SEARCH · Search NASA

Results for “ERROR ANALYSIS”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

All sources NASA NTRS DOE OSTI

DOE OSTI2021

Perspective: Reproducible Coherence Characterization of Superconducting Quantum Devices

As the field of superconducting quantum computing approaches maturity, optimization of single-device performance is proving to be a promising avenue towards large-scale quantum computers. However, this optimization is possible only if performance metrics can be accurately compared among measurements, devices, and laboratories. Currently such comparisons are inaccurate or impossible due to understudied errors from a plethora of sources. In this Perspective, we outline the current state of error analysis for qubits and resonators in superconducting quantum circuits, and discuss what future investigations are required before superconducting quantum device optimization can be realized.

McRae, Corey H.↗

DOE OSTI2022

Supervised learning and the finite-temperature string method for computing committor functions and reaction rates

A central object in the computational studies of rare events is the committor function. Though costly to compute, the committor function encodes complete mechanistic information of the processes involving rare events, including reaction rates and transition-state ensembles. Under the framework of transition path theory, Rotskoff et al. [Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, Proceedings of Machine Learning Research (PLMR, 2022), Vol. 145, pp. 757–780] proposes an algorithm where a feedback loop couples a neural network that models the committor function with importance sampling, mainly umbrella sampling, which collects data needed for adaptive training. Here, in this work, we show additional modifications are needed to improve the accuracy of the algorithm. The first modification adds elements of supervised learning, which allows the neural network to improve its prediction by fitting to sample-mean estimates of committor values obtained from short molecular dynamics trajectories. The second modification replaces the committor-based umbrella sampling with the finite-temperature string (FTS) method, which enables homogeneous sampling in regions where transition pathways are located. We test our modifications on low-dimensional systems with non-convex potential energy where reference solutions can be found via analytical or finite element methods, and show how combining supervised learning and the FTS method yields accurate computation of committor functions and reaction rates. We also provide an error analysis for algorithms that use the FTS method, using which reaction rates can be accurately estimated during training with a small number of samples. The methods are then applied to a molecular system in which no reference solution is known, where accurate computations of committor functions and reaction rates can still be obtained.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-grained particle- or agent-based simulations; these SDEs then provide useful coarse surrogate models of the fine scale dynamics. We approximate the drift and diffusivity functions in these effective SDEs through neural networks, which can be thought of as effective stochastic ResNets. The loss function is inspired by, and embodies, the structure of established stochastic numerical integrators (here, Euler–Maruyama and Milstein); our approximations can thus benefit from backward error analysis of these underlying numerical schemes. They also lend themselves naturally to “physics-informed” gray-box identification when approximate coarse models, such as mean field equations, are available. Existing numerical integration schemes for Langevin-type equations and for stochastic partial differential equations can also be used for training; we demonstrate this on a stochastically forced oscillator and the stochastic wave equation. Our approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot. We consider both the case where the coarse collective observables are known in advance, as well as the case where they must be found in a data-driven manner.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

An evaluation for geometries, formation enthalpies, and dissociation energies of diatomic and triatomic (C, H, N, O), NO 3 , and HNO 3 molecules from the PAW DFT method with PBE and optB88-vdW functionals

The structural geometries, formation enthalpies, and dissociation energies of all diatomic and triatomic molecules consisting of the four basic elements C, H, N, and/or O are calculated using the projector augmented wave density functional theory (DFT) method with the Perdew–Burke–Ernzerhof and optB88-vdW exchange-correlation functionals. The calculations are also extended to two larger molecules NO 3 and HNO 3 , which consist of four and five atoms, respectively. In total, 82 molecules or isomers are considered in the calculations. The geometric parameters including 42 bond lengths and 15 bond angles of these molecules calculated using the planewave DFT method are highly satisfactory, relative to the available experimental data. The error analysis is also performed for 49 formation enthalpies and 138 dissociation energies (including 51 atomization energies as well as the corresponding bond dissociation energies). The results are also compared with the previous data from various atomic-orbital-based methods for molecules and from similar or different planewave DFT methods for various solids and other molecules. This provides an informative and instructive evaluation especially for calculating the large-size material systems containing these small molecules as well as for developing the DFT methods further.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics

In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original “zeroth-level” shadow energy functionals and potentials used in extended Lagrangian BOMD. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Relativistic resolution-of-the-identity with Cholesky integral decomposition

