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At least 613 records · Page 34
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Efficient Onboard Attitude Commanding for Fast Maneuvering of Lunar Reconnaissance Orbiter

To support Lunar Reconnaissance Orbiter’s extended science missions, an algorithm for autonomous optimization of fast occultation avoidance maneuvers was developed. The fast attitude maneuvers are inserted to the spacecraft attitude control system as trajectories to be tracked. Executing maneuvers in this way requires transmission and storage of a large number of time-tagged attitude waypoints on the spacecraft. For more efficient day-to-day operations, an interpolating filter was designed to perform onboard interpolation between sparse samples of commands. The interpolating filter – called FastXMan for efficient fast maneuvering – was patched into LRO’s flight software in late 2023 and is presently operational. This paper presents an overview of the issues related to the practical implementation of the filter and illustrates the flight performance of the new scheme.

Operations↗
DOE OSTI2019

Power system disturbance location determination based on rate of change of frequency

A method for determining a location of a disturbance in a power system is provided. The method includes receiving data from a plurality of sensors distributed across the power system; determining, with one or more processors, for each sensor, an extremum of the data corresponding to the sensor; interpolating, with the one or more processors, the extrema; and presenting, on one or more display units, a location corresponding to a global maximum of the interpolated extrema as the location of the disturbance. The method may further include, if a difference between the largest extremum and each of remaining extremum is greater than a predetermined threshold, skipping the interpolating step and the presenting step, and presenting a location of the sensor corresponding to the largest extremum as the location of the disturbance.

You, Shutang↗
DOE OSTI2020

Development and Validation of Passive Yaw in the Open-Source WEC-Sim Code: Preprint

A passive yaw implementation is developed, validated, and explored for the Wave Energy Converter Simulator (WEC-Sim), an open-source wave energy converter modeling tool that works within MATLAB/Simulink. The Reference Model 5 (RM5) is selected for this investigation, and a WEC-Sim model of the device is modified to allow yaw motion. A boundary element method (BEM) code was used to calculate the excitation force coefficients for a range of wave headings. An algorithm was implemented in WEC-Sim to determine the equivalent wave heading from a body’s instantaneous yaw angle and interpolate the appropriate excitation coefficients to ensure the correct time-domain excitation force. This approach is able to determine excitation force for a body undergoing large yaw displacement. For the mathematically simple case of regular wave excitation, the dynamic equation was integrated numerically and found to closely approximate the results from this implementation in WEC-Sim. A case study is presented for the same device in irregular waves. In this case, computation time is increased by 32x when this interpolation is performed at every time step. To reduce this expense, a threshold yaw displacement can be set to reduce the number of interpolations performed. A threshold of 0.01 was found to increase computation time by only 22x without significantly affecting time domain results. Similar amplitude spectra for yaw force and displacements are observed for all threshold values less than or equal to 1, for which computation time is only increased by 2.2x.

50 EE - Wind and Water Power Program - Water (EE-4↗
DOE OSTI2023

Dynamic Model Agnostic Reliability Evaluation of Machine-Learning Models Integrated in Instrumentation & Control Systems

In recent years, the field of data-driven neural network-based machine learning (ML) algorithms has grown significantly and spurred research in its applicability to instrumentation and control systems. While they are promising in operational contexts, the trustworthiness of such algorithms is not adequately assessed. Failures of ML-integrated systems are poorly understood; the lack of comprehensive risk modeling can degrade the trustworthiness of these systems. In recent reports by the National Institute for Standards and Technology, trustworthiness in ML is a critical barrier to adoption and will play a vital role in intelligent systems' safe and accountable operation. Thus, in this work, we demonstrate a real-time model-agnostic method to evaluate the relative reliability of ML predictions by incorporating out-of-distribution detection on the training dataset. It is well documented that ML algorithms excel at interpolation (or near-interpolation) tasks but significantly degrade at extrapolation. This occurs when new samples are "far" from training samples. The method, referred to as the Laplacian distributed decay for reliability (LADDR), determines the difference between the operational and training datasets, which is used to calculate a prediction's relative reliability. LADDR is demonstrated on a feedforward neural network-based model used to predict safety significant factors during different loss-of-flow transients. LADDR is intended as a "data supervisor" and determines the appropriateness of well-trained ML models in the context of operational conditions. Ultimately, LADDR illustrates how training data can be used as evidence to support the trustworthiness of ML predictions when utilized for conventional interpolation tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Generating An Advanced Cross-section Library For HTGR Pebble Bed Depletion Calculations Using Reduced-Order Model Generation Techniques

