative application solutions were created and used to generate sensitivity data. Varying plutonium and chlorine concentrations were considered to examine the impact of these differences on the chlorine sensitivities and uncertainties. The data-induced uncertainty in k eff resulting from chlorine was calculated directly from uncertainty information calculated in the TSUNAMI-1D sequence. In all cases, this uncertainty was less than 0.1 %Δk. This result could potentially be used to justify a reactivity margin to account for the validation gap related to chlorine in the validation set. On the other hand, given that the experiments were performed, the community should endeavor to extract as much value from them and their results as possible. The results can be used to examine the actual bias associated with chlorine in these systems once the evaluations have been released. These data can be compared with the data-induced uncertainty margin discussed above to test the sufficiency of the validation gap penalty. This result will provide an indication of the performance of the chlorine covariance data specifically and the S/U validation approach generally. More advanced S/U techniques may also be employed to determine reactivity sensitivities associated with the chlorine in the experiments, potentially generating a more robust test of the chlorine covariance data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Tax Credits for Clean Electricity: The Distributional Impacts of Supply-Push Policies in the Power Sector

We evaluate distributional and efficiency consequences of the bulk power clean electricity tax credits authorized by the 2022 Inflation Reduction Act. To do so, we link detailed electricity capacity expansion, computable general equilibrium, microsimulation, and air pollution models to estimate economic welfare and health incidence across demographic groups. We evaluate trade-offs between policy efficiency and income progressivity by comparing the tax credits to cap-and-trade policies. The tax credits encourage increased clean electricity investment, resulting in a reallocation of capital from elsewhere in the economy, higher prices for capital and other goods, lower power prices, and lower emissions. The tax credits yield progressive outcomes for economic welfare at the expense of efficiency while all modeled policies demonstrate progressivity in health impacts. The health benefits, absent climate benefits, exceed total policy costs and provide greater benefits for low-income and historically marginalized households given coincidence of household locations and emissions exposure intensity.

distributional impacts↗

DOE OSTI2021

Proton pairing in neutron stars from chiral effective field theory

Here, we study the 1 S 0 proton pairing gap in beta-equilibrated neutron star matter within the framework of chiral effective field theory. We focus on the role of three-body forces, which strongly modify the effective proton-proton spin-singlet interaction in dense matter. We find that three-body forces generically reduce both the size of the pairing gap and the maximum density at which proton pairing may occur. The pairing gap is computed within BCS theory using a single-particle dispersion relation calculated up to second order in perturbation theory. Model uncertainties are estimated by varying the nuclear potential (its order in the chiral expansion and high-momentum cutoff) and the choice of single-particle spectrum in the gap equation. We find that a second-order perturbative treatment of the single-particle spectrum suppresses the proton 1 S 0 pairing gap relative to the use of a free spectrum. We estimate the critical temperature for the onset of proton superconductivity to be T c = (3:2–5:1) 10 9 K, which is consistent with previous theoretical results in the literature and marginally within the range deduced from a recent Bayesian analysis of neutron star cooling observations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Hydrological Perspectives on Integrated, Coordinated, Open, Networked (ICON) Science

Hydrologic sciences depend on data monitoring, analyses, and simulations of hydrologic processes to ensure safe, sufficient, and equal water distribution. These hydrologic data come from but are not limited to primary (lab, plot, and field experiments) and secondary sources (remote sensing, UAVs, hydrologic models) that typically follow FAIR Principles (Findable, Accessible, Interoperable, and Reusable: (go-fair.org)). Easy availability of FAIR data has become possible because the hydrology-oriented organizations have pushed the community to increase coordination of the protocols for generating data and sharing model platforms. In addition, networking at all levels has emerged with an invigorated effort to activate community science efforts that complement conventional data collection methods. However, it has become difficult to decipher various complex hydrologic processes with increasing data. Machine learning, a branch of artificial intelligence, provide more accurate and faster alternatives to better understand different hydrological processes. The Integrated, Coordinated, Open, Networked (ICON) framework provides a pathway for water users to include and respect diversity, equity, and inclusivity. In addition, ICONs support the integration of peoples with historically marginalized identities into this professional discipline of water sciences. This article comprises three independent commentaries about the state of ICON principles in hydrology and discusses the opportunities and challenges of adopting them.

