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DOE OSTI2024

Efficient estimation of the modified Gromov–Hausdorff distance between unweighted graphs

Abstract Gromov–Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov–Hausdorff distance is equivalent to solving an NP-hard optimization problem, deeming the notion impractical for applications. In this paper we propose a polynomial algorithm for estimating the so-called modified Gromov–Hausdorff (mGH) distance, a relaxation of the standard Gromov–Hausdorff (GH) distance with similar topological properties. We implement the algorithm for the case of compact metric spaces induced by unweighted graphs as part of Python library , and demonstrate its performance on real-world and synthetic networks. The algorithm finds the mGH distances exactly on most graphs with the scale-free property. We use the computed mGH distances to successfully detect outliers in real-world social and computer networks.

Oles, Vladyslav (ORCID:0000000188727463)↗

DOE OSTI2026

A Multi-Region SEIR Model Incorporating Inter-County Mobility and Time-Dependent Transmission Dynamics: Application to COVID-19 Disease Outbreak Data in North Carolina.

Classical infectious disease compartmental models typically do not incorporate spatial heterogeneity or mobility. We develop a multi-region susceptible-exposed-infected-recovered (SEIR) model in which disease dynamics are coupled via inter-region mobility and the transmission rate is both region and time dependent. We calibrate the model using rolling averages of daily COVID-19 data in all 100 North Carolina counties. Mobility parameters are prescribed using daily inter-county commuter data. The number of transmission rate parameters is substantially reduced by hypothesizing that the dynamics correlate with county-level population density. Parameter estimation is carried out using several objective functions with error terms at different scales. An additive combination of least squares error at the county-level and the state-level, along with a quadratic transmission rate polynomial, yields the lowest overall error at both spatial scales. The calibrated model is used to simulate regional effects of perturbing disease transmission rates in adjacent counties and to illustrate effects of the state’s mobility infrastructure on disease dynamics and spread for a new disease outbreak.

COVID-19 modeling↗

DOE OSTI2024

Data-Driven Surrogate Modeling with Microstructure-Sensitivity of Viscoplastic Creep in Grade 91 Steel

Abstract To support the development of advanced steel alloys tailored to withstand extreme conditions, it is imperative to account for the mechanical performance of components, while considering the influence of local microstructure on the macroscopic response. To this end, this study focuses on the development of microstructure-sensitive constitutive models for the mechanical response of Grade 91 steel exposed to extreme thermo-mechanical environments. Polynomial chaos expansion (PCE) surrogates are used to emulate high-fidelity polycrystal simulations of the viscoplastic response of Grade 91 steel as a function of the microstructure fingerprint (e.g., dislocations and precipitates). To cover a wide temperature–stress domain, two separate PCE surrogates—one that captures softening and the other that captures hardening behavior—are combined using another (sparse) Gaussian process regression model. The resulting constitutive creep surrogate model is integrated within the MOOSE finite element framework to simulate the intricate effects of microstructure, in particular MX-phase precipitates, on a component with a graded microstructure. Surrogate sensitivity analysis is applied to quantify the relevant impact of spatially varying microstructure on the creep response in a test-case involving a Grade 91 alloy with a prototypical weld.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Coupling Approaches with Non-matching Grids for Classical Linear Elasticity and Bond-based Peridynamic Models in 1D

Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal grids usually require a finer resolution than local grids. In that case, it is often convenient to resort to interpolation operators so that models can exchange information in the overlap regions when nodes from the two grids do not coincide. This paper studies three existing coupling approaches, namely 1) a method that enforces matching displacements in an overlap region, 2) a variant that enforces a constraint on the stresses instead, and 3) a method that considers a variable horizon in the vicinity of the interfaces. Further, the effect of the interpolation order and of the grid ratio on the performance of the three coupling methods with non-matching grids is carefully studied on one-dimensional examples using polynomial manufactured solutions. The numerical results show that the degree of the interpolants should be chosen with care to avoid introducing additional modeling errors, or simply minimize these errors, in the coupling approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Impact of U-10Mo HALEU fuel element tolerances on the Massachusetts Institute of Technology reactor safety and operational performance – Thermal hydraulics

