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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Kernel polynomial method for linear spin wave theory

Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially in systems with large magnetic unit cells, such as those with incommensurate magnetic structures or quenched disorder. In this paper, we demonstrate an efficient scheme based on the kernel polynomial method for calculating dynamical correlations of relevance to inelastic neutron scattering experiments. This method reduces the scaling of numerical cost from cubic to linear in the magnetic unit cell size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗
DOE OSTI2024

Computing the QRPA level density with the finite amplitude method

Here, we describe a new algorithm to calculate the vibrational nuclear level density of an atomic nucleus. Fictitious perturbation operators that probe the response of the system are generated by drawing their matrix elements from some probability distribution function. We use the Finite Amplitude Method to explicitly compute the response for each such sample. With the help of the Kernel Polynomial Method, we build an estimator of the vibrational level density and provide the upper bound of the relative error in the limit of infinitely many random samples. The new algorithm can give accurate estimates of the vibrational level density. Since it is based on drawing multiple samples of perturbation operators, its computational implementation is naturally parallel and scales like the number of available processing units.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Vacancy-Induced Tunable Kondo Effect in Twisted Bilayer Graphene

In single sheets of graphene, vacancy-induced states have been shown to host an effective spin-1/2 hole that can be Kondo screened at low temperatures. Here, we show how these vacancy-induced impurity states survive in twisted bilayer graphene (TBG), which thus provides a tunable system to probe the critical destruction of the Kondo effect in pseudogap hosts. Ab initio calculations and atomic-scale modeling are used to determine the nature of the vacancy states in the vicinity of the magic angle in TBG, demonstrating that the vacancy can be treated as a quantum impurity. Utilizing this insight, we construct an Anderson impurity model with a TBG host that we solve using the numerical renormalization group combined with the kernel polynomial method. We determine the phase diagram of the model and show how there is a strict dichotomy between vacancies in the AA/BB versus AB/BA tunneling regions. In AB/BA vacancies, the Kondo temperature at the magic angle develops a broad distribution with a tail to vanishing temperatures due to multifractal wave functions at the magic angle. Finally, we argue that scanning tunneling microscopy in the vicinity of the vacancy can act as a probe of both the critical single-particle states and the underlying many-body ground state in magic-angle TBG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Polynomial range estimation as a troubled-cell indicator for high-order methods

Two troubled-cell indicators based on polynomial range estimation methods are used to flag cells that may violate positivity constraints. One method uses interval extension, and the second uses the range enclosure property of the Bernstein polynomial basis. Furthermore, both methods reduce compute time for the positivity preserver by limiting its application to a subset of cells. The Bernstein polynomial method remains effective as the problem dimensionality increases. Interval extension applied to the internal energy equation permits the use of the troubled-cell indicators for rational functions, though performance suffers compared to directly applying the indicators to polynomial functions.

42 ENGINEERING↗
DOE OSTI2026

Direct Nonlinear Approximation for Security Region Boundary of Integrated Energy Systems: A Polynomial Chaos Expansion Solution

The strong interdependence of electricity, gas, and heating systems can facilitate fault propagation within integrated energy systems (IESs), posing significant challenges to secure operation. This paper proposes a polynomial chaos expansion (PCE)-based approximation method to accurately characterize the IES security region boundary (IES–SRB). By integrating the Karush-Kuhn-Tucker conditions with PCE theory, the IES-SRB approximation problem is reformulated as a set of nonlinear equations concerning the approximation coefficients. Using the Galerkin projection method, these equations are further transformed into a system of projection equations that govern the polynomial approximation coefficients in the IES-SRB approximation. To reduce computational complexity while maintaining high approximation accuracy, a piecewise polynomial approximation method is proposed. Numerical studies on the E39-G20-H6 and E118-G96-H52 IES test systems demonstrate that the proposed method can accurately and effectively construct IES security regions.

Wu, Chenghao [Northeast Electric Power University]↗
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 OSTI2024

An enrichment wall modeling framework for spectral element methods

In the present work, a first-of-its-kind enrichment wall-model is developed within the spectral element method (SEM) framework for large-eddy simulations (LES) of wall-bounded turbulent flows. The method augments the polynomial solution in the wall-adjacent elements with an analytical law-of-the-wall enrichment function representing the mean velocity near the wall. In the solution representation, this enrichment function captures the large gradients in the boundary layer, which allows the polynomial modes to represent the turbulent fluctuations. The enriched solution is able to resolve the shear stress at the wall without any modification to the no-slip wall boundary conditions, which allows for greater accuracy in the near-wall region compared to traditional methods. The enrichment wall modeling approach is implemented in a high-order SEM computational fluid dynamics solver, Nek5000, and its performance is assessed in turbulent channel flow wall-modeled LES for a range of Reynolds numbers. It is demonstrated that the enrichment wall-model improves solution accuracy on under-resolved near-wall grids as compared to traditional shear stress wall-models.

