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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 OSTI2013

Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems

The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is {sup 98}Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2018

Infrared and Raman spectroscopy of α-ZrW 2 O 8 : A comprehensive density functional perturbation theory and experimental study

We report that cubic zirconium tungstate (α-ZrW 2 O 8 ), a well-known negative thermal expansion material, has been investigated within the framework of density functional perturbation theory (DFPT), combined with experimental characterization to assess and validate computational results. Using combined Fourier transform infrared measurements and DFPT calculations, new and extensive assignments were made for the far-infrared (<400 cm -1 ) spectrum of α-ZrW 2 O 8 . Lastly, a systematic comparison of DFPT-simulated infrared, Raman, and phonon density-of-state spectra with Fourier transform far-/mid-infrared and Raman data collected in this study, as well as with available inelastic neutron scattering measurements, shows the superior accuracy of the PBEsol exchange-correlation functional over standard PBE calculations for studying the spectroscopic properties of this material.

36 MATERIALS SCIENCE↗
DOE OSTI2023

NWChem: Recent and Ongoing Developments

In this paper we summarize developments in the NWChem computational chemistry suite since the last major release (NWChem 7.0). Specifically, we focus on functionalities, along with input blocks, that are currently accessible in the current stable release (NWChem 7.2) and master branches, interfaces to quantum computing simulators, interfaces to external libraries, the NWChem GitHub repository, and containerization of NWChem executable images. In conclusion, some of the ongoing developments that will be available in the near future are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Accelerating full-waveform inversion using source stacking: synthetic experiments at the global scale in a realistic 3-D earth model

SUMMARY The spectral element method is currently the method of choice for computing accurate synthetic seismic wavefields in realistic 3-D earth models at the global scale. However, it requires significantly more computational time, compared to normal mode-based approximate methods. Source stacking, whereby multiple earthquake sources are aligned on their origin time and simultaneously triggered, can reduce the computational costs by several orders of magnitude. We present the results of synthetic tests performed on a realistic radially anisotropic 3-D model, slightly modified from model SEMUCB-WM1 with three component synthetic waveform ‘data’ for a duration of 10 000 s, and filtered at periods longer than 60 s, for a set of 273 events and 515 stations. We consider two definitions of the misfit function, one based on the stacked records at individual stations and another based on station-pair cross-correlations of the stacked records. The inverse step is performed using a Gauss–Newton approach where the gradient and Hessian are computed using normal mode perturbation theory. We investigate the retrieval of radially anisotropic long wavelength structure in the upper mantle in the depth range 100–800 km, after fixing the crust and uppermost mantle structure constrained by fundamental mode Love and Rayleigh wave dispersion data. The results show good performance using both definitions of the misfit function, even in the presence of realistic noise, with degraded amplitudes of lateral variations in the anisotropic parameter ξ. Interestingly, we show that we can retrieve the long wavelength structure in the upper mantle, when considering one or the other of three portions of the cross-correlation time series, corresponding to where we expect the energy from surface wave overtone, fundamental mode or a mixture of the two to be dominant, respectively. We also considered the issue of missing data, by randomly removing a successively larger proportion of the available synthetic data. We replace the missing data by synthetics computed in the current 3-D model using normal mode perturbation theory. The inversion results degrade with the proportion of missing data, especially for ξ, and we find that a data availability of 45 per cent or more leads to acceptable results. We also present a strategy for grouping events and stations to minimize the number of missing data in each group. This leads to an increased number of computations but can be significantly more efficient than conventional single-event-at-a-time inversion. We apply the grouping strategy to a real picking scenario, and show promising resolution capability despite the use of fewer waveforms and uneven ray path distribution. Source stacking approach can be used to rapidly obtain a starting 3-D model for more conventional full-waveform inversion at higher resolution, and to investigate assumptions made in the inversion, such as trade-offs between isotropic, anisotropic or anelastic structure, different model parametrizations or how crustal structure is accounted for.

