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At least 235 records · Page 13

The bar rotation rate as a diagnostic of dark matter content in the centre of disc galaxies

We investigate the link between the bar rotation rate and dark matter content in barred galaxies by concentrating on the cases of the lenticular galaxies NGC 4264 and NGC 4277. These two gas-poor galaxies have similar morphologies, sizes, and luminosities. But, NGC 4264 hosts a fast bar, which extends to nearly the corotation, while the bar embedded in NGC 4277 is slow and falls short of corotation. We derive the fraction of dark matter ƒ DM, bar within the bar region from Jeans axisymmetric dynamical models by matching the stellar kinematics obtained with the MUSE integral-field spectrograph and using SDSS images to recover the stellar mass distribution. We build mass-follows-light models as well as mass models with a spherical halo of dark matter, which is not tied to the stars. We find that the inner regions of NGC 4277 host a larger fraction of dark matter (⁠ƒ DM,bar = 0.53±0.02⁠) with respect to NGC 4264 (⁠(⁠ƒ DM,bar = 0.33±0.04⁠) in agreement with the predictions of theoretical works and the findings of numerical simulations, which have found that fast bars live in baryon-dominated discs, whereas slow bars experienced a strong drag from the dynamical friction due to a dense DM halo. This is the first time that the bar rotation rate is coupled to fDM, bar derived from dynamical modelling.

79 ASTRONOMY AND ASTROPHYSICS↗

MAS-CCD: New technique for measuring low-level charge content based on the multiple amplifier architecture

Low-noise detectors are a key technology for the next generation of astronomical instruments aimed at spectroscopy of faint objects and the search for exoplanets. In this context, the multiple-amplifier sensing charge-coupled device (MAS-CCD) emerges as a promising technology for future scientific instruments. A critical parameter affecting the performance of these devices is spurious charge, produced by the clocking of the gates. Its measurement is typically challenging with existing methods. In practice, the optimization of this parameter often relies on empirical procedures that require significant time and careful consideration of the trade-off with full-well capacity. In this work, we present a new technique to estimate spurious charge based on covariance analysis of the output amplifiers of the MAS-CCD, which measures the same charge packet in different amplifiers at different times. The method enables fast and precise measurements of spurious charge under operating conditions where conventional approaches are difficult to apply. We develop the theoretical framework of the method and validate the model through simulations. The results demonstrate the feasibility of this approach and suggest that it could serve as a basis for reliable large-scale characterization of sensor performance.

Gamero, Miqueas E. [Buenos Aires, CONICET; Fermila↗

Real-time capable modeling of ICRF heating on NSTX and WEST via machine learning approaches

Abstract A real-time capable core Ion Cyclotron Range of Frequencies (ICRF) heating model on NSTX and WEST is developed. The model is based on two nonlinear regression algorithms, the random forest ensemble of decision trees and the multilayer perceptron neural network. The algorithms are trained on TORIC ICRF spectrum solver simulations of the expected flat-top operation scenarios in NSTX and WEST assuming Maxwellian plasmas. The surrogate models are shown to successfully capture the multi-species core ICRF power absorption predicted by the original model for the high harmonic fast wave and the ion cyclotron minority heating schemes while reducing the computational time by six orders of magnitude. Although these models can be expanded, the achieved regression scoring, computational efficiency and increased model robustness suggest these strategies can be implemented into integrated modeling frameworks for real-time control applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Examining the Feasibility of Modeling the Inner Current Loop of a Grid-Following Inverter in the Phasor-Based Solver

Historically, when modeling a grid-following (GFL) inverter in the phasor domain, the fast inner current loop is typically ignored. To achieve a more accurate modeling, the authors have attempted to model the inner current loop in the phasor domain, but experienced significant numerical stability issues. This paper conducts a detailed analysis and provides insight into the feasibility of modeling the inner current loop of a GFL inverter in the phasor domain. It points out that: a) because of the neglection of the inverter filter dynamic, the bandwidth of the inner current loop becomes infinite with typical parameters in the phasor domain, resulting in an inaccurate representation of the actual inner current loop, whose bandwidth is typically between 600 Hz to 2 kHz, and b) the relatively large simulation time step in the phasor simulation causes numerical stability issues when simulating such an inner current loop with an infinite bandwidth. Detailed electromagnetic (EMT) and phasor modeling, and frequency response analysis are performed to explain this phenomenon. The findings of this paper explain why it is inappropriate to model the fast current loop of a GFL inverter in the phasor domain.