(ICON) principles to address↗

DOE OSTI2022

Machine Learning Solutions for a Stable Grid Recovery

Grid operating security studies are typically employed to establish operating boundaries, ensuring secure and stable operation for a range of operation under NERC guidelines. However, if these boundaries are severely violated, existing system security margins will be largely unknown, as would be a secure incremental dispatch path to higher security margins while continuing to serve load. As an alternative to the use of complex optimizations over dynamic conditions, this work employs the use of machine learning to identify a sequence of secure state transitions which place the grid in a higher degree of operating security with greater static and dynamic stability margins. Several reinforcement learning solution methods were developed using deep learning neural networks, including Deep Q-learning, Mu-Zero, and the continuous algorithms Proximal Reinforcement Learning, and Advantage Actor Critic Learning. The work is demonstrated on a power grid with three control dimensions but can be scaled in size and dimensionality, which is the subject of ongoing research.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Analyzing Impact of Distributed PV Generation on Integrated Transmission & Distribution System Voltage Stability—A Graph Trace Analysis Based Approach

The use of a Graph Trace Analysis (GTA)-based power flow for analyzing the voltage stability of integrated Transmission and Distribution (T&D) networks is discussed in the context of distributed Photovoltaic (PV) generation. The voltage stability of lines and the load carrying capability of buses is analyzed at various PV penetration levels. It is shown that as the PV generation levels increase, an increase in the steady state voltage stability of the system is observed. Moreover, within certain regions of stability margin changes, changes in voltage stability margins of transmission lines are shown to be linearly related to changes in the loading of the lines. Two case studies are presented, where one case study involves a model with eight voltage levels and 784,000 nodes. In one case study, a voltage-stability heat map is used to demonstrate the identification of weak lines and buses.

14 SOLAR ENERGY↗

DOE OSTI2026

Designing a Robust MEA-Based Post-Combustion Carbon Capture Process with Capture Rate Guarantees

This work presents an application of the nonlinear two-stage robust optimization solver PyROS to the model-based design and operation of a monoethanolamine scrubbing process for CO2 capture under epistemic uncertainty. Through this application, risk-averse process designs are successfully obtained for CO2 capture targets ranging from 90% to over 99%. In particular, the risk-averse solutions for CO2 capture targets of up to 98% are shown to be only marginally more expensive than their nominally optimal counterparts. Thus, the results demonstrate the utility of recently developed nonlinear robust optimization approaches for the solution of large-scale chemical process models under uncertainty.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2026

A scalable superconducting nanowire memory array with row–column addressing

Scalable superconducting memory is required for the development of low-energy superconducting computers and fault-tolerant quantum computers. Conventional superconducting logic-based memory cells possess a large footprint that limits scaling; nanowire-based superconducting memory cells, although more compact, have high error rates, which hinders integration into large arrays. Here we report a 4 × 4 superconducting nanowire memory array that is designed for scalable row–column operations and has a functional density of 2.6 Mbit cm −2 . Each memory cell is based on a nanowire loop consisting of two temperature-dependent superconducting switches and a variable kinetic inductor. The arrays operate at 1.3 K, where we implement and characterize multiflux quanta state storage and destructive read-out. By optimizing the write- and read-pulse sequences, we minimize bit errors and maximize operating margins. We achieve a minimum bit error rate of 10 −5 . Here, we also use circuit-level simulations to understand the memory cell’s dynamics, performance limits and stability under varying pulse amplitudes.