Geochemistry & Geophysics↗
DOE OSTI2023

Scalable Bayesian optimization with randomized prior networks

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Stationary Distribution and Perturbation Bounds for a Stochastic Inventory Model

In this paper, we use the theory of generalized inverses to compute the stationary distribution of the (s, S) inventory model directly from the transition matrix of the underlying Markov chain and to provide perturbation bounds. Indeed, approximations are employed to build a tractable model, and statistical methods are used to estimate the unknown parameters and distributions. Hence, the system is subject to perturbations that may cause deviation in the characteristics. The proposed perturbation bound provides a means to estimate the impact of the perturbations on the performance measures of the considered inventory system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations

The burnup equations can in principle be solved by computing the exponential of the burnup matrix. However, due to the difficult numerical characteristics of burnup matrices, the problem is extremely stiff and the matrix exponential solution has previously been considered infeasible for an entire burnup system containing over a thousand nuclides. It was recently discovered by the author that the eigenvalues of burnup matrices are generally located near the negative real axis, which prompted introducing the Chebyshev rational approximation method (CRAM) for solving the burnup equations. CRAM can be characterized as the best rational approximation on the negative real axis and it has been shown to be capable of simultaneously solving an entire burnup system both accurately and efficiently. In this paper, the accuracy of CRAM is further studied in the context of burnup equations. The approximation error is analyzed based on the eigenvalue decomposition of the burnup matrix. It is deduced that the relative accuracy of CRAM may be compromised if a nuclide concentration diminishes significantly during the considered time step. Numerical results are presented for two test cases, the first one representing a small burnup system with 36 nuclides and the second one a full a decay system with 1531 nuclides. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Numerical similarity solution for a variable coefficient K(m, n) equation

A technique for finding numerical similarity solutions to an initial boundary value problem (IBVP) for generalized K(m, n) equations is described. The equation under consideration is nonlinear and has variable coefficients. The original problem is transformed with the aid of Lie symmetries to an initial value problem (IVP) for a nonlinear third-order ordinary differential equation. The existence and uniqueness of the solution are examined, and the problem is consequently solved with the aid of a finite-difference scheme for various values of the governing parameters. In lieu of an exact symbolic solution, the scheme is validated by comparing the numerical solutions with the approximate analytic solutions obtained with the aid of the method of successive approximations in their region of validity. The accuracy, efficiency, and consistency of the scheme are demonstrated. Numerical solutions to the original initial boundary value problem are constructed for selected parameter values with the aid of the transforms. The qualitative behavior of the solutions as a function of the governing parameters is analyzed, and it is found that the examined IBVPs for generalized K(m, n) equations with variable coefficients that are functions of time, do not admit solitary wave or compacton solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Should thermostatted ring polymer molecular dynamics be used to calculate thermal reaction rates?

We apply Thermostatted Ring Polymer Molecular Dynamics (TRPMD), a recently proposed approximate quantum dynamics method, to the computation of thermal reaction rates. Its short-time transition-state theory limit is identical to rigorous quantum transition-state theory, and we find that its long-time limit is independent of the location of the dividing surface. TRPMD rate theory is then applied to one-dimensional model systems, the atom-diatom bimolecular reactions H + H{sub 2}, D + MuH, and F + H{sub 2}, and the prototypical polyatomic reaction H + CH{sub 4}. Above the crossover temperature, the TRPMD rate is virtually invariant to the strength of the friction applied to the internal ring-polymer normal modes, and beneath the crossover temperature the TRPMD rate generally decreases with increasing friction, in agreement with the predictions of Kramers theory. We therefore find that TRPMD is approximately equal to, or less accurate than, ring polymer molecular dynamics for symmetric reactions, and for certain asymmetric systems and friction parameters closer to the quantum result, providing a basis for further assessment of the accuracy of this method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A discrete dislocation dynamics study of precipitate bypass mechanisms in nickel-based superalloys

