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DOE OSTI2022

Ultrafast Error-bounded Lossy Compression for Scientific Datasets

Today's scientific high-performance computing applications and advanced instruments are producing vast volumes of data across a wide range of domains, which impose a serious burden on data transfer and storage. Error-bounded lossy compression has been developed and widely used in the scientific community because it not only can significantly reduce the data volumes but also can strictly control the data distortion based on the user-specified error bound. Existing lossy compressors, however, cannot offer ultrafast compression speed, which is highly demanded by numerous applications or use cases (such as in-memory compression and online instrument data compression). In this paper, we propose a novel ultrafast error-bounded lossy compressor that can obtain fairly high compression performance on both CPUs and GPUs and with reasonably high compression ratios. The key contributions are threefold. (1) We propose a generic error-bounded lossy compression framework---called SZx---that achieves ultrafast performance through its novel design comprising only lightweight operations such as bitwise and addition/subtraction operations, while still keeping a high compression ratio. (2) We implement SZx on both CPUs and GPUs and optimize the performance according to their architectures. (3) We perform a comprehensive evaluation with six real-world production-level scientific datasets on both CPUs and GPUs. Experiments show that SZx is 2~16x faster than the second-fastest existing error-bounded lossy compressor (either SZ or ZFP) on CPUs and GPUs, with respect to both compression and decompression.

Yu, Xiaodong↗

DOE OSTI2022

Numerical simulations of noisy quantum circuits for computational chemistry

The opportunities afforded by near-term quantum computers to calculate the ground-state properties of small molecules depend on the structure of the computational ansatz as well as the errors induced by device noise. Here we investigate the behavior of these noisy quantum circuits using numerical simulations to estimate the accuracy and fidelity of the prepared quantum states relative to the ground truth obtained by conventional means. We implement several different types of ansatz circuits derived from unitary coupled cluster theory for the purposes of estimating the ground-state energy of sodium hydride using the variational quantum eigensolver algorithm. We show how relative error in the energy and the fidelity scale with the levels of gate-based noise, the internuclear configuration, the ansatz circuit depth, and the parameter optimization methods.

36 MATERIALS SCIENCE↗

NASA NTRS1975

Semi-empirical calculation of depletion region width in n+-p silicon solar cells

An extension of the width calculation for impurity distributions of complementary error function and the Gaussian function, in addition to the exponential function is used in combination with experimental width values deduced from capacitance measurements at zero bias to numerically determine the width occurring in both the n+ and p junctions. The total possible error o the semi-empirical calculation is less than plus or minus 3%. Results show considerable variation in the depletion widths occurring in the n+ and p regions for different impurity profiles.

Wang, E. Y.↗

DOE OSTI2022

Spatial resolution of different discretizations over long-time for the Dirac equation with small potentials

In this report we compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic potentials characterized by $\varepsilon \in (0, 1]$ a dimensionless parameter. We begin with the simple and widely used finite difference time domain (FDTD) methods, and establish rigorous error bounds of them, which are valid up to the time at $O(1/\varepsilon)$. In the error estimates, we pay particular attention to how the errors depend explicitly on the mesh size $h$ and time step $\tau$ as well as the small parameter $\varepsilon$. Based on the results, in order to obtain "correct" numerical solutions up to the time at $O(1/\varepsilon)$, the $\varepsilon$-scalability (or meshing strategy requirement) of the FDTD methods should be taken as $h = O(\varepsilon^{1/2})$ and $\tau = O(\varepsilon^{1/2})$. To improve the spatial resolution capacity, we apply the Fourier spectral method to discretize the Dirac equation in space. Error bounds of the resulting finite difference Fourier pseudospectral (FDFP) methods show that they exhibit uniform spatial errors in the long-time regime, which are optimal in space as suggested by the Shannon's sampling theorem. Extensive numerical results are reported to confirm the error bounds and demonstrate that they are sharp.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

A Quantized State Integrator With Second Order Errors Over Monotonic Segments

We introduce a novel quantized state integration method that is analogous to the explicit, second order Runge-Kutta technique. A feature of this method is that, for a single differential equation over an interval where the solution is monotonic, it exhibits an error proportional to the square of the integration quantum. We offer a theoretical proof of this behavior and demonstrate it with a numerical example. At the same time, an extension of the method to a system with input causes the errors to become proportional to the integration quantum. The latter observation fits established theory; the former appears to be a new result that might offer new insights into the construction of quantized state integration methods.

