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DOE OSTI2020

Performance Optimization for Relative-Error-Bounded Lossy Compression on Scientific Data

Scientific simulations in high-performance computing (HPC) environments generate vast volume of data, which may cause a severe I/O bottleneck at runtime and a huge burden on storage space for postanalysis. Unlike traditional data reduction schemes such as deduplication or lossless compression, not only can error-controlled lossy compression significantly reduce the data size but it also holds the promise to satisfy user demand on error control. Pointwise relative error bounds (i.e., compression errors depends on the data values) are widely used by many scientific applications with lossy compression since error control can adapt to the error bound in the dataset automatically. Pointwise relative-error-bounded compression is complicated and time consuming. In this article, we develop efficient precomputation-based mechanisms based on the SZ lossy compression framework. Our mechanisms can avoid costly logarithmic transformation and identify quantization factor values via a fast table lookup, greatly accelerating the relative-error-bounded compression with excellent compression ratios. In addition, we reduce traversing operations for Huffman decoding, significantly accelerating the decompression process in SZ. Experiments with eight well-known real-world scientific simulation datasets show that our solution can improve the compression and decompression rates (i.e., the speed) by about 40 and 80 p, respectively, in most of cases, making our designed lossy compression strategy the best-in-class solution in most cases.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

DOE OSTI2018

Efficient Lossy Compression for Scientific Data Based on Pointwise Relative Error Bound

An effective data compressor is becoming increasingly critical to today's scientific research, and many lossy compressors are developed in the context of absolute error bounds. Based on physical/chemical definitions of simulation fields or multiresolution demand, however, many scientific applications need to compress the data with a pointwise relative error bound (i.e., the smaller the data value, the smaller the compression error to tolerate). To this end, we propose two optimized lossy compression strategies under a state-of-the-art three-staged compression framework (prediction + quantization + entropy-encoding). The first strategy (called block-based strategy) splits the data set into many small blocks and computes an absolute error bound for each block, so it is particularly suitable for the data with relatively high consecutiveness in space. The second strategy (called multi-threshold-based strategy) splits the whole value range into multiple groups with exponentially increasing thresholds and performs the compression in each group separately, which is particularly suitable for the data with a relatively large value range and spiky value changes. We implement the two strategies rigorously and evaluate them comprehensively by using two scientific applications which both require lossy compression with point-wise relative error bound. Experiments show that the two strategies exhibit the best compression qualities on different types of data sets respectively. In conclusion, the compression ratio of our lossy compressor is higher than that of other state-of-the-art compressors by 17.2-618 percent on the climate simulation data and 30-210 percent on the N-body simulation data, with the same relative error bound and without degradation of the overall visualization effect of the entire data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Accelerating Relative-error Bounded Lossy Compression for HPC datasets with Precomputation-Based Mechanisms

Scientific simulations in high-performance computing (HPC) environments are producing vast volume of data, which may cause a severe I/O bottleneck at runtime and a huge burden on storage space for post-analysis. Unlike the traditional data reduction schemes (such as deduplication or lossless compression), not only can error-controlled lossy compression significantly reduce the data size but it can also hold the promise to satisfy user demand on error control. Point-wise relative error bounds (i.e., compression errors depends on the data values) are widely used by many scientific applications in the lossy compression, since error control can adapt to the precision in the dataset automatically. Point-wise relative error bounded compression is complicated and time consuming. In this work, we develop efficient precomputation-based mechanisms in the SZ lossy compression framework. Our mechanisms can avoid costly logarithmic transformation and identify quantization factor values via a fast table lookup, greatly accelerating the relative-error bounded compression with excellent compression ratios. In addition, our mechanisms also help reduce traversing operations for Huffman decoding, and thus significantly accelerate the decompression process in SZ. Experiments with four well-known real-world scientific simulation datasets show that our solution can improve the compression rate by about 30% and decompression rate by about 70% in most of cases, making our designed lossy compression strategy the best choice in class in most cases.

compression rate↗

DOE OSTI2016

Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights

Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Optimising the processing and storage of visibilities using lossy compression