42 ENGINEERING↗
DOE OSTI2025

Many-Body Basis Set Amelioration Method for Incremental Full Configuration Interaction

Incremental full configuration interaction (iFCI) is a polynomial-cost electronic structure method that systematically approaches the FCI limit by employing the method of increments to solve the Schrödinger equation through a many-body expansion. This article introduces the many-body basis set amelioration (MBBSA) method, which is designed to allow iFCI to be applicable to larger atomic orbital basis sets. MBBSA uses a series of inexpensive iFCI calculations to approximate the correlation energy that would be found using a more expensive, highly accurate iFCI calculation. Here, when compared to standard iFCI computations on smaller molecules in triple-zeta and larger basis sets, MBBSA provides approximations to the total and relative energies within chemical accuracy. MBBSA exhibits a reduced cost of between 60-92% when compared to standard iFCI calculations, with larger systems experiencing the largest benefit. Tests of MBBSA on two reactions that involve highly correlated systems, the automerization of cyclobutadiene and a Criegee intermediate reaction, show that MBBSA has practical utility for studying realistic chemistries.

Basis sets↗
DOE OSTI2025

Decayheatml

This code is designed to predict and analyze the decay heat generated in molten salt reactors (MSRs) using a hybrid approach that combines machine learning and segmented polynomial fitting. The accurate prediction of decay heat is essential for reactor safety and the optimization of spent fuel storage. The code operates through several key components: 1) Data Architecture: It incorporates a modular data architecture that handles various MSR-specific operational parameters such as power density, humidity content, and air ingress. These parameters are sampled using Sobol sequences to ensure comprehensive coverage of operational uncertainties. 2) Machine Learning Framework: The code employs a diverse set of machine learning models, including polynomial regression, decision trees, random forests, gradient boosting, support vector regression, k-nearest neighbors, multi-layer perceptrons, and symbolic regression. These models are trained to predict decay heat over a wide temporal range, from immediate shutdown up to 10,000 years. 3) Region-Optimized Training: The temporal domain is divided into multiple regions, each modeled separately to capture distinct decay heat characteristics across different time scales. This approach significantly improves the accuracy and interpretability of predictions. 4) Segmented Polynomial Interpretation (SPI): The SPI method translates machine learning predictions into piecewise polynomial equations. These equations are physically interpretable and can be directly integrated into existing engineering workflows and safety analyses. 5) Front-End Interfaces: The code includes both a Jupyter notebook interface for research development and a Streamlit web application for operational deployment. These interfaces allow users to interactively explore decay heat predictions, adjust operational parameters, and visualize results in real-time. 6) Applications: The framework supports various applications, including safety system validation and spent fuel container optimization. It enables real-time evaluation of worst-case decay heat scenarios, informing the design of passive safety systems and optimizing container designs for long-term storage. Overall, this code provides a robust, accurate, and user-friendly tool for predicting decay heat in MSRs, enhancing reactor safety, and optimizing spent fuel management.

Retamales, Mauricio Eduardo Tano [Idaho National L↗
DOE OSTI2025

High-Fidelity CFD Simulation of Mixed Convection and Forced Convection in a Pebble Bed Test Reactor Core