The U.S. is coordinating efforts for the conversion of six U.S. High Performance Research Reactors (USHPRR) including one critical facility from highly enriched uranium (HEU) to low-enriched uranium (LEU). In order to continue the mission of these reactors, including the Massachusetts of Institute of Technology Reactor (MITR), and achieve similar performance, high-assay low-enriched uranium (HALEU) with a high-density metallic alloy of uranium with 10 wt% molybdenum (U-10Mo) is being evaluated. The impact of the fabrication specification and tolerances was assessed following the preliminary design of the MITR LEU fuel elements using the U-10Mo monolithic alloy. This research focuses on the analysis of fabrication specification impact on thermal hydraulics (TH) characteristic of the MITR LEU core as a function of the variation of the relevant fuel specification parameters (e.g., coolant channel gap thickness, fuel plate thickness, etc.). The analyses are performed based on an all-fresh LEU fuel conversion plan identified in a preliminary safety analysis report submitted to the Nuclear Regulatory Commission. The reactor power margin to the onset of nucleate boiling (ONB) is assessed under the limiting safety system settings (LSSS), where a scram occurs, to ensure there is sufficient margin to the reactor safety limit, which is defined by the onset of flow instability that occurs after the ONB. The best estimate plus uncertainty approach is employed to analyze this TH characteristic, which yields realistic results while maintaining adequate conservatism, utilizing a statistical uncertainty propagation method with the STAT7 code. The TH characteristic is analyzed as a function of the variability of the specification parameters resulting from the fabrication process. The main findings of this study show that the MITR core can meet the TH safety and operational requirements at the all-LEU initial core startup (cycle 1), selected transition cycles (most reactive cycle and most limiting cycle: cycle 3 and 5, respectively) and equilibrium (cycle 14) cores under all limiting fabrication parameter combinations considered. In addition, the analyses show that the dependency of the core power margin to ONB on those specification parameters that have the most direct impact on TH performance is non-linear but monotonically decreasing within the specification tolerances. The third order polynomial fit curves are reported in detail for selected limiting cases and can serve as a powerful tool for future MITR fuel management in cases such as when HALEU supply is established that may allow additional cycle length or other operational benefits.

Conversion↗

DOE OSTI2025

Hybrid data-driven cement-stabilized soil design: An integration of machine learning, multi-objective optimization, and life cycle assessment

Soil stabilization is crucial in geotechnical engineering, yet conventional methods are often time-consuming, resource-intensive, and environmentally unsustainable. Despite growing interest in Machine Learning (ML) and optimization tools for mix design, few studies integrate these methods with decision-making techniques and environmental assessment to support practical implementation. This study proposes a hybrid data-driven framework for predicting strength, optimizing mix compositions, and evaluating environmental impacts via life cycle assessment of cement-stabilized soft soils. Six ML models were evaluated, and the top-performing eXtreme Gradient Boosting (XGB) model was further improved using the Grey Wolf Optimizer (GWO). The optimized XGB-GWO model, integrated with a polynomial cost function, served as the objective function in a multi-objective optimization problem solved via the Non-Dominated Sorting Genetic Algorithm II (NSGA-II), with final mix selection guided by the entropy-weighted TOPSIS method. Validation through a case study produced mix designs offering superior strength-cost trade-offs, with the optimal mix achieving 2243.2 kPa unconfined compressive strength and a 16.07 % reduction in carbon emissions compared to the highest-cost design. In conclusion, this study offers a sustainable, scalable approach to soil stabilization and supports informed decision-making in construction.

Life cycle assessment↗

DOE OSTI2025

Boosting efficiency and reducing graph reliance: Basis adaptation integration in Bayesian multi-fidelity networks

The computational cost of high-fidelity numerical models makes outer-loop analysis, which requires repeated interrogation of the model such as uncertainty quantification, computationally demanding. Multi-fidelity methods, which construct a surrogate model using data from an ensemble of models of varying cost and accuracy, can substantially reduce the cost of outer-loop analysis. However, these methods can be difficult to apply when the model ensemble does not admit a clear hierarchy a priori and the correlations between models are low. Consequently, in this paper, we present a multi-fidelity method that leverages dimension reduction to enhance the correlation between models, thereby reducing the amount of data needed to train a surrogate from an unordered ensemble of models. Our method utilizes basis adaptation to build low-dimensional polynomial chaos expansions of each model and employs Multi-fidelity Networks to encode the relationships among models. We show that the resulting method exhibit two notable advantages over its counterpart: (1) enhanced accuracy (both reduced bias and variance); and (2) reduced dependency on the graph structure encoding relationships among models. We demonstrate the approach on an analytical test problem and a challenging finite element model for a spent nuclear fuel. Our method produces a surrogate model that is significantly more accurate than either a single-fidelity surrogate or a multi-fidelity surrogate constructed without basis adaptation.