The next-generation radio astronomy instruments are providing a massive increase in sensitivity and coverage, largely through increasing the number of stations in the array and the frequency span sampled. The two primary problems encountered when processing the resultant avalanche of data are the need for abundant storage and the constraints imposed by I/O, as I/O bandwidths drop significantly on cold storage. An example of this is the data deluge expected from the SKA Telescopes of more than 60 PB per day, all to be stored on the buffer filesystem. While compressing the data is an obvious solution, the impacts on the final data products are hard to predict. In this paper, we chose an error-controlled compressor – MGARD – and applied it to simulated SKA-Mid and real pathfinder visibility data, in noise-free and noise-dominated regimes. As the data have an implicit error level in the system temperature, using an error bound in compression provides a natural metric for compression. MGARD ensures the compression incurred errors adhere to the user-prescribed tolerance. To measure the degradation of images reconstructed using the lossy compressed data, we proposed a list of diagnostic measures, exploring the trade-off between these error bounds and the corresponding compression ratios, as well as the impact on science quality derived from the lossy compressed data products through a series of experiments. We studied the global and local impacts on the output images for continuum and spectral line examples. We found relative error bounds of as much as 10%, which provide compression ratios of about 20, have a limited impact on the continuum imaging as the increased noise is less than the image RMS, whereas a 1% error bound (compression ratio of 8) introduces an increase in noise of about an order of magnitude less than the image RMS. For extremely sensitive observations and for very precious data, we would recommend a 0.1% error bound with compression ratios of about 4. These have noise impacts two orders of magnitude less than the image RMS levels. At these levels, the limits are due to instabilities in the deconvolution methods. We compared the results to the alternative compression tool DYSCO, in both the impacts on the images and in the relative flexibility. MGARD provides better compression for similar error bounds and has a host of potentially powerful additional features.

Techniques: interferometric↗

DOE OSTI2025

Out-of-Distribution Generalization for Learning Quantum Channels with Low-Energy Coherent States

When experimentally learning the action of a continuous-variable quantum process by probing it with inputs, there will often be some restriction on the input states used. One experimentally simple way to probe a quantum channel is to use low-energy coherent states. Learning a quantum channel in this way presents difficulties, due to the fact that two channels may act similarly on low-energy inputs but very differently for high-energy inputs. They may also act similarly on coherent-state inputs but differently on nonclassical inputs. Extrapolating the behavior of a channel for more general input states from its action on the far more limited set of low-energy coherent states is a case of out-of-distribution generalization. To be sure that such generalization gives meaningful results, one needs to relate error bounds for the training set to bounds that are valid for all inputs. We show that for any pair of channels that act sufficiently similarly on low-energy coherent-state inputs, one can bound how different the input-output relations are for any (high-energy or highly nonclassical) input. This proves that out-of-distribution generalization is always possible for learning quantum channels using low-energy coherent states, as long as enough samples are used.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Fast and Accurate Intersections on a Sphere

We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and numerical robustness over the ones traditionally implemented in geoscience software. We then show how algorithms based on the concept of error-free transformations (EFT) can be applied to evaluate this formula within a relative error bound that is on the order of machine precision. Here, we demonstrate that, with a vectorized and parallelized implementation, this enhanced accuracy is achieved with no compute time overhead compared to a direct calculation in hardware floating point, making our algorithm suitable for performance-sensitive applications like regridding of high-resolution climate data. In contrast, evaluating our formula using high-precision data types like quadruple precision and arbitrary precision, or using the robust intersection computation routines from the Computational Geometry Algorithms Library, leads to significant computational overhead, especially since these alternatives inhibit vectorization. More generally, our work demonstrates how EFT techniques can be combined and extended to implement nontrivial geometric calculations with high accuracy and speed.

Environmental sciences↗

DOE OSTI2022

A Framework for Error-Bounded Approximate Computing, with an Application to Dot Products

Approximate computing techniques, which trade off the computation accuracy of an algorithm for better performance and energy efficiency, have been successful in reducing computation and power costs in several domains. However, error sensitive applications in high-performance computing are unable to benefit from existing approximate computing strategies that are not developed with guaranteed error bounds. While approximate computing techniques can be developed for individual high-performance computing applications by domain specialists, this often requires additional theoretical analysis and potentially extensive software modification. Hence, the development of low-level error-bounded approximate computing strategies that can be introduced into any high-performance computing application without requiring additional analysis or significant software alterations is desirable. In this paper, we provide a contribution in this direction by proposing a general framework for designing error-bounded approximate computing strategies and apply it to the dot product kernel to develop \bf qdot---an error-bounded approximate dot product kernel. Following the introduction of qdot, here we perform a theoretical analysis that yields a deterministic bound on the relative approximation error introduced by qdot. Empirical tests are performed to illustrate the tightness of the derived error bound and to demonstrate the effectiveness of qdot on a synthetic dataset, as well as two scientific benchmarks---the conjugate gradient (CG) and power methods. In some instances, using qdot for the dot products in CG can result in many components being quantized to half precision without increasing the iteration count required for convergence to the same solution as CG using a double precision dot product.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Further Investigation of Employing Binomial Small-Sample Estimator in M-LROM

