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DOE OSTI2022

Anisotropic yield models for lattice unit cell structures exploiting orthotropic symmetry

We report numerical homogenization enables efficient computational analysis and design of multiscale structures made of micro-architected materials including lattice unit cells. However, predicting yield is nontrivial because it requires accurate and efficient predictions of the maximum stress inside the homogenized unit cells. To address this challenge, we develop a macroscale anisotropic yield function for micro-architected materials. The yield function depends on the three-dimensional macroscale stress state and the parameters describing a family of micro-architectures, such as the radii of the struts in a lattice unit cell. To ensure accuracy, we determine the maximum stress using three-dimensional continuum finite-element analysis. To ensure efficiency, we construct surrogate models from the aforementioned high-fidelity results for yield prediction. To reduce simulation costs and surrogate modeling complexity, we leverage orthotropic symmetry commonly found in lattice unit cells. In this paper, we provide a thorough presentation of group representations and the systematic procedure to exploit orthotropic domain symmetry in homogenization and surrogate modeling. We illustrate the use of linear homogenization results to predict yield in specific unit cells without further simulations. We furthermore show that surrogate modeling presents a viable option for anisotropic yield prediction in a continuously parametrized family of micro-architectures. More specifically, despite the dimensionality and degree of nonlinearity in the maximum micro von Mises stress within the unit cell, the surrogate models can predict it with less than 5% error at least 90% of the time. Moreover, the largest under-prediction error, which is more critical than the over-prediction error, is typically less than 10%.

42 ENGINEERING↗
DOE OSTI2023

$\text{GPLaSDI}$: Gaussian Process-based interpretable Latent Space Dynamics Identification through deep autoencoder

Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently, machine learning advances have enabled the creation of non-linear projection methods, such as Latent Space Dynamics Identification (LaSDI). LaSDI maps full-order PDE solutions to a latent space using autoencoders and learns the system of ODEs governing the latent space dynamics. By interpolating and solving the ODE system in the reduced latent space, fast and accurate ROM predictions can be made by feeding the predicted latent space dynamics into the decoder. In this paper, we introduce GPLaSDI, a novel LaSDI-based framework that relies on Gaussian process (GP) for latent space ODE interpolations. Using GPs offers two significant advantages. First, it enables the quantification of uncertainty over the ROM predictions. Second, leveraging this prediction uncertainty allows for efficient adaptive training through a greedy selection of additional training data points. This approach does not require prior knowledge of the underlying PDEs. Consequently, GPLaSDI is inherently non-intrusive and can be applied to problems without a known PDE or its residual. Here we demonstrate the effectiveness of our approach on the Burgers equation, Vlasov equation for plasma physics, and a rising thermal bubble problem. Our proposed method achieves between 200 and 100,000 times speed-up, with up to 7% relative error.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Assessing boundary condition and parametric uncertainty in numerical-weather-prediction-modeled, long-term offshore wind speed through machine learning and analog ensemble

To accurately plan and manage wind power plants, not only does the time-varying wind resource at the site of interest need to be assessed but also the uncertainty connected to this estimate. Numerical weather prediction (NWP) models at the mesoscale represent a valuable way to characterize the wind resource offshore, given the challenges connected with measuring hub-height wind speed. The boundary condition and parametric uncertainty associated with modeled wind speed is often estimated by running a model ensemble. However, creating an NWP ensemble of long-term wind resource data over a large region represents a computational challenge. Here, we propose two approaches to temporally extrapolate wind speed boundary condition and parametric uncertainty using a more convenient setup in which a mesoscale ensemble is run over a short-term period (1 year), and only a single model covers the desired long-term period (20 year). We quantify hub-height wind speed boundary condition and parametric uncertainty from the short-term model ensemble as its normalized across-ensemble standard deviation. Then, we develop and apply a gradient-boosting model and an analog ensemble approach to temporally extrapolate such uncertainty to the full 20-year period, for which only a single model run is available. As a test case, we consider offshore wind resource characterization in the California Outer Continental Shelf. Both of the proposed approaches provide accurate estimates of the long-term wind speed boundary condition and parametric uncertainty across the region (R 2 >0.75), with the gradient-boosting model slightly outperforming the analog ensemble in terms of bias and centered root-mean-square error. At the three offshore wind energy lease areas in the region, we find a long-term median hourly uncertainty between 10 % and 14 % of the mean hub-height wind speed values. Finally, we assess the physical variability in the uncertainty estimates. In general, we find that the wind speed uncertainty increases closer to land. Also, neutral conditions have smaller uncertainty than the stable and unstable cases, and the modeled wind speed in winter has less boundary condition and parametric sensitivity than summer.