42 ENGINEERING↗

DOE OSTI2024

Spectral scheme for atomic structure calculations in density functional theory

In this study, we present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial interpolation on a Chebyshev grid, with derivative operators approximated using the Chebyshev differentiation matrix, and integrations using Clenshaw-Curtis quadrature. We demonstrate the accuracy and efficiency of the scheme through spin-polarized and unpolarized calculations for representative atoms, while considering local, semilocal, and hybrid exchange-correlation functionals. In particular, we find that $\mathcal{O}$(200) grid points are sufficient to achieve an accuracy of 1 microhartree in the eigenvalues for optimized norm conserving Vanderbilt pseudopotentials spanning the periodic table from atomic number Ζ = 1 to 83.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2026

A projection method for particle resampling

Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase-space due to their better scalability than continuum approaches with respect to dimension. Complex processes collectively referred to as particle noise hamper long time simulations with particle methods. One approach to address this problem is particle mesh adaptivity, or remapping, known as particle resampling and remeshing. Here, this work introduces a resampling method that projects particles to and from a (finite element) function space. The method is simple, using standard sparse linear algebra and finite element techniques, and it preserves all moments up to the order of a polynomial represented exactly by the continuum function space. It is distinguished from most other mesh-based methods in that new particle positions and number are decoupled from the mesh, allowing particle and continuum meshes to be adapted relatively independently. While this work is developed with structured particle and continuum phase-space grids on 1X + 1V Vlasov-Poisson models of Landau damping and two-stream instability, the method is well-suited to unstructured grids. Stable long time dynamics are demonstrated up to time T = 500. Reproducibility artifacts and data are publicly available.

Kinetic methods↗

DOE OSTI2026

Surrogate model evaluation and building energy benchmarking for commercial buildings

Building energy consumption benchmarking involves challenges associated with various energy patterns for different building types; heating, ventilating, and air-conditioning (HVAC) system types; and climates. Given significant variation in energy use patterns, accurate prediction of long-term energy use using surrogate models remains challenging. Multiple linear regression (MLR) is commonly used for building energy benchmarking because of its simple structure; however, it lacks accuracy compared to other black-box models. Although many studies have compared surrogate models and offer guidance on model selection based on metrics, they do not provide detailed analysis on improving the surrogate model accuracy. In this paper, we implement a surrogate model using polynomial ridge regression (i.e., MLR with interaction terms combined with ridge regularization) for small office and retail strip mall buildings across six HVAC system types and all climate zones, for electricity and natural gas in baseline and proposed scenarios. A simulation workflow is developed using OpenStudio TM /EnergyPlus TM to generate simulation data using measures over a wide range of efficiency inputs. Enhancements based on statistical insights are used for improving the model accuracy using filters, input transformations, and change points. Surrogate models achieved average coefficient of variation of the root mean squared error (CVRMSE) values of 2.17, 1.06, 2.05, and 3.26 for proposed electricity, proposed natural gas, baseline electricity, and baseline natural gas, respectively, with enhancements reducing CVRMSE by an average of 14.9% across all combinations. We provide model interpretation via Shapley additive explanations to determine which input variables most influence energy consumption and provide supportive arguments for enhancements.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2025

Dual-season thermal energy storage-integrated heat pump system for load shifting: experiments, modeling and nationwide analysis