In this study, we present an efficient integral decomposition approach called the restricted-kinetic-balance resolution-of-the-identity (RKB-RI) algorithm, which utilizes a tunable RI method based on the Cholesky integral decomposition for in-core relativistic quantum chemistry calculations. The RKB-RI algorithm incorporates the restricted-kinetic-balance condition and offers a versatile framework for accurate computations. Notably, the Cholesky integral decomposition is employed not only to approximate symmetric large-component electron repulsion integrals but also those involving small-component basis functions. In addition to comprehensive error analysis, we investigate crucial conditions, such as the kinetic balance condition and variational stability, which underlie the applicability of Dirac relativistic electronic structure theory. Here we compare the computational cost of the RKB-RI approach with the full in-core method to assess its efficiency. To evaluate the accuracy and reliability of the RKB-RI method proposed in this work, we employ actinyl oxides as benchmark systems, leveraging their properties for validation purposes. This investigation provides valuable insights into the capabilities and performance of the RKB-RI algorithm and establishes its potential as a powerful tool in the field of relativistic quantum chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Second release of the CoRe database of binary neutron star merger waveforms

Abstract We present the second data release of gravitational waveforms from binary neutron star (BNS) merger simulations performed by the Computational Relativity ( CoRe ) collaboration. The current database consists of 254 different BNS configurations and a total of 590 individual numerical-relativity simulations using various grid resolutions. The released waveform data contain the strain and the Weyl curvature multipoles up to ℓ = m = 4 . They span a significant portion of the mass, mass-ratio, spin and eccentricity parameter space and include targeted configurations to the events GW170817 and GW190425. CoRe simulations are performed with 18 different equations of state, seven of which are finite temperature models, and three of which account for non-hadronic degrees of freedom. About half of the released data are computed with high-order hydrodynamics schemes for tens of orbits to merger; the other half is computed with advanced microphysics. We showcase a standard waveform error analysis and discuss the accuracy of the database in terms of faithfulness. We present ready-to-use fitting formulas for equation of state-insensitive relations at merger (e.g. merger frequency), luminosity peak, and post-merger spectrum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Least H 2 norm updating of quadratic interpolation models for derivative-free trust-region algorithms

One particular class of derivative-free optimization algorithms is trust-region algorithms based on quadratic models given by the under-determined interpolation. Different techniques in updating the quadratic model from iteration to iteration will give different interpolation models. We propose a new way to update the quadratic model by minimizing the $H^{2}$ norm of the difference between neighboring quadratic models. The motivation for applying the $H^{2}$ norm is given. The theoretical properties of our new updating technique are also presented. We propose the projection in the sense of $H^{2}$ norm and the interpolation error analysis of our model function. We obtain the coefficients of the quadratic model function using the Karush–Kuhn–Tucker (KKT) conditions. Numerical results show the advantages of our model on the test set considered, and the derivative-free algorithms based on our least $H^{2}$ norm updating quadratic model functions can solve test problems with fewer function evaluations than the algorithm based on the least Frobenius norm updating model and the other compared methods.

derivative-free optimization↗

DOE OSTI2026

Linear complexity

We present factorization and solution phases for a new linear complexity direct solver designed for concurrent batch operations on fine-grained parallel architectures, for matrices amenable to hierarchical representation. We focus on the strong-admissibility-based $\mathscr{H}^{2}$ format, where strong recursive skeletonization factorization compresses remote interactions. We build upon previous implementations of $\mathscr{H}^{2}$ matrix construction for efficient factorization and solution algorithm design, which are illustrated graphically in stepwise detail. The algorithms are ‘blackbox’ in the sense that the only inputs are the matrix and right-hand side, without analytical or geometrical information about the origin of the system. We demonstrate linear complexity scaling in both time and memory on four representative families of dense matrices up to one million in size. Parallel scaling up to 16 threads is enabled by a multi-level matrix graph coloring and avoidance of dynamic memory allocations thanks to prefix-sum memory management. An experimental backward error analysis is included. We break down the timings of different phases, identify phases that are memory-bandwidth limited, and discuss alternatives for phases that may be sensitive to the trend to employ lower precisions for performance.