17 WIND ENERGY↗
DOE OSTI2025

Informed total-error-minimizing priors: Interpretable cosmological parameter constraints despite complex nuisance effects

While Bayesian inference techniques are standard in cosmological analyses, it is common to interpret resulting parameter constraints with a frequentist intuition. This intuition can fail, for example, when marginalizing high-dimensional parameter spaces onto subsets of parameters, because of what has come to be known as projection effects or prior volume effects. We present the method of informed total-error-minimizing (ITEM) priors to address this problem. An ITEM prior is a prior distribution on a set of nuisance parameters, such as those describing astrophysical or calibration systematics, intended to enforce the validity of a frequentist interpretation of the posterior constraints derived for a set of target parameters (e.g., cosmological parameters). Our method works as follows. For a set of plausible nuisance realizations, we generate target parameter posteriors using several different candidate priors for the nuisance parameters. We reject candidate priors that do not accomplish the minimum requirements of bias (of point estimates) and coverage (of confidence regions among a set of noisy realizations of the data) for the target parameters on one or more of the plausible nuisance realizations. Of the priors that survive this cut, we select the ITEM prior as the one that minimizes the total error of the marginalized posteriors of the target parameters. As a proof of concept, we applied our method to the density split statistics measured in Dark Energy Survey Year 1 data. We demonstrate that the ITEM priors substantially reduce prior volume effects that otherwise arise and that they allow for sharpened yet robust constraints on the parameters of interest.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

EXERGETIC: De-Risking Next-Generation Resilient Geothermal Hybrids via At-Scale Evaluation Using Virtual Emulation Digital Twin Environment for Efficient Operation

The DOE-GTO-funded project, award number 5.1.2.12, entitled "EXERGETIC - De-risking Next Generation Resilient Geothermal Hybrids via at-Scale Evaluation Using a Virtual Emulation Digital Twin Environment for Efficient Operation," advances the solution to these challenges by developing and validating a geothermal co-emulation environment implemented at the National Laboratory of the Rockies (NLR)'s Advanced Research on Integrated Energy Systems (ARIES) platform. This framework enables the de-risking of next-generation geothermal and geothermal hybrid systems through high-fidelity modeling, real-time digital emulation, advanced control strategies, and techno-economic assessment. The project focused on geothermal hybrid configurations that integrate geothermal power plants with concentrated solar power and underground thermal energy storage, enabling enhanced efficiency, flexibility, and grid support capabilities. The main goal of this project was the development of a geothermal digital co-emulation environment to demonstrate the technical and economic value of geothermal hybrid systems and their contribution to grid stability and flexibility. The EXERGETIC framework combined physics-based models, controls, and real assets at ARIES, including digital real-time simulators (DRTS), a 20-MW-scale controllable grid interface (CGI), and a 2-MW conventional generator. Detailed transient models were developed for the key subsystems of a hybrid geothermal plant, including parabolic trough solar collectors, reservoir thermal energy storage (RTES), and a binary Organic Rankine Cycle (ORC) power plant. The ORC model explicitly captured thermal inertia and off-design operation and integrated control strategies to dynamically respond to electric load profiles. The models were validated against published experimental and numerical studies, demonstrating strong agreement and confirming the accuracy and robustness of the modeling approach. The resulting digital twin represents geothermal-solar-storage systems at multiple scales (1 MW to 100 MW) and enables realistic emulation of grid-connected operation. The control architecture allows the geothermal resource to provide stable baseload generation, while solar and stored thermal energy supply flexible, dispatchable support during periods of high demand or variable grid conditions. A key contribution of the EXERGETIC project is the demonstration that geothermal hybrid systems can be designed to be active grid assets rather than passive baseload generators. Using the ARIES platform, the digital twin was evaluated under multiple grid scenarios, including load following, voltage support at the distribution level, and frequency response at the transmission level. Results show that hybrid geothermal systems can respond effectively to dynamic grid conditions, providing inertia-like behavior, primary frequency support, and voltage regulation through coordinated control. In addition to the performance and grid services capability analysis of geothermal and hybrid geothermal systems, the EXERGETIC project also focused on scalability and techno-economic analysis of geothermal hybrid plants. In particular, for the scalability analysis, machine-learning (ML)-based surrogate models were trained using data generated from the geothermal digital twin under different grid-connected scenarios and plant capacities. These ML models demonstrated strong interpolation and extrapolation capabilities across plant sizes, accurately reproducing both steady-state and transient responses with very low errors. Regarding the techno-economic analysis, plant performance results were integrated with cost models for hybrid geothermal systems, and the levelized cost of electricity (LCOE) was used as the main economic metric to evaluate system performance across a range of system capacities, solar shares, solar multiples, and storage durations. Results indicate that economies of scale significantly reduce geothermal LCOE as plant capacity increases, with large-scale systems (25-100 MW) achieving substantially lower costs than small plants. Hybridization with solar thermal energy and storage further improves economic performance by increasing capacity utilization and enabling flexible dispatch. In addition, thermal storage plays a critical role in reducing LCOE by maximizing geothermal, solar, and stored energy resources. In summary, the results from this project demonstrate that geothermal hybrid systems represent a promising alternative for increasing the energy conversion efficiency of geothermal technologies, contributing to the preservation of geothermal resources, and supporting the transition of geothermal plants from traditional baseload resources into flexible, resilient, and cost-competitive energy conversion technologies.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Augmenting machine learning of Grad–Shafranov equilibrium reconstruction with Green's functions