Mahawattege, Rasika↗

NASA NTRS1979

Shuttle entry trajectory reconstruction using inflight accelerometer and gyro measurements

An error analysis has been made of a Shuttle postflight entry trajectory reconstruction process to obtain trajectory state estimation errors and to assess the impact of these errors on Shuttle aerodynamic force coefficient extraction. In this analysis, the entry trajectory is assumed to be reconstructed via numerical integration of onboard accelerometer and gyro measurements and constrained to satisfy ground-based radio tracking. The trajectory state estimation errors are calculated using a Kalman-Schmidt sequential filter assuming various measurement error models and combinations of ground-based tracking. The resultant trajectory estimation errors are analyzed in a simplified perturbation process to establish the accuracy to which postflight aerodynamic force coefficients can be determined. Results are presented which show that the principal error sources affecting the trajectory reconstruction and thus the force coefficient extraction, assuming perfect atmospheric density knowledge, are the accelerometer and gyro resolution, acceleration-sensitive gyro drifts, and the alignment uncertainties associated with integration on the Shuttle.

Compton, H. R.↗

DOE OSTI2023

11-th order of accuracy for numerical solution of 3-D Poisson equation with irregular interfaces on unfitted Cartesian meshes

For the first time the optimal local truncation error method (OLTEM) with 125-point stencils and unfitted Cartesian meshes has been developed in the general 3-D case for the Poisson equation for heterogeneous materials with smooth irregular interfaces. The 125-point stencils equations that are similar to those for quadratic finite elements are used for OLTEM. The interface conditions for OLTEM are imposed as constraints at a small number of interface points and do not require the introduction of additional unknowns, i.e., the sparse structure of global discrete equations of OLTEM is the same for homogeneous and heterogeneous materials. The stencils coefficients of OLTEM are calculated by the minimization of the local truncation error of the stencil equations. These derivations include the use of the Poisson equation for the relationship between the different spatial derivatives. Such a procedure provides the maximum possible accuracy of the discrete equations of OLTEM. In contrast to known numerical techniques with quadratic elements and third order of accuracy on conforming and unfitted meshes, OLTEM with the 125-point stencils provides 11-th order of accuracy, i.e., an extremely large increase in accuracy by 8 orders for similar stencils. The numerical results show that OLTEM yields much more accurate results than high-order finite elements with much wider stencils. The increased numerical accuracy of OLTEM leads to an extremely large increase in computational efficiency. Additionally, a new post-processing procedure with the 125-point stencil has been developed for the calculation of the spatial derivatives of the primary function. The post-processing procedure includes the minimization of the local truncation error and the use of the Poisson equation. It is demonstrated that the use of the partial differential equation (PDE) for the 125-point stencils improves the accuracy of the spatial derivatives by 6 orders compared to post-processing without the use of PDE as in existing numerical techniques. At an accuracy of 0.1% for the spatial derivatives, OLTEM reduces the number of degrees of freedom by 900 - 4∙10 6 times compared to quadratic finite elements. The developed post-processing procedure can be easily extended to unstructured meshes and can be independently used with existing post-processing techniques (e.g., with finite elements).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

The pp → W(→ lν) + γ process at next-to-next-to-leading order

We present details of the calculation of the pp → W(→ lν)γ process at next-to-next-to-leading order in QCD, calculated using the jettiness slicing method. The calculation is based entirely on analytic amplitudes. Because of the radiation zero, the NLO QCD contribution from the gq channel is as important as the contribution from the Born $ q\overline{q} $ process, disrupting the normal counting of leading and sub-leading contributions. We also assess the importance of electroweak (EW) corrections, including the EW corrections to both the six-parton channel 0 →$ \overline{u} d\nu {e}^{+}\gamma g $ and the five-parton channel 0 →$ \overline{u} d\nu {e}^{+}\gamma $. Previous experimental results have been shown to agree with theoretical predictions, taking into account the large experimental errors. With the advent of run II data from the LHC, the statistical errors on the data will decrease, and will be competitive with the error on theoretical predictions for the first time. We present numerical results for $ \sqrt{s} $ = 7 and 13 TeV. Analytic results for the one-loop six-parton QCD amplitude and the tree-level seven-parton QCD amplitude are presented in appendices.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