For code development, Advanced Reactor Technologies - Gas Cooled Reactors Program (ART-GCR) rely on a collaboration with the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, but the cross sections generation and the methodology definition is part of this program area goals. Based on previous studies in FY23, the size of microscopic cross section libraries increases rapidly with the number of tabulations, requiring significant amount of memory and drastically slowing down the Griffin calculations when evaluating cross sections via the multivariate linear interpolation approach. Rising to these challenges, this work investigates constructing Reduced-order Models (ROMs) for the multi-group microscopic cross sections to accelerate the cross section evaluation in Griffin. A database of multigroup cross sections is first collected considering all possible parameters that a designer could change for optimization. Down-selection of the ROM techniques afterward shows Deep Neural Network (DNN) as the best candidate when jointly consider memory efficiency, predictive accuracy, computational cost, scalability, flexibility and ease of implementation of the algorithms in comparison to the multidimensional interpolation. This work develops a specific interface that enables the cross section predictions using pre-trained DNN models into Griffin leveraging the existing ROM capabilities. DNNs have been trained for all isotopes for use in Griffin. Preliminary Griffin testing shows that DNNs exhibit exceptional predictive accuracy and the use of DNNs provides orders of magnitude improvement in memory efficiency compared to conventional interpolation techniques. With such ROM techniques, it holds great promise to further increase the fidelity of the Pebble Bed Reactor (PBR) simulation by increasing the number of tabulations/state variables during cross section evaluation, while maintaining the computational cost affordable in Griffin.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Reduce-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which usually consists of a database of tabulated values, used to calculate the cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of micro cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. To address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multi-group cross section data across isotopes, reaction types and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs for have been trained for all isotopes in this work and systematic Griffin testing is ongoing at this moment to ensure the feasibility of this ROM technique for cross section predictions.

42 - ENGINEERING↗
DOE OSTI2024

Reduced-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Abstract – Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which consist of databases of tabulated values, used to calculate the neutron cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of microscopic cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. In order to address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multigroup cross section data across isotopes, reaction types, and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs have been trained for all isotopes in this work and systematic Griffin testing is ongoing to ensure the feasibility of this ROM technique for predicting cross section and reducing memory requirements without a significant sacrifice in computational performance.

42 - ENGINEERING↗
DOE OSTI2024

Advanced Cross Section Library Generation using Reduced Order Models

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which consist of databases of tabulated values, used to calculate the neutron cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of microscopic cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. In order to address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multigroup cross section data across isotopes, reaction types, and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs have been trained for all isotopes in this work and systematic Griffin testing is ongoing to ensure the feasibility of this ROM technique for predicting cross section and reducing memory requirements without a significant sacrifice in computational performance.

42 - ENGINEERING↗
DOE OSTI2013

Interpolatability distinguishes LOCC from separable von Neumann measurements

Local operations with classical communication (LOCC) and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement. Separable operations are strictly more powerful than LOCC, but no simple explanation of this phenomenon is known. We show that, in the case of von Neumann measurements, the ability to interpolate measurements is an operational principle that sets apart LOCC and separable operations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Sandwiched Rényi divergence satisfies data processing inequality

Sandwiched (quantum) α-Rényi divergence has been recently defined in the independent works of Wilde et al. [“Strong converse for the classical capacity of entanglement-breaking channels,” preprint http://arxiv.org/abs/arXiv:1306.1586 (2013)] and Müller-Lennert et al. [“On quantum Rényi entropies: a new definition, some properties and several conjectures,” preprint http://arxiv.org/abs/arXiv:1306.3142v1 (2013)]. This new quantum divergence has already found applications in quantum information theory. Here we further investigate properties of this new quantum divergence. In particular, we show that sandwiched α-Rényi divergence satisfies the data processing inequality for all values of α > 1. Moreover we prove that α-Holevo information, a variant of Holevo information defined in terms of sandwiched α-Rényi divergence, is super-additive. Our results are based on Hölder's inequality, the Riesz-Thorin theorem and ideas from the theory of complex interpolation. We also employ Sion's minimax theorem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Superconvergence analysis for nonlinear parabolic equation with EQ{sub 1}{sup rot} nonconforming finite element