This work presents a method for predicting plasma equilibria in tokamak fusion experiments and reactors. The approach involves representing the plasma current as a linear combination of basis functions using principal component analysis of plasma toroidal current densities (J t ) from the EFIT-AI equilibrium database. Then utilizing EFIT's Green's function tables, basis functions are created for the poloidal flux (ψ) and diagnostics generated from the toroidal current (J t ). Similar to the idea of a physics-informed neural network (NN), this physically enforces consistency between ψ, J t , and the synthetic diagnostics. First, the predictive capability of a least squares technique to minimize the error on the synthetic diagnostics is employed. The results show that the method achieves high accuracy in predicting ψ and moderate accuracy in predicting J t with median R 2 = 0.9993 and R 2 = 0.978, respectively. A comprehensive NN using a network architecture search is also employed to predict the coefficients of the basis functions. The NN demonstrates significantly better performance compared to the least squares method with median R 2 = 0.9997 and 0.9916 for J t and ψ, respectively. The robustness of the method is evaluated by handling missing or incorrect data through the least squares filling of missing data, which shows that the NN prediction remains strong even with a reduced number of diagnostics. Additionally, the method is tested on plasmas outside of the training range showing reasonable results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Calibration and Uncertainty Estimation Using the Ensemble Kalman Filter with a Large Subsurface Flow and Transport Model - 20321

At routinely monitored groundwater contamination sites, periodically measured environmental conditions such as groundwater levels and contaminant concentrations are used to inform and confirm a conceptual site model (CSM) and guide the development and calibration of a numerical groundwater flow and transport model. The calibration of groundwater flow and transport models after each measurement (sampling) event can illuminate deficiencies in a CSM, identify areas where additional monitoring is warranted, and predict the behavior of the system to guide decision making. However, manual and automated (e.g. PEST) model calibration tools can be time-consuming and computationally expensive to implement after each sampling event. Perhaps as a result, such calibration tools generally utilize all available monitoring data simultaneously rather than sequentially assimilating monitoring data one sampling event at a time as the results from sampling become available. A more real-time data assimilation approach may reduce parameter uncertainty, quantify the value of additional monitoring data, and produce a usable model more quickly and with less effort. To mitigate the potential time-consuming aspects of manual and widely applied automated calibration techniques, a data assimilation algorithm called the ensemble Kalman filter (EnKF) was evaluated as a relatively efficient method of model calibration and uncertainty assessment via the sequential integration of monitoring data into a model. The EnKF was able to successfully and efficiently assimilate monitoring and modeling data to calibrate a complex flow and transport model at a real-world site with significant subsurface heterogeneity, uncertainty, and 12 years of monitoring data (over 4,000 individual measurements of groundwater levels and over 2,500 measurements of contaminant concentrations). Starting with an uncalibrated model data from annual sampling events were sequentially assimilated, and the resultant predication errors and estimated parameter uncertainties were tracked. After all monitoring data were assimilated, both flow and transport residuals at the end of the EnKF process were comparable to those produced via a concurrent PEST calibration effort but required fewer model simulations. Both uncertainty and prediction errors decreased over time. In a real-time application, the adequacy of the model could be assessed after each sampling event. The benefits of such a real-time approach to utilizing monitoring data include reduced costs (in the form of model updates or site characterization efforts), early flagging of possible errors in the CSM, and a reduced risk of overfitting and corresponding increased confidence in model predictions. This tool may be particularly useful compared to other calibration techniques (e.g. manual, PEST) when model runtimes are long, calibration parameters are many, or parameter uncertainty is large. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