WeakIdent: Weak formulation for identifying differential equation using narrow-fit and trimming

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation with two new mechanisms, narrow-fit and trimming, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise, and two new mechanisms, narrow-fit and trimming, improve the coefficient support and value recoveries respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to 100% noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Stability boundary and optimal operating parameter identification in milling using Bayesian learning

Here, this paper describes a novel Bayesian learning approach for stability boundary and optimal parameter identification in milling without the knowledge of the underlying tool dynamics or material cutting force coefficients. The paper is divided into two parts. First, a Bayesian learning method for stability lobe identification using test results is described. Each axial depth and spindle speed combination is characterized by a probability of stability which is updated using Bayes’ rule when a test result (stable or unstable) is made available. A novel likelihood function is defined which incorporates knowledge of the stability behavior. Numerical results show convergence to the analytical stability lobe diagram. Second, an adaptive experimental strategy to identify optimal operating parameters that maximize material removal rate is described. Numerical evaluation shows convergence to the optimal operating point with error less than 15 % within ten tests on average. The approach is validated using experimental results. Results show that the proposed method is an efficient and robust learning method to identify the stability lobe diagram and optimal operating parameters with a limited number of tests/data points.

Bayesian machine learning↗

DOE OSTI2023

malbacR: A Package for Standardized Implementation of Batch Correction Methods for Omics Data

Mass spectrometry is a powerful tool for identifying and analyzing small molecules, such as metabolites and lipids, in com-plex biological samples. Liquid chromatography and gas chromatography mass spectrometry studies quite commonly in-volve large numbers of samples, which can require significant time for sample preparation and analyses. To accommodate such studies, the samples are commonly split into batches. Inevitably, variations in sample handling, temperature fluctua-tion, imprecise timing, column degradation and other factors result in systematic errors or biases of the measured abundances between the batches. Numerous methods are available via R packages to assist with batch correction for small molecule om-ics data; however, since these methods were developed by different research teams, the algorithms are available in separate R packages, each with different data input and output formats. We introduce the malbacR package which consolidates eleven common batch effect correction methods for small molecule omics data into one place so users can easily implement and compare: pareto scaling, power scaling, range scaling, ComBat, EigenMS, NOMIS, RUV-random, QC-RLSC, WaveI-CA2.0, TIGER, and SERRF. The malbacR package standardizes data input and output formats across these batch correction methods. The package works in conjunction with the pmartR package, allowing users to seamlessly include batch effect cor-rection in a pmartR workflow without needing any additional data manipulation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Shaded fraction and backtracking in single-axis trackers on rolling terrain

A generalized closed-form equation for the shaded collector fraction in solar arrays on rolling or undulating terrain is provided for single-axis tracking and fixed-tilt systems. The equation accounts for different rotation angles between the shaded and shading trackers, cross-axis slope between the two trackers, and offset between the collector plane and axis of rotation. The validity of the equation is demonstrated through comparison with numerical ray-tracing simulations and remaining minor sources of error are quantified. Additionally, a simple procedure to determine backtracking rotations for each row in an array installed on the rolling terrain (varying in the direction perpendicular to the tracker axes) is provided. The backtracking equation accounts for a desired shaded fraction (including complete shade avoidance) as well as an axis-collector offset. Test cases are provided to facilitate implementation of these equations.

14 SOLAR ENERGY↗

DOE OSTI2020

Influence of birefringent fibre joints on the visibility drift in a Mach – Zehnder interferometer

It is shown that imperfect joints of linear birefringent fibres in a fibre interferometer may result in an uncontrolled visibility drift under varying environmental conditions even with a standard phase matching device. As an example, a double Mach – Zehnder interferometer is considered, which is employed in schemes of quantum key distribution. Results of numerical simulation demonstrate the standard deviation of the quantum bit error rate (QBER), which is comparable to an average QBER value. (paper)