EQ{sub 1}{sup rot} nonconforming finite element method (FEM) applied to a class of nonlinear parabolic equation is discussed. First, by use of two typical characters of this element (one is that the associated FE interpolation operator is identical to its traditional Ritz projection operator; the other is that the consistency error is of order O(h{sup 2}), one order higher than the interpolation error, when the exact solution of the problems belongs to H{sup 3}(Ω)), the supercloseness of order O(h{sup 2}) in broken H{sup 1}-norm for semi-discrete scheme is obtained without the boundedness of numerical solution in L{sup ∞}-norm through splitting the numerical solution into several parts. Moreover, we get the desired result with requirement of u,u{sub t}∈H{sup 3}(Ω) only. Secondly, a linearized Crank–Nicolson fully discrete scheme is proposed and the superclose property of order O(h{sup 2}+τ{sup 2}) is derived by constructing a suitable auxiliary problem. Finally, a numerical example is carried out to confirm our theoretical analysis. Here, h is the subdivision parameter and τ is the time step.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

New discretization of Caputo–Fabrizio derivative

We derive a numerical approximation, namely L1–2 formula, to the Caputo–Fabrizio derivative by using a quadratic interpolation. Quadratic and cubic convergence rates are achieved for L1 and L1–2 formulas using Lagrange interpolation, respectively. We compute Caputo–Fabrizio derivatives of some known functions both theoretically and numerically. In addition, we solve non/linear sub-diffusion equations to test theoretical findings. Numerical results confirm the theoretically observed convergence rates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

H{sub 2}{sup +}, HeH and H{sub 2}: Approximating potential curves, calculating rovibrational states

Analytic consideration of the Bohr–Oppenheimer (BO) potential curves for diatomic molecules is proposed: accurate analytic interpolation for a potential curve consistent with its rovibrational spectra is found. It is shown that in the BO approximation for four lowest electronic states 1sσ{sub g} and 2pσ{sub u}, 2pπ{sub u} and 3dπ{sub g} of H{sub 2}{sup +}, the ground state X{sup 2}Σ{sup +} of HeH and the two lowest states {sup 1}Σ{sub g}{sup +} and {sup 3}Σ{sub u}{sup +} of H{sub 2}, the potential curves can be analytically interpolated in full range of internuclear distances R with not less than 4–5–6 s.d. Approximation based on matching the Laurant-type expansion at small R and a combination of the multipole expansion with one-instanton type contribution at large distances R is given by two-point Padé approximant. The position of minimum, when exists, is predicted within 1% or better. For the molecular ion H{sub 2}{sup +} in the Lagrange mesh method, the spectra of vibrational, rotational and rovibrational states (ν,L) associated with 1sσ{sub g} and 2pσ{sub u}, 2pπ{sub u} and 3dπ{sub g} potential curves are calculated. In general, it coincides with spectra found via numerical solution of the Schrödinger equation (when available) within six s.d. It is shown that 1sσ{sub g} curve contains 19 vibrational states (ν,0), while 2pσ{sub u} curve contains a single one (0,0) and 2pπ{sub u} state contains 12 vibrational states (ν,0). In general, 1sσ{sub g} electronic curve contains 420 rovibrational states, which increases up to 423 when we are beyond BO approximation. For the state 2pσ{sub u} the total number of rovibrational states (all with ν=0) is equal to 3, within or beyond Bohr–Oppenheimer approximation. As for the state 2pπ{sub u} within the Bohr–Oppenheimer approximation the total number of the rovibrational bound states is equal to 284. The state 3dπ{sub g} is repulsive, no rovibrational state is found. It is confirmed in Lagrange mesh formalism the statement that the ground state potential curve of the heteronuclear molecule HeH does not support rovibrational states. Accurate analytical expression for the potential curves of the hydrogen molecule H{sub 2} for the states {sup 1}Σ{sub g}{sup +} and {sup 3}Σ{sub u}{sup +} is presented. The ground state {sup 1}Σ{sub g}{sup +} contains 15 vibrational states (ν,0),ν=0–14. In general, this state supports 301 rovibrational states. The potential curve of the state {sup 3}Σ{sub u}{sup +} has a shallow minimum: it does not support any rovibrational state, it is repulsive.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Optimizing shift selection in multilevel Monte Carlo for disconnected diagrams in lattice QCD