ABACUSSUMMIT : a massive set of high-accuracy, high-resolution N -body simulations

We present the public data release of the AbacusSummit cosmological N-body simulation suite, produced with the Abacus N-body code on the Summit supercomputer of the Oak Ridge Leadership Computing Facility. Abacus achieves $\mathcal {O}(10^{-5})$ median fractional force error at superlative speeds, calculating 70M particle updates per second per node at early times, and 45M particle updates per second per node at late times. The simulation suite totals roughly 60 trillion particles, the core of which is a set of 139 simulations with particle mass $2\times 10^{9}\, h^{-1}\, \mathrm{M}_\odot$ in box size $2\, h^{-1}\, \mathrm{Gpc}$. The suite spans 97 cosmological models, including Planck 2018, previous flagship simulation cosmologies, and a linear derivative and cosmic emulator grid. A subsuite of 1883 boxes of size $500\, h^{-1}\, \mathrm{Mpc}$ is available for covariance estimation. AbacusSummit data products span 33 epochs from z = 8 to 0.1 and include light cones, full particle snapshots, halo catalogues, and particle subsets sampled consistently across redshift. AbacusSummit is the largest high-accuracy cosmological N-body data set produced to date.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Physics-Informed and Data-Driven Prediction of Residual Stress in Three-Dimensional Machining

Efficient and reliable prediction of machining-induced residual stress (RS) is a key requirement for truly integrated computational materials engineering (ICME). Currently available process modeling approaches, including empirical, analytical, and numerical methodologies lack predictive power and require substantial calibration and validation data. Moreover, most model-based approaches consider only two-dimensional (2D) (i.e., orthogonal), cutting processes. Meanwhile, industrial processes such as milling, turning, and drilling are inherently three-dimensional (3D). The present work attempts to bridge the gap between 2D and 3D through careful consideration of the process physics, including geometric, kinematic, and size-effect constraints to realize robust prediction of how RS develops in 3D machining. Using a novel in-situ experimental technique and digital image correlation (DIC) to determine equivalent Hertzian contact widths, contact pressures, and friction coefficients, the proposed methodology leverages a discretized conversion algorithm that includes multi-pass shakedown effects. This paper presents a semi-analytical model to predict machining-induced RS in 3D turning operations, which are used representatively for 3D processes more generally. Rather than follow a ‘brute force’ 3D FEM approach or conduct countless experiments to train a purely data-driven machine learning algorithm, the proposed approach builds on previous 2D modeling work. Through careful consideration of the process physics, including complex geometry/kinematic considerations of 3D turning, the authors demonstrated an experimentally calibrated approach, as well as validation based on published RS data. Model predictions and previously published measurement data of RS depth profiles for turning of Inconel 718 were compared for a range of process parameters. Correlation between the proposed 3D model and validation data was found to be within the margin of experimental error for most conditions. The proposed model appears to capture the overall behavior of 3D RS depth profiles with acceptable accuracy, particularly the key metrics of near-surface stress, peak stress magnitude and location, as well as overall stress profile depth. This report presents a physics-informed, data-driven approach for efficient calibration of a 2D model for machining-induced RS through DIC analysis of in-situ characterized subsurface displacement fields.