Order strengthening in nickel-based superalloys is associated with the extra stress required for dislocations to bypass the $\gamma'$ precipitates distributed in the $\gamma$ matrix. Depending on the operating conditions and microstructure, a rich variety of bypass mechanism has been identified, with various shearing and Orowan looping processes gradually giving way to climb bypass as the operating conditions change from the low/intermediate temperatures and high stress regime, to the high temperature and low stress regime. When anti phase boundary (APB) shearing and Orowan looping mechanisms operate, the classical picture is that, at for a given volume fraction, the bypass mechanism changes from shearing to looping with increased particle size and within a broad coexistence size window. Another possibility, which is supported by indirect experimental evidence, is that a third “hybrid” transition mechanism may operate. Here, in this paper we use discrete dislocation dynamics (DDD) simulations to study dislocation bypass mechanisms in Ni-based superalloys. We develop a new method to compute generalized stacking fault forces in DDD simulations, based on a concept borrowed from complex analysis and known as the winding number of a closed curve about a point. We use this method to study the mechanisms of bypass of a square lattice of spherical $\gamma'$ precipitates by $a/2\langle110\rangle$ {111} edge dislocations, as a function of the precipitates volume fraction and size. We show that not only the hybrid mechanism is possible, but also that it operates as the transition mechanism between the shearing and looping regimes over a wide range of precipitates volume fraction and radii. Based on our simulation results, we propose a simple model for the strength of this mechanism. We also consider the effects of a $\gamma$/$\gamma'$ lattice misfit on the bypass mechanisms, which we approximate by an additional precipitate stress computed according to Eshelby’s inclusion theory. We show that in the shearing and hybrid looping-shearing regimes, a lattice misfit generally results in an increased bypass stress. For sufficiently high lattice misfit, the critical bypass configuration in attractive dislocation-precipitates interactions changes dramatically, and the bypass stress is controlled by the pinning of the trailing dislocation on the exit side of the precipitates, similar to what has been reported in the high-temperature creep literature.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Monte Carlo electron-photon transport using GPUs as an accelerator: Results for a water-aluminum-water phantom

An electron-photon coupled Monte Carlo code ARCHER - Accelerated Radiation-transport Computations in Heterogeneous Environments - is being developed at Rensselaer Polytechnic Institute as a software test bed for emerging heterogeneous high performance computers that utilize accelerators such as GPUs. In this paper, the preliminary results of code development and testing are presented. The electron transport in media was modeled using the class-II condensed history method. The electron energy considered ranges from a few hundred keV to 30 MeV. Moller scattering and bremsstrahlung processes above a preset energy were explicitly modeled. Energy loss below that threshold was accounted for using the Continuously Slowing Down Approximation (CSDA). Photon transport was dealt with using the delta tracking method. Photoelectric effect, Compton scattering and pair production were modeled. Voxelised geometry was supported. A serial ARHCHER-CPU was first written in C++. The code was then ported to the GPU platform using CUDA C. The hardware involved a desktop PC with an Intel Xeon X5660 CPU and six NVIDIA Tesla M2090 GPUs. ARHCHER was tested for a case of 20 MeV electron beam incident perpendicularly on a water-aluminum-water phantom. The depth and lateral dose profiles were found to agree with results obtained from well tested MC codes. Using six GPU cards, 6x10{sup 6} histories of electrons were simulated within 2 seconds. In comparison, the same case running the EGSnrc and MCNPX codes required 1645 seconds and 9213 seconds, respectively, on a CPU with a single core used. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

A greedy algorithm for computing eigenvalues of a symmetric matrix with localized eigenvectors

Here, we present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its components have large magnitudes, the proposed algorithm identifies the location of these components in a greedy manner, and obtains approximations to the desired eigenpairs of $H$ by computing eigenpairs of a submatrix extracted from the corresponding rows and columns of $H$. Even when the eigenvector is not completely localized, the approximate eigenvectors obtained by the greedy algorithm can be used as good starting guesses to accelerate the convergence of an iterative eigensolver applied to $H$. We discuss a few possibilities for selecting important rows and columns of $H$ and techniques for constructing good initial guesses for an iterative eigensolver using the approximate eigenvectors returned from the greedy algorithm. We demonstrate the effectiveness of this approach with examples from nuclear quantum many-body calculations and many-body localization studies of quantum spin chains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Variational quantum simulation of the critical Ising model with symmetry averaging

Here we investigate the use of deep multiscale entanglement renormalization ansatz (DMERA) circuits as a variational ansatz. We use the exactly solvable one-dimensional critical transverse-field Ising model as a test bed. Numerically exact simulation of the quantum circuit ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, the DMERA strongly outperforms a standard quantum approximate optimization algorithm (QAOA)–style ansatz, and that a major source of systematic error in correlation functions approximated using the DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. Here, we propose that this technique for mitigating systematic error could be applied to noisy intermediate-scale quantum (NISQ) simulations of physical systems with other symmetries.