Boukaram, Wajih↗

DOE OSTI2021

GAMA/DEVILS: constraining the cosmic star formation history from improved measurements of the 0.3–2.2 μm extragalactic background light

We present a revised measurement of the optical extragalactic background light (EBL), based on the contribution of resolved galaxies to the integrated galaxy light (IGL). The cosmic optical background radiation (COB), encodes the light generated by star formation, and provides a wealth of information about the cosmic star formation history (CSFH). We combine wide and deep galaxy number counts from the Galaxy And Mass Assembly survey (GAMA) and Deep Extragalactic VIsible Legacy Survey (DEVILS), along with the Hubble Space Telescope (HST) archive and other deep survey data sets, in nine multiwavelength filters to measure the COB in the range from 0.35 μm to 2.2 μm. We derive the luminosity density in each band independently and show good agreement with recent and complementary estimates of the optical-EBL from very high-energy (VHE) experiments. Our error analysis suggests that the IGL and γ-ray measurements are now fully consistent to within $\sim 10{{\ \rm per\ cent}}$, suggesting little need for any additional source of diffuse light beyond the known galaxy population. We use our revised IGL measurements to constrain the CSFH, and place amplitude constraints on a number of recent estimates. As a consistency check, we can now demonstrate convincingly, that the CSFH, stellar mass growth, and the optical-EBL provide a fully consistent picture of galaxy evolution. Here, we conclude that the peak of star formation rate lies in the range 0.066–0.076 M ⊙ yr -1 Mpc -3 at a lookback time of 9.1 to 10.9 Gyr.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Nuclear properties with semilocal momentum-space regularized chiral interactions beyond N 2 LO

We present a comprehensive investigation of few-nucleon systems as well as light and medium-mass nuclei up to A = 48 using the current Low Energy Nuclear Physics International Collaboration two-nucleon interactions in combination with the third-order (N 2 LO) three-nucleon forces. To address the systematic overbinding of nuclei starting from A ≈ 10 found in our earlier study utilizing the N 2 LO two- and three-nucleon forces, we take into account higher-order corrections to the two-nucleon potentials up through fifth order in chiral effective field theory. Here, the resulting Hamiltonian can be completely determined using the A = 3 binding energies and selected nucleon-deuteron cross sections as input. It is then shown to predict other nucleon-deuteron scattering observables and spectra of light p-shell nuclei, for which a detailed correlated truncation error analysis is performed, in agreement with experimental data. Moreover, the predicted ground state energies of nuclei in the oxygen isotopic chain from 14 O to 26 O as well as 40 Ca and 48 Ca show a remarkably good agreement with experimental values, given that the Hamiltonian is fixed completely from the A ≤ 3 data, once the fourth-order (N 3 LO) corrections to the two-nucleon interactions are taken into account. On the other hand, the charge radii are found to be underpredicted by ≈10% for the oxygen isotopes and by almost 20% for 40 Ca and 48 Ca.

20 ≤ A ≤ 38↗

DOE OSTI2021

Lattice determination of 𝐼=0 and 2 𝜋⁢𝜋 scattering phase shifts with a physical pion mass

Phase shifts for 𝑠-wave 𝜋⁢𝜋 scattering in both the 𝐼 =0 and 𝐼 =2 channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of 32 3 ×64. These results support our recent 2021 study of direct 𝐶⁢𝑃 violation in 𝐾 → 𝜋⁢𝜋 decay, improving our earlier 2015 calculation. The phase shifts are determined for both stationary and moving 𝜋⁢𝜋 systems, at three (𝐼 = 0) and four (𝐼 = 2) different total momenta. We implement several 𝜋⁢𝜋 interpolating operators including a scalar bilinear “𝜎” operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States

The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo–based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Ytterbium ion trap quantum computing: The current state-of-the-art

In this work, we present an overview of contemporary quantum computing with ytterbium ion traps, placing the emphasis on industry implementations. We provide brief, concrete descriptions of various key features, such as trap loading, electronic structure, qubit function, gates, error analysis, and benchmarking. We focus on the underlying science and current technologies to provide readers with a holistic picture of available techniques for using ytterbium in contemporary ion trap designs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

SNS: A Solution-Based Nonlinear Subspace Method for Time-Dependent Model Order Reduction