Here, this paper proposes and validates a dual-season thermal energy storage-integrated heat pump (TES-HP) system that shifts building electric load in both cooling and heating modes using a single phase-change TES. The design uses the TES as a heat sink for the condenser in summer and a heat source for the evaporator in winter, thereby reducing on-peak electric demand while ensuring compatible with existing air-distribution systems. A 14-kW TES-HP prototype with six operating modes and novel refrigerant charge management strategies was experimentally tested under varied conditions. Subsequently, data-driven polynomial performance curves were developed and validated against experiments, then coupled with a phase change material (PCM) model and a calibrated building model within a rule-based controller. Single-day case studies demonstrated effective on-peak demand reduction while maintaining thermal comfort. During cooling, hourly power was lowered by up to 1.5 kW; in heating, average hourly power decreased from over 3.5 kW to 1.8 kW, compared to an HP-only system, achieving 64.5 % load shifting, and the need for resistance heating was eliminated. Seasonal simulations showed typical on-peak electricity savings of 25–35 % in cooling and 40–65 % in heating, with the largest benefits on the hottest and coldest days. Extended response-surface analysis and nationwide mapping quantified load shifting as functions of ambient and TES temperatures, revealing a seasonal trade-off in TES phase-change temperature. These results demonstrate the TES-HP system as a practical and scalable solution for grid-interactive buildings that reduces on-peak demand and electricity use while maintaining thermal comfort and enhancing grid flexibility and reliability.

Grid-interactive buildings↗

DOE OSTI2026

Parametric reduced order models for graded lattice structures

Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. Here, to address these challenges, this paper introduces a novel Efficient Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to efficiently manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be efficiently assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method's modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to biomedical engineering.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Stable isotope equilibria in the dihydrogen-water-methane-ethane-propane system. Part 2: Experimental determination of hydrogen isotopic equilibrium for ethane-H2 from 30 to 200 °C and propane-H2 from 75 to 200 °C

The stable isotopic compositions of light n-alkanes, including methane, ethane, and propane, are often used to identify the sources and thermal maturity of natural gas samples. Though stable isotopic compositions of these molecules are commonly assumed to be controlled by kinetic isotope effects, recent studies have proposed both carbon and hydrogen isotopic equilibrium may also occur in some samples. Assessing whether samples are in isotopic equilibrium requires knowledge of light alkane equilibrium fractionation factors over geologically relevant temperatures for formation and storage (up to ∼300 °C). In this study, we report experimental results of hydrogen isotopic equilibrium between ethane and H2 from 30 to 200 °C and propane and H2 from 75 to 200 °C. We compare these results with high-level theoretical calculations and provide a preferred polynomial fit to describe equilibrium fractionation factors. Comparison of these fractionation factors with a compilation of ∼500 compiled environmental gas samples supports the proposal that many (∼50%) of these natural gas samples exhibit hydrogen isotopic compositions consistent with having formed in or attained methane-ethane-propane hydrogen isotopic equilibrium over geologically relevant temperatures for formation and storage (50–300 °C).

Turner, Andrew C↗

DOE OSTI2026

High-Throughput Uniformity and Defect Monitoring in Low-Temperature Electrolysis Porous Transport Layers Using X-Ray Radiography

Effective quality control (QC) for manufacturing proton exchange membrane water electrolysis (PEMWE) components is critical to enabling widespread adoption of the technology for hydrogen generation. This study investigates X-ray radiography as a novel, high-throughput, potentially in-line QC technique for detecting defects and assessing material property distributions in titanium-based porous transport layers (PTLs) which constitute a crucial component of low temperature PEMWE stacks. We obtain radiographs of a set of fifteen PTLs and model their absorbance of the broadband radiation as a second-order polynomial to account for the non-monoenergetic radiation source used in this study. The resulting model serves as a basis for predicting the areal density and porosity distributions of the PTLs. We find radiography successful in detecting multiple instances of defects, including holes/depressions, cracks, and excess material on the surface or in the pores of the material, demonstrating its potential as a robust in-line QC tool for PTL manufacturing.

08 HYDROGEN↗

DOE OSTI2025

High-temperature stability and thermal expansion behavior of equi-atomic refractory multi-principal element alloys based on MoNbTi system for Gen IV reactor applications