42 ENGINEERING↗
DOE OSTI2020

Super-resolution surface slope metrology of x-ray mirrors

We present experimental, analytical, and numerical methods developed for reconstruction (deconvolution) of one-dimensional (1D) surface slope profiles over the spatial frequency range where the raw data are significantly perturbed due to the limited resolution of the measurement instrument. We characterize the spatial resolution properties of a profiler with the instrument's transfer function (ITF). To precisely measure the ITF, we apply a recently developed method utilizing test surfaces with 1D linear chirped height profiles of constant slope amplitude. Based on the results of the ITF calibration, we determine parameters of an analytical model for the ITF that is used in the original reconstruction software. Here, we treat surface slope metrology data obtained with the Optical Surface Measuring System (OSMS), using as a sensor an electronic autocollimator (AC) ELCOMAT-3000. The spatial resolution of the OSMS is limited by the size of the AC light-beam-collimating aperture. For the purposes of this investigation, the OSMS is equipped with a circular aperture with a diameter of 2.5 mm. This is a typical arrangement of most AC-based slope profilers developed for surface slope metrology of state-of-the-art x-ray mirrors. Using the example of surface slope metrology of two state-of-the-art elliptically shaped x-ray focusing mirrors, we demonstrate that the developed data reconstruction procedure allows us to significantly improve the accuracy of surface slope metrology with the OSMS over the spatial wavelength range from ~1.6 mm to 7 mm. Thus, the amplitude of the quasi-periodic error characteristic of the deterministic polishing process used appears to be higher by a factor of~2 than is apparent from the rough metrology data. Underestimation of the surface slope errors in this spatial wavelength range can lead to serious errors in the expected performance of x-ray mirrors in synchrotron beamlines, especially at modern light sources utilizing coherent x rays, where the perturbations can lead to increased speckle-like intensity variation.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Dynamics of qudit gates and effects of spectator modes on optimal control pulses

Qudit gates for high-dimensional quantum computing can be synthesized with high precision using numerical quantum optimal control techniques. Large circuits are broken down into modules and the tailored pulses for each module can be used as primitives for a qudit compiler. Application of the pulses of each module in the presence of extra modes may decrease their effectiveness due to crosstalk. In this paper, we address this problem by simulating qudit dynamics for circuit quantum electrodynamics systems. As a test case, we take pulses for single-qudit swap gates optimized in isolation and then apply them in the presence of spectator modes each of which are in Fock states. We provide an experimentally relevant scaling formula that can be used as a bound on the fidelity decay. Our results show that frequency shift from spectator mode populations has to be ≲ 0.1 % of the qudit's nonlinearity in order for high-fidelity single-qudit gates to be useful in the presence of occupied spectator modes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Ensemble Effects on Hydroxide Bond Dissociation Free Energies in Polyoxovanadate Clusters

Understanding structure-property relationships is foundational to numerous modern chemistries, such as proton-coupled electron transfer (PCET). However, an experimentally measured property is the result of the behavior from an ensemble of molecules. Neglecting ensemble effects, especially under complex chemical environments, may obfuscate these relationships and lead to discrepancies between theory and experiment. In this work, we demonstrate the impact of configurational entropy and local chemical environments on hydroxide bond dissociation free energies [BDFE- (O−H)] for a set of polyoxovanadate nanoclusters, at ambient conditions. The O−H bond strengths are investigated via density functional theory (DFT) coupled with statistical thermodynamic analysis and bilinear modeling, and compared with previous experimental results on the same systems, namely electrochemical solutions of: [V 6 O 13−x (OH) x (TRIOL R ) 2 ] −2 (x = 2, 4, 6; R = NO 2 , Me) and [V 6 O 11−x (OMe) 2 (OH) x (TRIOL NO 2 ) 2 ] −2 (x = 2, 4). Interestingly, we find that ensemble effects, even at room temperature, can account for a significant portion of the BDFE(O−H) trend with the degree of reduction via H atom binding, which cannot be fully captured by single-structure, static DFT calculations. Moreover, we find that the ensemble effects may be replicated statistically, requiring only enumeration of energetically accessible H-binding sites. With the ensemble effects resolved, we present a simple bilinear model to reconcile remaining biases between experiment and ensemble-informed theory, which corelate with clusterspecific electronic environment differences. The bilinear model achieves outstanding accuracy vs experiments with a root-mean squared error of 0.4 kcal/mol. Finally, based on the physicochemical characteristics of hydrogen interaction with polyoxometalates, we present a simple methodology that captures the BDFE(O−H) trend while dramatically reducing required DFT calculations by 98% and achieving accuracy within 1 kcal/mol. Overall, this work elucidates the roles and structural origins of configurational entropy and chemical effects on polyoxometalate hydroxide bond energies, with potential applicability to various atomically precise metal oxide systems. Importantly, it introduces models for rapid and highly accurate property calculations in connection with experiments.