Several reduced order models have been successfully developed for nonlinear dynamical systems. To achieve a considerable speed-up, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. Many hyper-reduction techniques require the construction of nonlinear term basis, which introduces a computationally expensive offline phase. A novel way of constructing nonlinear term basis within the hyper-reduction process is introduced. In contrast to the traditional hyper-reduction techniques where the collection of nonlinear term snapshots is required, the SNS method avoids collecting the nonlinear term snapshots. Instead, it uses the solution snapshots that are used for building a solution basis, which enables avoiding an extra data compression of nonlinear term snapshots. As a result, the SNS method provides a more efficient offline strategy than the traditional model order reduction techniques, such as the DEIM, GNAT, and ST-GNAT methods. The SNS method is theoretically justified by the conforming subspace condition and the subspace inclusion relation. It is useful for model order reduction of large-scale nonlinear dynamical problems to reduce the offline cost. It is especially useful for ST-GNAT that has shown promising results, such as a good accuracy with a considerable online speed-up for hyperbolic problems in a recent paper by Choi and Carlberg [SIAM J. Sci. Comput., 41 (2019), pp. A26--A58], because ST-GNAT involves an expensive offline cost related to collecting nonlinear term snapshots. Error analysis for the SNS method is presented. Numerical results support that the accuracy of the solution from the SNS method is comparable to the traditional methods and a considerable speed-up (i.e., a factor of two to a hundred) is achieved in the offline phase.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A Fast Time-Stepping Strategy for Dynamical Systems Equipped with a Surrogate Model

Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper and simpler ways to describe the dynamics of these systems but are inexact and introduce additional approximation errors. In order to overcome the computational difficulties of the full complex models, on one hand, and the limitations of surrogate models, on the other, this work proposes a new accelerated time-stepping strategy that combines information from both. This approach is based on the multirate infinitesimal general-structure additive Runge--Kutta framework. The inexpensive surrogate model is integrated with a small time step to guide the solution trajectory, and the full model is treated with a large time step to occasionally correct for the surrogate model error and ensure convergence. Here, we provide a theoretical error analysis, and several numerical experiments, to show that this approach can be significantly more efficient than using only the full or only the surrogate model for the integration.

Surrogate models↗

DOE OSTI2024

Parallel Randomized Tucker Decomposition Algorithms

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. Here, we propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two algorithms that scale to large data and many processors, significantly reduce both computation and communication cost compared to previous deterministic and randomized approaches, and obtain nearly the same approximation errors. The key idea in our algorithms is to perform randomized sketches with Kronecker-structured random matrices, which reduces computation compared to unstructured matrices and can be implemented using a fundamental tensor computational kernel. We provide probabilistic error analysis of our algorithms and implement a new parallel algorithm for the structured randomized sketch. Our experimental results demonstrate that our combination of randomization and parallelization achieves accurate Tucker decompositions much faster than alternative approaches. We observe up to a 16X speedup over the fastest deterministic parallel implementation on 3D simulation data.

Tucker decompositions↗

DOE OSTI2021

Evaluation of KDP Estimation Algorithm Performance in Rain Using a Known-Truth Framework

Accurate estimation of specific differential phase ( K DP ) is necessary for rain rate estimation, attenuation correction, and hydrometeor classification algorithms. There are numerous published methods to process polarimetric radar observations of propagation differential phase shift (Φ DP ) and estimate K DP , but the corresponding K DP estimate uncertainty is unquantified. This study provides guidance on how commonly used K DP estimation algorithms perform in various environments. Here, we create numerous synthetic (“true”) K DP profiles, integrate over them to obtain “smoothed” Φ DP , and then add noise typical of S-band operational weather radar measurements. Each algorithm is applied to our noisy Φ DP profiles and compared to the true K DP profile such that the errors and uncertainty are quantified. The synthetic K DP profiles are Gaussian in shape, which allows systematic variations in their magnitude and width to determine how each algorithm performs in smooth, slowly changing K DP profiles, as well as steep profiles. Results demonstrate that algorithm performance is dependent on the Φ DP field received. These results are further supported by an error analysis of each algorithm for two more complicated synthetic K DP profiles. Some K DP algorithms allow users to change various tuning parameters; a subset of these tuning parameters is tested to provide guidance on how changing these parameters impacts algorithm performance. We then provide evidence that our known-truth framework provides insight into algorithm performance in observed data through two case studies.

54 ENVIRONMENTAL SCIENCES↗