Reduced Order Modeling (ROM) is essential to enable the identification of the so-called active parameter subspace for high-fidelity models that are employed in computationally intensive analyses such as uncertainty characterization and data assimilation. Given the complexity of models for real-world application, brute force methods to identify the active subspace may not be computationally efficient to realize the value of reduction, since in realistic problems, the full scale model must be executed few hundred times, which may be computationally taxing. Earlier work has introduced a new approach, which represents a further development of our previous work on ROM, referred to as multi-level ROM (M-LROM). In M-LROM, approximate models are employed to identify the active subspace instead of the full scale model. In this summary, we present our recent results on M-LROM, specifically in regard to the construction of reliable error metrics that can bound the errors resulting from the reduction. The idea is to employ a lower fidelity model, i.e., an approximation of the full scale or high fidelity model, to build the active subspace, and via the proposed error bound, the quality of the active subspace can be determined by calculating an upper bound on the errors resulting from the reduction. For this approach to be practical, the error bound must be realistic, implying that it should be close to the actual errors expected, and not much higher. Therefore, an important goal of this summary is to compare different error bounds in terms of the relation between their estimated bounds to the actual errors. In particular, we compare the proposed error bound which numerically construct an estimator using binomial distribution to the widely used small-sample norm estimators. Unlike most probabilistic error estimation methods, the proposed bound employs a binomial distribution to construct the estimator whereas in other conventional methods, the distribution employed is typically the standard Gaussian, normalized over a unit hypersphere as initially proposed by the seminal paper of J. Dixon on random matrix theory. Previous publications provided evidence that the binomial distribution calculates more realistic bounds as compared to the Gaussian distribution, which tends to be conservative, implying that the bound is much bigger than the actual errors, which diminishes the value of the reduction, as now must increase the size of the active subspace to reach the desired upper bound on the reduction errors. This work has provided a rigorous approach by which error bounds on the reduction errors can be established without having to execute the high fidelity model during the construction of the active subspace. The high fidelity model is only need to test the error bound using small number of executions. This methodology paves the way for a more efficient application of ROM to complex engineering models, where standard ROM techniques may be too taxing to optimally realize their value in practical situations. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Computing the QRPA level density with the finite amplitude method

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

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2016

Limited‐memory adaptive snapshot selection for proper orthogonal decomposition

Summary Reduced order models are useful for accelerating simulations in many‐query contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models (ROMs) can have prohibitively expensive memory and floating‐point operation costs in high‐performance computing applications, where memory per core is limited. To overcome this limitation for proper orthogonal decomposition, we propose a novel adaptive selection method for snapshots in time that limits offline training costs by selecting snapshots according an error control mechanism similar to that found in adaptive time‐stepping ordinary differential equation solvers. The error estimator used in this work is related to theory bounding the approximation error in time of proper orthogonal decomposition‐based ROMs, and memory usage is minimized by computing the singular value decomposition using a single‐pass incremental algorithm. Results for a viscous Burgers' test problem demonstrate convergence in the limit as the algorithm error tolerances go to zero; in this limit, the full‐order model is recovered to within discretization error. A parallel version of the resulting method can be used on supercomputers to generate proper orthogonal decomposition‐based ROMs, or as a subroutine within hyperreduction algorithms that require taking snapshots in time, or within greedy algorithms for sampling parameter space. Copyright © 2016 John Wiley & Sons, Ltd.

Oxberry, Geoffrey M.↗

DOE OSTI2016

Minimax Quantum Tomography: Estimators and Relative Entropy Bounds

A minimax estimator has the minimum possible error (“risk”) in the worst case. Here we construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O (1/$\sqrt{N}$ ) —in contrast to that of classical probability estimation, which is O (1/N) —where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. Lastly, this makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Optimizing Error-Bounded Lossy Compression for Scientific Data by Dynamic Spline Interpolation

Today's scientific simulations are producing vast volumes of data that cannot be stored and transferred efficiently because of limited storage capacity, parallel I/O bandwidth, and network bandwidth. The situation is getting worse over time because of the ever-increasing gap between relatively slow data transfer speed and fast-growing computation power in modern supercomputers. Error-bounded lossy compression is becoming one of the most critical techniques for resolving the big scientific data issue, in that it can significantly reduce the scientific data volume while guaranteeing that the reconstructed data is valid for users because of its compression-error-bounding feature. In this paper, we present a novel error-bounded lossy compressor based on a state-of-the-art prediction-based compression framework. Our solution exhibits substantially better compression quality than all of the existing error-bounded lossy compressors, with comparable compression speed. Specifically, our contribution is threefold. (1) We provide an in-depth analysis of why the best-existing prediction-based lossy compressor can only minimally improve the compression quality. (2) We propose a dynamic spline interpolation approach with a series of optimization strategies that can significantly improve the data prediction accuracy, substantially improving the compression quality in turn. (3) We perform a thorough evaluation using six real-world scientific simulation datasets across different science domains to evaluate our solution vs. all other related works. Experiments show that the compression ratio of our solution is higher than that of the second-best lossy compressor by 20%similar to 460% with the same error bound in most of the cases.