Cluster chemistry↗
DOE OSTI2023

Multiphysics Simulations of MSRE with NEAMS Thermal Hydraulics Tools

This report documents the benchmarks being developed and simulations performed using tools and codes developed under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, utilizing MSRE experimental data. In FY23, three main work scopes were investigated under the NEAMS MSR work package at ANL. The first scope investigated the Griffin-SAM coupling model for simulating the pump startup transient experiment of MSRE. The analyses start with a simple model (single-channel, single-lattice), gradually adding more details (multi-channel, full-core) into the model. The results show that the reactivity loss curve is very sensitive to the axial boundary conditions and the radial core discretization. The simple model can predict a similar reactivity trend as that of the more sophisticated model, which is likely due to error cancellation. Accurately modeling the axial boundary condition may further improve the reactivity trend but would require significant efforts to generate the mesh of the MSRE inlet and upper plenum. The core channel radial discretization for the Griffin-SAM coupled model also depends on the flow distribution. Given the complex geometry in the inlet plenum, the flow distribution needed to be calculated from CFD analysis, which was performed using the NekRS code. This analysis employed a MSRE CAD model developed by Copenhagen Atomics. The CAD model was disassembled to keep the inlet plenum region only, which was subsequently cleaned and modified so that the mesh generated is under the memory limit. The results are merged to a few radial regions to show that the flow rate is highest in the central region. This would be useful for future improvement of the Griffin-SAM coupling model of the MSRE core. The last task investigated is tritium transport modeling using the standalone SAM code. This task aimed to initiate the effort to demonstrate and validate the tritium transport model implemented in SAM. The preliminary investigation employed an MSRE model consisting of the primary loop. Three tritium transport pathways were examined including the retention in the graphite, the permeation through the HX tube wall, and the removal from the off-gas system. The results compare well with the MSRE data, but improvements are still needed on the initial conditions (i.e., the present state may not have reached equilibrium), the boundary conditions, the off-gas system modeling, and a better numerical strategy to reach the equilibrium state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Application of Modified Meshgraphnets for Subsurface Prediction during CO2 Sequestration

In the face of the increasingly dire consequences of anthropogenic climate change, capturing and storing carbon dioxide is paramount. However, several impediments exist to the safe and effective subsurface storage of CO2, such as cost of transport, identification of suitable sites for subsurface storage, and assessment of long-term risk from storage in subsurface aquifers. Accurate subsurface modeling is necessary to ensure that CO2 storage is both safe and effective. Still, such modeling has traditionally required either substantial time and computational power (numerical simulation) or a substantial amount of pre-existing data for training (machine learning models). Additionally, these models lack flexibility in dealing with both changes in discretization of the input data and generalizability beyond the data on which they are trained. In order to address these issues, this research applies graph neural networks (GNNs) to predict subsurface saturation and pressure during CO₂ injection in a model of the Illinois Basin-Decatur Project (IBDP). GNNs provide a flexible, intuitive method for representing and manipulating complex unstructured data, which is often found in many practical domain problems such as fluid flow and subsurface characterization. These unstructured grids are easily represented in GNNs by representing spatially-localized features such as permeability, porosity, saturation, and pressure as nodes in a graph and relationships between these properties as edges connecting these nodes. This research applies a specific GNN model called MeshGraphNets (MGN) to model the change in CO2 saturation and pressure over a 50-month time period (36 months of injection, 14 months post-injection). The MGN model leverages a message passing process that allows the network to learn both the spatial and temporal dynamics of this system simultaneously. Additionally, training on a limited dataset (64 realizations, 20 time points each) resulted in a high degree of accuracy in saturation prediction both within the same timeframe as the training (20 months, 0.039 average RMSE) and when projecting out to the end of injection (36 months, 0.053 average RMSE). Temporal predictions such as those generated by MGNs and other similar models are prone to accumulated error over time; in order to address this, a multi-step rollout (MSR) training process was applied to calculate training loss. This method mimics the forward prediction during inference by “rolling out” multiple time points in a single training step using the previous prediction as input to the MGN model. By calculating the loss several time steps forward from the current prediction, the model is forced to find a more stable state over time. Application of MSR to the MGN model resulted in an average 15% reduction in inference error over time during forward prediction. This study showcases the immense potential of GNNs as a game-changing methodology for predicting pressure and saturation evolution in CCS projects, ultimately paving the way for more sustainable and effective carbon storage solutions. Presentation prepared for the 2024 AiChE Annual Meeting, October 27 to November 1 2024, San Diego, CA.