The present study investigates the thermal stability and thermal expansion behavior of seven equi-atomic refractory multi-principal element alloys (MPEAs) based on the MoNbTi ternary system composed of low neutron absorption cross section elements. Through an integrated approach utilizing in-situ high-temperature X-ray diffraction (HT-XRD) in conjunction with differential scanning calorimetry (DSC), dilatometry and ageing heat treatment, the thermal stability of the MPEAs was comprehensively analyzed. In-situ HT-XRD experiment confirmed the stability of the room temperature phases up to 1000 °C with no peaks observed corresponding to additional phases in the HT-XRD patterns at 500, 800 and 1100 °C. DSC thermograms showed the absence of peaks up to 1000 °C, while peaks and valleys corresponding to exothermic and endothermic events were observed above 1000 °C. Coefficient of thermal expansion (CTE) derived from second order polynomial fitting of linear thermal expansion data from the dilatometry experiment showed linear increment up to 1000 °C for all the alloys except those containing Zr. The Cr containing alloys exhibited notably higher CTE values, particularly the Al containing alloy exhibited the highest value. Ageing heat treatment at 800 and 1000 °C for 96 h and subsequent microstructural analysis revealed significant precipitation of secondary phases in MoNbTiZr, MoNbTiZrV and MoNbTiCrAl. In conclusion, a substantial increase in hardness was observed in MoNbTiZr and MoNbTiCrAl due to secondary phase precipitation, while the other alloys maintained hardness values comparable to their as-cast and homogenized states.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

A block-spectral adaptive H-/$p$-refinement strategy for shock-dominated problems

An adaptive H-/p-refinement strategy using a novel sensor is devised and tested in a block-spectral compressible Euler code equipped with adaptive-mesh refinement (AMR) and high-order flux-reconstruction numerics. At each Gauss quadrature point (or solution point) within each spectral block (or mesh element) the discrete velocity jump ΔU = ∂U/∂y 1 Δy 1 + ∂V/∂y 2 Δy 2 + ∂W/∂y 3 Δy 3 is calculated and normalized by the local speed of sound, a. Here, the grid spacing, Δx i , is calculated in each direction as the distance between auxiliary Gauss-Lobatto points, staggered relative to the solution points. The polynomial order is increased from p = 0 to p = p max in regions of weak compression, (ΔU/a) crit < ΔU/a < 0 and kept at p = p max in regions of flow expansion ΔU/a ≥ 0, while staying at the H = 0 base mesh level. Regions experiencing strong compressions, i.e. ΔU/a < (ΔU/a) crit , are H-refined up to H = H max where H max is applied at the location of maximum compression, ΔU/a = min(ΔU/a) in the domain, while keeping p = 0 to guarantee robustness and monotonicity of the solution in the H refined region. The critical value of (ΔU/a) crit = -0.06 is found to effectively separate smooth and non-smooth solution regions, supported by a 1D detonation initiation test case in ideal gas and a shock-to-detonation transition in high explosives. Using this value, the Sod shock tube, Shu-Osher problem, double Mach reflection and a 2D detonation in a high-explosive are simulated with the proposed adaptive H-/p-refinement. In the Sod shock tube case, p-refinement resolves the (weak) contact discontinuity while H-refinement enhances the grid resolution in the shock exploiting the monotonicity of the p = 0 reconstruction. For the Shu-Osher problem, p-refinement captures the small-scale oscillations trailing the shock that would be otherwise attenuated, while H-refinement triggered by the ΔU-sensor appropriately tracks the shock. In the double Mach reflection problem, H-refinement confines the numerical diffusion around the reflected shock while p-refinement recaptures many physical features trailing the shock. Finally, in the 2D high-explosive detonation case, H-refinement follows the leading shock and resolves the curvature of the detonation wave, while p-refinement adds resolution to the trailing reaction zone. Finally, the proposed methodology is tested in a detonation-wave propagation test case in high-explosives with numerical predictions comparing favorably against experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗

DOE OSTI2026

Efficient data-driven regression for reduced-order modeling of spatial pattern formation

We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically accurate numerical simulations. The method can be applied to general nonlinear systems through the use of polynomial model form, while not requiring knowledge of the underlying physical model, governing equations, or numerical solvers. The process of learning ROMs is posed as a low-cost least-squares problem in a reduced-order subspace identified via Proper Orthogonal Decomposition (POD). Numerical experiments on classical pattern-forming systems–including the Schnakenberg and Mimura–Tsujikawa models–demonstrate that higher-order surrogate models significantly improve prediction accuracy while maintaining low computational cost. The proposed method provides a flexible, non-intrusive model reduction framework, well suited for the analysis of complex spatio-temporal pattern formation phenomena.

Data-driven modeling↗