The calculation of disconnected diagram contributions to physical signals is a computationally expensive task in Lattice QCD. To extract the physical signal, the trace of the inverse Lattice Dirac operator, a large sparse matrix, must be stochastically estimated. Because the variance of the stochastic estimator is typically large, variance reduction techniques must be employed. Multilevel Monte Carlo (MLMC) methods reduce the variance of the trace estimator by utilizing a telescoping sequence of estimators. Frequency Splitting is one such method that uses a sequence of inverses of shifted operators to estimate the trace of the inverse lattice Dirac operator, however there is no a priori way to select the shifts that minimize the cost of the multilevel trace estimation. Here we present a sampling and interpolation scheme that is able to predict the variances associated with Frequency Splitting under displacements of the underlying space time lattice. The interpolation scheme is able to predict the variances to high accuracy and therefore chooses shifts that correspond to an approximate minimum of the cost for the trace estimation. We show that Frequency Splitting with the chosen shifts displays significant speedups over multigrid deflation, and that these shifts can be used for multiple configurations within the same ensemble with no penalty to performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Implicit and explicit schemes for mass consistency preservation in hybrid particle/finite-volume algorithms for turbulent reactive flows

This work addresses the issue of particle mass consistency in Large Eddy Simulation/Probability Density Function (LES/PDF) methods for turbulent reactive flows. Numerical schemes for the implicit and explicit enforcement of particle mass consistency (PMC) are introduced, and their performance is examined in a representative LES/PDF application, namely the Sandia–Sydney Bluff-Body flame HM1. A new combination of interpolation schemes for velocity and scalar fields is found to better satisfy PMC than multilinear and fourth-order Lagrangian interpolation. A second-order accurate time-stepping scheme for stochastic differential equations (SDE) is found to improve PMC relative to Euler time stepping, which is the first time that a second-order scheme is found to be beneficial, when compared to a first-order scheme, in an LES/PDF application. An explicit corrective velocity scheme for PMC enforcement is introduced, and its parameters optimized to enforce a specified PMC criterion with minimal corrective velocity magnitudes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, by coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Data-driven models of nonautonomous systems

Nonautonomous dynamical systems are characterized by time-dependent inputs, which complicates the discovery of predictive models describing the spatiotemporal evolution of the state variables of quantities of interest from their temporal snapshots. When dynamic mode decomposition (DMD) is used to infer a linear model, this difficulty manifests itself in the need to approximate the time-dependent Koopman operators. Our approach is to approximate the original nonautonomous system with a modified system derived via a local parameterization of the time-dependent inputs. The modified system comprises a sequence of local parametric systems, which are subsequently approximated by a parametric surrogate model using the DRIPS (dimension reduction and interpolation in parameter space) framework. The offline step of DRIPS relies on DMD to build a linear surrogate model, endowed with reduced-order bases for the observables mapped from training data. The online step interpolates on suitable manifolds to construct a sequence of iterative parametric surrogate models; the target/test parameter points on these manifolds are specified by a local parameterization of the test time-dependent inputs. Here, we use numerical experimentation to demonstrate the robustness of our method and compare its performance with that of deep neural networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Diffusion coefficient of three-dimensional Yukawa liquids

The purpose of this work is an investigation of the diffusion coefficient of the dust component in complex plasma. The computer simulation of the Yukawa liquids was made on the basis of the Langevin equation, which takes into account the influence of buffer plasma on the dust particles dynamics. The Green–Kubo relation was used to calculate the diffusion coefficient. Calculations of the diffusion coefficient for a wide range of the system parameters were performed. Using obtained numerical data, we constructed the interpolation formula for the diffusion coefficient. We also show that the interpolation formula correctly describes experimental data obtained under microgravity conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