Holcomb, Paul↗
DOE OSTI2024

Relating flow resistance to equivalent roughness

Describing flow resistance using the physical properties of an underlying surface is a recalcitrant problem in overland flow models. If discharge measurements are available, an equivalent roughness (e.g., Manning’s n) can be calibrated to represent the effects of surface properties within the domain with a single numerical value. Alternatively, the flow resistance can be estimated from discharge and velocity measured at a point, typically a runoff plot outlet. However, such experimental estimates are often inconsistent with the equivalent roughness determined from calibration to discharge, even if both derive from the same dataset. For example, if Manning’s equation is used to parameterize flow resistance, the Manning’s n obtained by calibrating a model to discharge differs from the value of n calculated from measured flow and velocity at the hillslope outlet. Here, this discrepancy is resolved by deriving a correction factor relating experimentally-determined flow resistance to the equivalent roughness. The derived correction factor is tested for four commonly-used resistance formulations using 129 rainfall simulator experiments. The correction factor is necessary to reproduce measured velocities, and yields minor improvements in discharge prediction. Plain Language Summary: Accurate runoff prediction is needed for land and water management in dryland regions, where sporadic and limited rainfall necessitate efficient water use and drought mitigation strategies. The skill of runoff models is known to be hindered by out ability to estimate flow resistance, which is the quantity that describes how energy is lost from flowing water to the underlying surface. Typically, models represent flow resistance with an equivalent roughness, e.g., Manning’s n, that is adjusted until the model can reproduce available discharge observations at watershed scale. However, the flow resistance measured in plot-scale experiments (1–10 m) often exceeds equivalent roughness coefficients by a factor of 10. This means that the direct use of plot-scale experimental data to parameterize runoff models could cause errors in discharge and runoff velocity predictions. Here, we resolve these differences by deriving an analytic correction factor that relates flow resistance to the equivalent roughness required for models to reproduce experimental velocity and discharge data. This correction factor is tested using rainfall simulator data from 129 experiments performed in the US Southwest covering a wide range of precipitation intensities, soil textures and vegetation types. Use of the correction factor substantially improves model prediction of flow velocity, which is needed for reproducing the timing of flood events and the estimation of erosion.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Assessing the reliability of medical resource demand models in the context of COVID-19

Abstract Background Numerous medical resource demand models have been created as tools for governments or hospitals, aiming to predict the need for crucial resources like ventilators, hospital beds, personal protective equipment (PPE), and diagnostic kits during crises such as the COVID-19 pandemic. However, the reliability of these demand models remains uncertain. Methods Demand models typically consist of two main components: hospital use epidemiological models that predict hospitalizations or daily admissions, and a demand calculator that translates the outputs of the epidemiological model into predictions for resource usage. We conducted separate analyses to evaluate each of these components. In the first analysis, we validated various hospital use epidemiological models using a recent validation framework designed for epidemiological models. This allowed us to quantify the accuracy of the models in predicting critical aspects such as the date and magnitude of local COVID-19 peaks, among other factors. In the second analysis, we evaluated a range of demand calculators for ventilators, medical gowns, and COVID-19 test kits. To achieve this, we decoupled these demand calculators from the underlying epidemiological models and provided ground truth data for their inputs. This approach enabled a direct comparison of the demand calculators, comparing them against each other and actual usage data when available. The code is available athttps://doi.org/10.5281/zenodo.13712387. Results Performance varied greatly across the epidemiological models, with greater variability in COVID-19 hospital use predictions than for COVID-19 deaths as analyzed previously. Some models did not have any peaks. Among those that did, the models under-estimated date of peak approximately as often as they over-estimated, but were more likely to under-estimate magnitude of peak, with typical relative errors around 50%. Regarding demand calculator predictions, there was significant variability, including five-fold differences in predictions for gown models. Validation against actual or surrogate usage data illustrated the potential value of demand models while demonstrating their limitations. Conclusions The emerging field of demand modeling holds promise in averting medical resource shortages during future public health emergencies. However, achieving this potential necessitates focused efforts on standardization, transparency, and rigorous model validation before placing reliance on demand models in critical public health decision-making.