The Hermes low-power [35-MW(thermal)] reactor will be built and operated by Kairos Power LLC (KP) to demonstrate its fluoride salt-cooled high-temperature reactor (FHR) technology. In the KP FHR, the reactor core is composed of randomly packed pebbles with TRISO fuel particles inside with FLiBe flow upward through the core acting as a coolant. Previous numerical and experimental studies have been limited to either a small-size bed or to a lack of detailed measurements for heat transfer. Here, to address the lack of high-fidelity heat transfer data in a real-size FHR core, in this study, we simulated a pebble bed core with 34 374 pebbles randomly packed, similar to the Hermes reactor's size. The core radius was 14 times that of the pebble diameter, while the core height was 45 times. In this work, we were particularly interested in a mixed convection regime, where buoyancy is important. Therefore, we performed several large-eddy simulations at different Reynolds numbers (160 to 1000) with gravitational force included. The spectral element computational fluid dynamics code NekRS with graphics processing unit acceleration was used for this study. The low-Mach number approximation was applied to address property changes in the FLiBe and to account for buoyancy. A pure hexahedral mesh with 60 million elements was generated by the Voronoi cell method. At the polynomial order of 5, the total degrees of freedom was 7.5 billion. The developed case in this work is the first of its kind in terms of size and complexity. The local numerical data across the domain were obtained and compared with empirical correlations. After examining the data, we found the following conclusions. For pressure drop, the Reger correlation predicted less than a 5% error. On the other hand, for heat transfer, the Wakao correlation outperformed the others. Based on our findings, we recommend the use of the Wakao correlation for the Nusselt number calculation, and for pressure drop, the KTA (Kerntechnischer Ausschuss) correclation, among the available experimental correlations. In conclusion, the Reger direct numerical simulation-driven correlation for pressure drops should also be considered, given its best agreement with our calculations.

Mixed Convection↗
DOE OSTI2025

A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters

We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be used to locally bound any combination of these basis functions. This approach can be applied to any element/basis type at any approximation order, can provide local (i.e., subcell) extremum bounds to a desired level of accuracy, and can be evaluated efficiently on-the-fly in simulations. Furthermore, we show that this approach generally yields more accurate bounds in comparison to traditional methods based on convex hull properties (e.g., Bernstein polynomials). Furthermore, the efficacy of this technique is shown in applications such as mesh validity checks and optimization for high-order curved meshes, where positivity of the element Jacobian determinant can be ensured throughout the entire element, and continuously bounds-preserving limiters for hyperbolic systems, which can enforce maximum principle bounds across the entire solution polynomial.

Bounding box↗
DOE OSTI2024

Quantum Monte Carlo Calculations of Chemical Binding and Reactions

The auxiliary field quantum Monte Carlo method developed by the PIs has been shown to provide the most accurate description of strongly correlated electronic systems, from molecules to solids. Unlike other explicitly many‐body approaches, the quantum Monte Carlo method scales as a low order polynomial of systems size, similar to mean‐field methods such as density functional theory. However, the auxiliary field quantum Monte Carlo algorithm is significantly more expensive than traditional density functional calculations. This creates a bottleneck for applications to extended systems, such as large molecules and solids. One principal objective of this proposal was to develop new auxiliary field quantum Monte Carlo computational strategies to achieve improved scaling with system size, using downfolding and localization schemes, without sacrificing the predictive power of the calculations. A second goal is to extend the reach of auxiliary field quantum Monte Carlo to calculate excited states. This final report summarizes what has been achieved during the course the project toward these goals.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Efficient Simulation of Logical Magic State Preparation Protocols

Developing space- and time-efficient logical magic state preparation (MSP) protocols will likely be an essential step toward building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for simulating logical MSP protocols under the standard circuit-level noise model. When applied to protocols based on code-switching, magic state cultivation, and magic state distillation, our method yields a complexity polynomial in (i) the number of qubits and (ii) the nonstabilizerness, e.g., stabilizer rank or Pauli rank, of the target encoded magic state. The efficiency of our simulation method is rooted in a curious fact: every circuit-level Pauli error in these protocols propagates to a Clifford error at the end. This property is satisfied by a large family of protocols, including those that repeatedly measure a transversal Clifford that squares to a Pauli. We provide a proof-of-principle numerical simulation that prepares a magic state using such logical Clifford measurements. Our work enables practical simulation of logical MSP protocols without resorting to approximations or resource-intensive state-vector simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Advancing Multiscale Simulation of Plasma-Surface Interfaces

We report the development of an atomistic-informed, surface-state-dependent predictive model for particle exchange in a carbon-tungsten plasma-surface interface. The predictive model uses machine learning (ML) techniques to learn the energy and angular distributions for particle exchange and rate functions for surface state evolution from molecular dynamics simulations of cumulative bombardment of tungsten by energetic carbon ions. Each predictive component is sensitive to the energy and trajectory of incident plasma species and the surface state. The surface state is represented by a set of surface state descriptors, which were derived from the atomistic surface state for each independent carbon bombardment event. These descriptors are representative of the composition and degree of amorphization of the outermost angstrom of surface material and were chosen to optimize predictive performance for particle exchange at the interface. The distributions for particle exchange (reflection/sputtering) are demonstrated to vary with each surface state descriptor, motivating the development of surface-state-dependent particle exchange models for plasma simulations. The performance of various ML methods was compared, including polynomial quantile regression, artificial neural networks, k-nearest neighbors, and random forest algorithms, with polynomial regression performing the best for interpolation and extrapolation of learned relationships. In addition to the particle exchange model, a neutral network was developed and used to identify data sufficiency throughout surface descriptor space, which will enable real-time feedback during future data production to ensure data is produced where it is most needed, and we provide commentary on improvements to the data production workflow for future endeavors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Optimal Polynomial Smoothers and One‐Sided V‐Cycles for Poisson Problems