1-dimensional spin chains↗
DOE OSTI2014

A First-Passage Kinetic Monte Carlo method for reaction–drift–diffusion processes

Stochastic reaction–diffusion models are now a popular tool for studying physical systems in which both the explicit diffusion of molecules and noise in the chemical reaction process play important roles. The Smoluchowski diffusion-limited reaction model (SDLR) is one of several that have been used to study biological systems. Exact realizations of the underlying stochastic processes described by the SDLR model can be generated by the recently proposed First-Passage Kinetic Monte Carlo (FPKMC) method. This exactness relies on sampling analytical solutions to one and two-body diffusion equations in simplified protective domains. In this work we extend the FPKMC to allow for drift arising from fixed, background potentials. As the corresponding Fokker–Planck equations that describe the motion of each molecule can no longer be solved analytically, we develop a hybrid method that discretizes the protective domains. The discretization is chosen so that the drift–diffusion of each molecule within its protective domain is approximated by a continuous-time random walk on a lattice. New lattices are defined dynamically as the protective domains are updated, hence we will refer to our method as Dynamic Lattice FPKMC or DL-FPKMC. We focus primarily on the one-dimensional case in this manuscript, and demonstrate the numerical convergence and accuracy of our method in this case for both smooth and discontinuous potentials. We also present applications of our method, which illustrate the impact of drift on reaction kinetics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Haar-Like Wavelets on Hierarchical Trees

Here, discrete wavelet methods, originally formulated in the setting of regularly sampled signals, can be adapted to data defined on a point cloud if some multiresolution structure is imposed on the cloud. A wide variety of hierarchical clustering algorithms can be used for this purpose, and the multiresolution structure obtained can be encoded by a hierarchical tree of subsets of the cloud. Prior work introduced the use of Haar-like bases defined with respect to such trees for approximation and learning tasks on unstructured data. This paper builds on that work in two directions. First, we present an algorithm for constructing Haar-like bases on general discrete hierarchical trees. Second, with an eye towards data compression, we present thresholding techniques for data defined on a point cloud with error controlled in the $L$ $\infty$ norm and in a Hölder-type norm. In a concluding trio of numerical examples, we apply our methods to compress a point cloud dataset, study the tightness of the $L$ $\infty$ error bound, and use thresholding to identify MNIST classifiers with good generalizability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimizing multigrid reduction-in-time and Parareal coarse-grid operators for linear advection

Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent partial differential equations (PDEs) in modern high-performance computing environments. While these techniques have been very successful for parabolic equations, it has often been observed that their performance suffers dramatically when applied to advection-dominated problems or purely hyperbolic PDEs using standard rediscretization approaches on coarse grids. In this paper, we apply MGRIT or Parareal to the constant-coefficient linear advection equation, appealing to existing convergence theory to provide insight into the typically nonscalable or even divergent behavior of these solvers for this problem. To overcome these failings, we replace rediscretization on coarse grids with improved coarse-grid operators that are computed by applying optimization techniques to approximately minimize error estimates from the convergence theory. Therefore, one of our main findings is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behavior of the hyperbolic problem by tracking the characteristic curves. Our approach is tested for schemes of various orders using explicit or implicit Runge–Kutta methods combined with upwind-finite-difference spatial discretizations. In all cases, we obtain scalable convergence in just a handful of iterations, with parallel tests also showing significant speed-ups over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes

This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, k{sub eff}, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for k{sub eff} with directional dependence. General error estimators are derived for any given functional of the flux and applied to k{sub eff} to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The k{sub eff} goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