Medical Informatics↗
DOE OSTI2025

Simulations of the churning mode: Toroidally symmetric plasma convection and turbulence around the X-points in a snowflake divertor

Using a reduced MHD model, extended to include field-aligned thermal conduction, we present numerical simulations of the churning mode (CM): a toroidally symmetric, non-linear plasma vortex in the vicinity of the null points in a snowflake (SF) divertor [D. D. Ryutov et al., Phys. Scr. 89, 088002 (2014)]. Simulations are carried out across a range of inter-null separations, d xx ⁠, and inter-null orientations, θ⁠, primarily in conditions relevant to the MAST-U tokamak. We find that, when d xx is small, the CM induces additional transport across the X-points when β pm ≳8%, where β pm is the ratio of the plasma pressure in the null region to poloidal magnetic pressure at the midplane. This transport also increases approximately linearly as d xx is reduced. A diffusive model of this transport is shown to predict the total transport across the null points, where diffusion coefficients of up to ∼ 10 2 m 2 s −1 centered on a small region around the X-points are used. However, the CM also results in significant changes to the flux surfaces in the null region, which is not captured by this diffusive model. The changes in magnetic geometry mean the fractional exhaust power delivered to each divertor leg is highly sensitive to β pm ⁠, d xx ⁠, and θ⁠. For small values of θ⁠, the CM can induce a change in topology, redirecting exhaust power from a secondary divertor leg on the high field side to one on the low field side. Similar behavior is found in the fraction of exhaust power going to the inner and outer divertor. Such changes in the flux surfaces may not be captured by Grad–Shafranov solvers and so may be a source of error in the magnetic reconstruction of SF experiments. We consistently find that the fractional exhaust power going to a secondary divertor leg on the high field side is small, consistent with SF experiments.

Computer simulation↗
DOE OSTI2023

Code Coverage Status of ARC Code-DIF3D

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. DIF3D plays a pivotal role in the ARC system as the primary homogenized assembly neutronic calculation methodology for fast reactor problems. Over its 40 years history, ARC software usage with DIF3D has been applied to numerous fast and thermal spectrum reactor analysis projects with good to excellent comparison against experiments. With continued improvement of computation resources, many of the geometry modeling capabilities in DIF3D that were primarily used in low order schemes are not really needed anymore. Today, the diffusion and transport capabilities of DIF3D-VARIANT are primarily used in the reactor design process with some scattered usage of DIF3D-FD and DIF3D-Nodal. In recent work, the DIF3D software verification was completed for DIF3D-FD and DIF3D-VARIANT on the geometry options used in the Versatile Test Reactor project. While we can be confident that these capabilities of DIF3D are well used and thus trusted, it does not demonstrate that all possible input options of DIF3D are actually working, but just those that were tested as part of VTR are and that they are correct. Thus, the purpose of the present work is to identify a set of test problems for DIF3D and assess the code coverage of DIF3D for those test problems. The goal is to document what parts of the existing DIF3D code are touched by the set of test problems and which are not. Because the verification work done on DIF3D-VARIANT and DIF3D-FD was focused on the most common uses of DIF3D for fast reactor analysis, the code coverage assessment of those capabilities is the highest priority. This will ensure that nothing is being missed by the existing verification test problems that DIF3D relies upon. The DIF3D-Nodal capability will also be inspected for code coverage as part of this work to further ensure that regular regression testing of DIF3D will trap any likely errors the end user might experience with the DIF3D software. The code coverage analysis of DIF3D was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of DIF3D. The detailed coverage tables are given for each submodule of DIF3D separately, and for the submodules which are primarily developed for DIF3D, most of the source files could be at least partially touched. Most of the uncovered parts/files could be easily ignored, because they are either for error message and debugging output or obviously not needed by DIF3D. Out of the entire source codes of DIF3D, only a few uncovered modules deserve further investigation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