The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier‐Stokes equations needs robust preconditioning strategies. One such strategy is multigrid. To realize the potential of multigrid methods, effective smoothing strategies are needed. Chebyshev polynomial smoothers, in conjunction with pointwise Jacobi or additive Schwarz methods (ASMs), prove to be an effective smoother. Other polynomial smoothers, however, may provide superior convergence to the multigrid preconditioner. The authors compare the standard Chebyshev polynomial smoothers to both the novel fourth‐kind Chebyshev polynomial smoothers proposed by Lottes as well as smoothers based on the polynomial of best uniform approximation to as proposed by Kraus, Vassilevski, and Zikatanov. At the cost of symmetry, further improvements may be made. For example, a order polynomial smoother on both sides of the V‐cycle may be substituted with an order polynomial smoother on one side at no additional cost. The choice of omitting the postsmoother in favor of higher‐order polynomial presmoothing is advantageous in cases where the multigrid approximation property constant is large. The authors consider a 2D model problem based on finite differences to motivate the choice of polynomial smoother, order, and whether to apply postsmoothing for the target application of high‐order ‐geometric multigrid methods for GPU architectures. Results from both domains demonstrate the substantial improvement of these approaches over the standard Chebyshev polynomial smoother with a symmetric V‐cycle.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Deterministic Quantum Trajectory via Imaginary Time Evolution

Stochastic quantum trajectories, such as pure state evolutions under unitary dynamics and random measurements, offer a crucial ensemble description of many-body open system dynamics. Recent studies have highlighted that individual quantum trajectories also encode essential physical information. Prominent examples include measurement-induced phase transitions, where a pure quantum state corresponding to fixed measurement outcomes (trajectories) exhibits distinct entanglement phases, depending on the measurement rate. However, direct observation of this effect is hindered by an exponential postselection barrier, whereby the probability of realizing a specific trajectory is exponentially small. We propose a deterministic method to efficiently prepare quantum trajectories in polynomial time using imaginary time evolution and, thus, overcome this fundamental challenge. Here, we demonstrate that our method applies to a certain class of quantum states, and argue that universal approaches do not exist for any quantum trajectories. Our result paves the way for experimentally exploring the physics of individual quantum trajectories at scale and enables direct observation of certain postselection-dependent phenomena.

Mittal, Shivan [Los Alamos National Laboratory (LA↗
DOE OSTI2024

Interpolation of compound semiconductor alloy parameters from those of their constituents

Several methods have been proposed for interpolation of the value of physical parameters of quaternary alloys from those of their constituent ternary and binary sub-alloys. These expressions agree when non-linear bowing terms are not required; they differ in how the bowing terms of the bounding ternaries should be utilized. Common interpolation expressions for quaternaries can be generalized into two groups: (1) those that use a linear interpolation of the nearest ternary parameter values and (2) those that interpolate over binary values with a bowing term derived from the bounding ternaries. The second group of methods is equivalent to a polynomial expansion over the alloy’s interpolation space. For compound semiconductor alloys, the geometry of the composition space is the direct sum of the group-III and group-V mixture sub-spaces. The mixture sub-spaces are best described using barycentric coordinates on a regular simplex. A general polynomial expansion of the value of an alloy parameter using barycentric coordinates for the group-III and group-V simplex spaces is described along with an algorithm to generate interpolation expressions for alloys with arbitrary numbers of elements, including quinary and senary alloys. It is shown that a polynomial expansion produces values in closer agreement with the direct gap of quaternaries lattice-matched to common substrates than do approaches using an interpolation of the ternary values, despite a prominent recommendation to the contrary. Finally, a quaternary correction term is described that improves the predicted direct bandgap energies of GaInAsSb for compositions near those lattice matched to InP, InAs, and GaSb.

Olesberg, Jonathon T. [Sandia National Laboratorie↗