Electrical and electronic engineering↗

DOE OSTI2022

Preliminary Thermal-Hydraulic Analysis of the UTA–2 Subcritical Linear Accelerator–Driven System

The National Nuclear Security Administration’s mission includes establishing a reliable supply of 99 Mo without highly enriched uranium. Oak Ridge National Laboratory (ORNL) supports this objective through collaborative research and development with industrial partners. Niowave Inc., a current partner, is currently designing a subcritical linear accelerator-driven system (ADS) and preparing for the US Nuclear Regulatory Commission’s licensing process. Niowave’s system has the potential to efficiently supply medical radioisotopes. The technology includes a superconducting electron accelerator and a pile of both natural and low-enriched uranium (LEU) targets. The process fissions uranium and many valuable isotopes can then be extracted from the targets. Niowave is currently iterating through conceptual and detailed design processes for several system sizes. This report discusses UTA–2, which is at the demonstration stage. UTA–2 will validate numerical modeling results with experimental measurements before progressing to the detailed design of UTA–3, the commercial-sized ADS. The thermal-hydraulic behavior of the UTA–2 core design was numerically investigated using STAR-CCM+, as described in this report. STAR-CCM+, a state-of-the-art computational fluid dynamics (CFD) software that was commercially developed by Siemens, has an extensive user base and a set of validation studies. It is also compliant with the American Society of Mechanical Engineers’ Nuclear Quality Assurance 1 standard. Three cases are investigated in this report. Case 1 quantified the temperature field within the UTA–2 assembly and water tank using only conduction as the method of thermal energy transport. This simplified approach was overly conservative and yielded wetted cladding temperatures above the coolant saturation temperature. In this case, the maximum temperature of the wetted cladding surface of the highest power rod exceeded the saturation temperature of water by 63.8°C. Because of the overly conservative approach taken in Case 1 and its negative subcooled margin, buoyancy-driven natural circulation flow physics were implemented in Case 2. Adding coolant motion significantly distributed the thermal energy of the system through convective heat transfer. This relatively small amount of convective heat transfer significantly reduced system temperatures and increased the subcooled margin from –63.8 to 61.3°C. This margin confirmed that no boiling was expected during normal operation of UTA–2 at 230 W. Case 3 had no additional physics models but considered an overpower event during which the power of each LEU and natural uranium rod was at its respective peak values. This resulted in a study with the total assembly power equal to 176% of the nominal power of 230 W considered in Cases 1 and 2. The resulting natural circulation flows were slightly enhanced. The subcooled margin decreased slightly to 46.3°C, which is still a significant margin to local boiling of the water within the tank. This margin confirmed that no boiling was expected during an abnormal operation of UTA–2 at 406 W.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2023

Real-Time Regional PV Spinning Reserve Estimator with AGC Look-Ahead Windows

Curtailed PV generation is a zero-marginal cost spinning reserve that can be used for a number of active power control services. However, unlike the traditional spinning reserve providers, i.e., fossil-fueled generators, who have well-defined operating characteristics, e.g., available headroom or potential high limit (PHL), PV plants have by nature variable and uncertain operating characteristics. To ensure the effective coordination between PV plants and the system operator during an active power control event, accurate forecasts of the PV PHL are essential. A novel reference-control grouping based scaling method has been proposed by NREL to estimate the PV PHL in real-time. This work further enhances the methodology by: 1) improving the model accuracy through machine learning; 2) considering look-ahead windows introduced by the computation and communication latencies; 3) applying the method to regional spinning reserve estimation. A significant performance improvement, over 99% of estimation error reduction, has been observed based on real-world data collected by CAISO and PV plant operators.

potential high limit↗

DOE OSTI2023

Real-Time Regional PV Spinning Reserve Estimator with AGC Look-Ahead Windows: Preprint