36 MATERIALS SCIENCE↗

DOE OSTI2023

Nonequilibrium spectral moment sum rules of the Holstein–Hubbard model

Abstract We derive a general procedure for evaluating the n th derivative of a time-dependent operator in the Heisenberg representation and employ this approach to calculate the zeroth to third spectral moment sum rules of the retarded electronic Green’s function and self-energy for a system described by the Holstein–Hubbard model allowing for arbitrary spatial and time variation of all parameters (including spatially homogeneous electric fields and parameter quenches). For a translationally invariant (but time-dependent) Hamiltonian, we also provide sum rules in momentum space. The sum rules can be applied to various different phenomena like time-resolved angle-resolved photoemission spectroscopy and benchmarking the accuracy of numerical many-body calculations. This work also corrects some errors found in earlier work on simpler models.

Physics↗

DOE OSTI2020

Dynamic Power Network State Estimation with Asynchronous Measurements

The operation of distribution networks is becoming increasingly volatile, due to fast variations of renewables and, hence, net-loading conditions. To perform a reliable state estimation under these conditions, this paper considers the case where measurements from meters, phasor measurement units, and distributed energy resources are collected and processed in real time to produce estimates of the state at a fast time scale. Streams of measurements collected in real time and at heterogenous rates render the underlying processing asynchronous, and poses severe strains on workhorse state estimation algorithms. In this work, a real-time state estimation algorithm is proposed, where data are processed on the fly. Starting from a regularized least-squares model, and leveraging appropriate linear models, the proposed scheme boils down to a linear dynamical system where the state is updated based on the previous estimate and on the measurement gathered from a few available sensors. The estimation error is shown to be always bounded under mild condition. Numerical simulations are provided to corroborate the analytical findings.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Optimal Power Flow With State Estimation in the Loop for Distribution Networks

Here in this article, we propose a framework for running optimal control-estimation synthesis in distribution networks. Our approach combines a primal-dual gradient-based optimal power flow solver with a state estimation feedback loop based on a limited set of sensors for system monitoring, instead of assuming exact knowledge of all states. The estimation algorithm reduces uncertainty on unmeasured grid states based on certain online state measurements and noisy "pseudomeasurements." We analyze the convergence of the proposed algorithm and quantify the statistical estimation errors based on a weighted least-squares estimator. The numerical results on a 4521-node network demonstrate that this approach can scale to extremely large networks and provide robustness to both large pseudomeasurement variability and inherent sensor measurement noise.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

A new upper bound for the growth factor in Gaussian elimination with complete pivoting

Abstract The growth factor in Gaussian elimination measures how large the entries of an LU factorization can be relative to the entries of the original matrix. It is a key parameter in error estimates, and one of the most fundamental topics in numerical analysis. We produce an upper bound of for the growth factor in Gaussian elimination with complete pivoting — the first improvement upon Wilkinson's original 1961 bound of .

Bisain, Ankit [Department of Mathematics Massachus↗

DOE OSTI2024

Earth System Reanalysis in Support of Climate Model Improvements

Recent climate model developments, established through increased model resolution, have led to substantial improvements in model simulations of the time-evolving, coupled Earth system and its subcomponents. However, regardless of resolution, climate models will always produce climate features and variability that differ from the real world and will be prone to biases. This is due to many remaining uncertainties, such as in parametric and structural model uncertainty, in the initial conditions prescribed, and in the prescribed (scenario) forcing which varies on decadal to centennial timescales. Further model improvements are expected to arise specifically from improved representation of physical processes realized through model-data fusion. This will create an unprecedented opportunity to better exploit a large array of Earth observations, from in situ measurements to weather radars and satellite observations, as the resolved scales of the models approach those of the observations. For this, climate DA will be the central tool to bring models and observations into consistency, by improving initial conditions, inferring uncertain model parameters and structure, and quantifying uncertainty. Generally, there will be advantages and complementarities of adjoint-based smoother approaches, ensemble-based filter approaches, or new ML-inspired approaches. Yet, the ever-increasing model resolution will present growing challenges arising from computational cost, calling for new ways of performing data assimilation and model optimization. Using the complementarity in a hybrid approach, blending tools and concepts from variational, ensemble and ML methods might be what is required in the future. In this context ML could be important to handle non-linear responses, and to better approximate non-Gaussian distributions.

54 ENVIRONMENTAL SCIENCES↗