Mohiuddin, Sheik Mohammad↗

Ultrafast electronic relaxation pathways of the molecular photoswitch quadricyclane

Abstract The light-induced ultrafast switching between molecular isomers norbornadiene and quadricyclane can reversibly store and release a substantial amount of chemical energy. Prior work observed signatures of ultrafast molecular dynamics in both isomers upon ultraviolet excitation but could not follow the electronic relaxation all the way back to the ground state experimentally. Here we study the electronic relaxation of quadricyclane after exciting in the ultraviolet (201 nanometres) using time-resolved gas-phase extreme ultraviolet photoelectron spectroscopy combined with non-adiabatic molecular dynamics simulations. We identify two competing pathways by which electronically excited quadricyclane molecules relax to the electronic ground state. The fast pathway (<100 femtoseconds) is distinguished by effective coupling to valence electronic states, while the slow pathway involves initial motions across Rydberg states and takes several hundred femtoseconds. Both pathways facilitate interconversion between the two isomers, albeit on different timescales, and we predict that the branching ratio of norbornadiene/quadricyclane products immediately after returning to the electronic ground state is approximately 3:2.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Time delay lens modelling challenge

ABSTRACT In recent years, breakthroughs in methods and data have enabled gravitational time delays to emerge as a very powerful tool to measure the Hubble constant H0. However, published state-of-the-art analyses require of order 1 yr of expert investigator time and up to a million hours of computing time per system. Furthermore, as precision improves, it is crucial to identify and mitigate systematic uncertainties. With this time delay lens modelling challenge, we aim to assess the level of precision and accuracy of the modelling techniques that are currently fast enough to handle of order 50 lenses, via the blind analysis of simulated data sets. The results in Rungs 1 and 2 show that methods that use only the point source positions tend to have lower precision ($10\!-\!20{{\ \rm per\ cent}}$) while remaining accurate. In Rung 2, the methods that exploit the full information of the imaging and kinematic data sets can recover H0 within the target accuracy (|A| < 2 per cent) and precision (<6 per cent per system), even in the presence of a poorly known point spread function and complex source morphology. A post-unblinding analysis of Rung 3 showed the numerical precision of the ray-traced cosmological simulations to be insufficient to test lens modelling methodology at the percent level, making the results difficult to interpret. A new challenge with improved simulations is needed to make further progress in the investigation of systematic uncertainties. For completeness, we present the Rung 3 results in an appendix and use them to discuss various approaches to mitigating against similar subtle data generation effects in future blind challenges.

Ding, X.↗

Quantifying the Effect of Magnetic Field Line Curvature Scattering on the Loss of Ring Current Ions

During geomagnetic storms, the ring current ions sometimes exhibit rapid loss as suggested by the fast recovery of the Dst index on a time scale of a few hours. Here, the effects of magnetic field line curvature (FLC) scattering on the loss of ring current ions, which have not been well quantified, are studied here by test particle simulations under the T89c magnetic field model. Our simulation results show that the prediction of ion loss based on a single–value cutoff of the κ parameter or maximum of δμ/μ of a single FLC scattering is not accurate. Instead, the e–folding lifetime (τ) for the loss of ring current ions due to cumulative FLC scattering has been calculated for different initial ion energies, equatorial pitch angles, and L shells under different geomagnetic conditions. The results show that in general the FLC scattering loss is faster for ions of higher energy, higher mass, smaller pitch angle, higher L, and at high Kp level. Specifically, we find that at Kp = 6 the lifetime can be <10 h at L > 5 for 100 s keV protons and at L > 4 for 100 s keV O + , which demonstrates that FLC scattering can be an important mechanism for the observed fast loss (τ < 10 h) of ring current ions during geomagnetic storms. Furthermore, we formulate an empirical formula for τ as a function of ion energy, pitch angle, position, species, and Kp. The empirical formula can be directly included in ring current models to account for the FLC scattering effects.

79 ASTRONOMY AND ASTROPHYSICS↗

Demonstration of an AI-driven workflow for autonomous high-resolution scanning microscopy

Abstract Modern scanning microscopes can image materials with up to sub-atomic spatial and sub-picosecond time resolutions, but these capabilities come with large volumes of data, which can be difficult to store and analyze. We report the Fast Autonomous Scanning Toolkit (FAST) that addresses this challenge by combining a neural network, route optimization, and efficient hardware controls to enable a self-driving experiment that actively identifies and measures a sparse but representative data subset in lieu of the full dataset. FAST requires no prior information about the sample, is computationally efficient, and uses generic hardware controls with minimal experiment-specific wrapping. We test FAST in simulations and a dark-field X-ray microscopy experiment of a WSe 2 film. Our studies show that a FAST scan of <25% is sufficient to accurately image and analyze the sample. FAST is easy to adapt for any scanning microscope; its broad adoption will empower general multi-level studies of materials evolution with respect to time, temperature, or other parameters.