Curtailed PV generation is a zero-marginal cost spinning reserve that can be used for a number of active power control services. However, unlike the traditional spinning reserve providers, i.e., fossil-fueled generators, who have well-defined operating characteristics, e.g., available headroom or potential high limit (PHL), PV plants have by nature variable and uncertain operating characteristics. To ensure the effective coordination between PV plants and the system operator during an active power control event, accurate forecasts of the PV PHL are essential. A novel reference-control grouping based scaling method has been proposed by NREL to estimate the PV PHL in real-time. This work further enhances the methodology by: 1) improving the model accuracy through machine learning; 2) considering look-ahead windows introduced by the computation and communication latencies; 3) applying the method to regional spinning reserve estimation. A significant performance improvement, over 1.6% of estimation error reduction, has been observed based on real-world data collected by CAISO and PV plant operators.

potential high limit↗

DOE OSTI2021

Uniformly Ordered Binary Decision Algorithm for Benchmark Experiment Correlations in Whisper Validation

When performing a validation exercise for determining the upper subcritical limit of a nuclear criticality safety application, an analyst should select and perform a statistical analysis on a population of benchmark experiments that are neutronically similar to the application. The size of this population should be sufficiently large such that the statistical analysis has a high degree of confidence that the bias plus bias uncertainty (calculational margin) has been accurately quantified. A complication arises because many benchmark experiments share common components, leading to correlations in their measured effective multiplication factors. Correlations between benchmark experiments within the population reduces its predictive power. This motivates the need for methods that consider benchmark experiment correlations and ensure adequate statistical significance of results. The Whisper code is a statistical analysis pack- age that incorporates nuclear data sensitivity coefficients from MCNP to assess benchmark experiment similarity and then performs an extreme-value analysis to estimate the bias plus bias uncertainty. The original methodology in Whisper does not consider the effect of benchmark experiment correlations when making this estimation, and this summary proposes the uniformly ordered binary decision algorithm to address this shortcoming. The original methodology in Whisper computes similarity coefficients ck for an application compared to all benchmark experiments in its library and develops weighting factors for a selected population proportional to the ck values. The methodology can be interpreted as statistically emulating a validation exercise for a particular application where the weighting factors may be viewed as the likelihood that an analyst would include a particular benchmark experiment within the population. The effective sample size of the population is the expected or mean number of benchmark experiments in the population. The uniformly ordered binary decision algorithm identifies clusters of correlated benchmark experiments within the population and then computes adjusted weighting factors based on the magnitude of the correlation coefficients within the cluster to compute a reduced effective sample size accounting for the lower information content because of correlations. Benchmark experiments within the cluster are ordered randomly with equal probability and probabilistic decisions are made as to whether a benchmark. experiment within the cluster should treated as redundant with a previous one; if two redundant benchmark experiments are included, then the conservative worst case bias plus bias uncertainty is used and the pair is counted as a single benchmark experiment in the population. Results are provided for HEU solutions in a research version of the Whisper software using benchmark experiment correlations provided by DICE, the Database for the International Criticality Safety Benchmark Evaluation Project (ICSBEP). These show that there can be a significant increase in the bias plus bias uncertainty because the effective sample size is reduced, and therefore the algorithm, needing to meet sample size requirements, expands the benchmark experiment population by accepting less similar benchmark experiments that would have otherwise not been included.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Local structure graph models with higher-order dependence

Local structure graph models (LSGMs) describe random graphs and networks as a Markov random field (MRF)—each graph edge has a specified conditional distribution dependent on explicit neighbourhoods of other graph edges. Centered parameterizations of LSGMs allow for direct control and interpretation of parameters for large- and small-scale structures (e.g., marginal means vs. dependence). Here, we extend this parameterization to account for triples of dependent edges and illustrate the importance of centered parameterizations for incorporating covariates and interpreting parameters. Using a MRF framework, common exponential random graph models are also shown to induce conditional distributions without centered parameterizations and thereby have undesirable features. This work attempts to advance graph models through conditional model specifications with modern parameterizations, covariates and higher-order dependencies.

97 MATHEMATICS AND COMPUTING↗