Zhao, Kai↗

DOE OSTI2015

Numerical Uncertainty Estimation for Stochastic Particle-in-Cell Simulations Applied to Verification and Validation.

Systematic veri cation and validation (V&V) is necessary to establish the credibility for high consequence simulations. In this paper, we focus on a radiation-induced plasma experimental validation exercise for simulations which uses both numerical error estimation and input parameter uncertainty quanti cation to provide a direct comparison between Particle-In-Cell (PIC) plasma simulations and experiments. This approach demonstrates how careful validation can uncover missing physics in the simulation. Three di erent validation examples are shown; a vacuum space charge limited cavity, a gas lled space charge limited cavity, and a vacuum non space charge limited cavity. Two of the example are picked to show the importance of error estimation in uncovering inaccuracy/incomplete simulation models. We also report on a newly-developed numerical error estimation approach, StREEQ, which is a notable improvement to past approaches. In the StREEQ approach, a multi- tting scheme based on L 1 , L 2 , and L$\infty$ error norms and alternate weightings is used to propagate uncertainties in the relative importance of outliers and coarse/re ned discretization levels. Bootstrap sampling is used to represent the stochasticity in the response data. The resulting method appears to robustly and conservatively predict the fully-converged response within estimated numerical error bounds for stochastic simulations. The StREEQ approach is demonstrated on two related prototype electron diode problems, and preliminary results are reported for a radiation-induced plasma simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Orthogonality broadcasting and quantum position verification

The no-cloning theorem leads to information-theoretic security in various quantum cryptographic protocols. However, this security typically derives from a possibly weaker property that classical information encoded in certain quantum states cannot be broadcast. To formally capture this property, we introduce the study of ‘orthogonality broadcasting.’ When attempting to broadcast the orthogonality of two different qubit bases, we establish that the power of classical and quantum communication is equivalent. However, quantum communication is shown to be strictly more powerful for broadcasting orthogonality in higher dimensions. We then relate orthogonality broadcasting to quantum position verification and provide a new method for establishing error bounds in the no pre-shared entanglement model that can address protocols previous methods could not. Our key technical contribution is an uncertainty relation that uses the geometric relation of the states that undergo broadcasting rather than the non-commutative aspect of the final measurements.

quantum cryptography↗

DOE OSTI2022

Evaluation of dynamic testing of full-scale wind turbine drivetrains with hardware-in-the-loop

Dynamometer testing of full-scale wind turbine drivetrains involves subjecting integrated components to extreme static loads, fatigue loads, or dynamic loads to replicate field conditions. This paper provides a detailed evaluation of the uncertainty and errors in applied loads and measured responses, and their magnitude relative to established repeatability bounds for a drivetrain subjected to static and dynamic loads on the 7.5 MW test bench at the Clemson University Wind Turbine Drivetrain Testing Facility. An ideal drivetrain simulation model is utilized to isolate the influence of load tracking errors on test article responses. It is shown that the test article response variations are mainly driven by run out and clearances inherent to the drivetrain. For the dynamic profiles, the load tracking errors are within acceptable limits. Furthermore, a frequency analysis is used to show that the test bench controller tracking performance is acceptable for profiles with frequency content up to 1.5 Hz.

17 WIND ENERGY↗

DOE OSTI2026

A stiff order condition theory for Runge–Kutta methods applied to semilinear ODEs

Classical convergence theory of Runge–Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE). For stiff problems, that assumption is often violated, and a problematic degradation in accuracy, known as order reduction, can arise. Methods with high stage order, e.g., Gauss–Legendre and Radau, are known to avoid order reduction, but they must be fully implicit. For the broad class of semilinear ODEs, which consist of a stiff linear term and non-stiff nonlinear term, we show that weaker conditions suffice. Here, our new semilinear order conditions are formulated in terms of orthogonality relations and can be enumerated by rooted trees. Finally, we prove global error bounds that hold uniformly with respect to stiffness of the linear term.

Mathematics and Computing↗

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↗