47 OTHER INSTRUMENTATION↗

Atomic understanding of structural deformations upon ablation of graphene

We investigate the atomic rearrangement in graphene under femtosecond pulse illumination with reactive molecular dynamics simulations and compare with ultra-fast laser ablation experiments. To model the impact of the laser pulse irradiation, heat is locally applied to a selected area of the graphene layer and the resulting structural deformation is simulated as a function of time, providing a detailed understanding of the bond breaking process under laser illumination and subsequent re-equilibration afterAQ3 the pulse is turned off. Analysis of the atomic dynamics indicates that the types of defects formed depend on the pulse energy and exposure duration. By varying the exposed area, we determine that the shape of the ablated area is not only a function of the pulse energy, but also of the beam spot size and pulse repetition. Furthermore, we apply a machine learning approach to extrapolate our simulated data to experimental length scales and reproduce the trends in ablated area as a function of temperature. Furthermore, our study provides a first step towards understanding the design parameters for graphene nano-patterning.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Depletion capabilities in the OpenMC Monte Carlo particle transport code

A depletion solver has been implemented in OpenMC and is described herein. The depletion solver is implemented in Python and interfaces with OpenMC’s transport solver through a C++ application programming interface, which enables an in-memory transport-depletion coupling. Multiple integration methods for advancing in time have been implemented and exhibit tradeoffs in cost, accuracy, and memory use. For all time integration methods, evaluation of the matrix exponential is performed by using the incomplete partial fraction form of the Chebyshev rational approximation method. Simulations of a pressurized water reactor (PWR) pincell and a sodium-cooled fast reactor (SFR) assembly were carried out with OpenMC and Serpent. For both problems, the use of a high-fidelity depletion chain results in predictions of k eff that agree within 20–30 pcm between OpenMC and Serpent. Predicted actinide concentrations were found to agree to a fraction of a percent, and most fission product concentrations were found to agree within 1%. Here, the few cases where larger differences were observed can be attributed either to differences in how the energy dependence of fission product yields is handled or deficiencies in the nuclear data used. OpenMC simulations of the PWR and SFR problems using a simplified 228-nuclide depletion chain demonstrate that it achieves accuracy close to that of the full, high-fidelity depletion chain with respect to the studied responses.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Emulator-based Bayesian calibration of a subglacial drainage model

Subglacial drainage models, often motivated by the relationship between hydrology and ice flow, sensitively depend on numerous unconstrained parameters. We explore using borehole water-pressure time series to calibrate the uncertain parameters of a popular subglacial drainage model, taking a Bayesian perspective to quantify the uncertainty in parameter estimates and in the calibrated model predictions. To reduce the computation time associated with Markov Chain Monte Carlo sampling, we construct a fast Gaussian process emulator to stand in for the subglacial drainage model. We first carry out a calibration experiment using synthetic observations consisting of model simulations with hidden parameter values as a demonstration of the method. Using real borehole water pressures measured in western Greenland, we find meaningful constraints on four of the eight model parameters and a factor-of-three reduction in uncertainty of the calibrated model predictions. These experiments illustrate Gaussian process-based Bayesian inference as a useful tool for calibration and uncertainty quantification of complex glaciological models using field data. However, significant differences between the calibrated model and the borehole data suggest that structural limitations of the model, rather than poorly constrained parameters or computational cost, remain the most important constraint on subglacial drainage modelling.

58 GEOSCIENCES↗

Quantum Electromagnetic Transients Program

This work devises a quantum electromagnetic transients program (QEMTP) which is the first attempt to tackle the computational challenges in solving EMTP through quantum computing. The main contributions lie in: (1) A quantum-enabled EMTP formulation with Dommel's model encoded in quantum states; 2) An Harrow-Hassidim-Lloyd (HHL)-based QEMTP to solve the discrete-time nodal equations; 3) An iteration-based HHL revision for mitigating temporal errors to achieve high accuracy of QEMTP with limited quantum resources. Case studies verify the correctness and efficacy of QEMTP in simulating both fast and slow dynamics.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Exascale Multiphysics Nuclear Reactor Simulations for Advanced Designs

ENRICO is a coupled application developed under the U.S. Department of Energy's Exascale Computing Project (ECP) targeting the modeling of advanced nuclear reactors. It couples radiation transport with heat and fluid simulation, including the high-fidelity, highresolution Monte-Carlo code Shift and the Computational fluid dynamics code NekRS. NekRS is a highly-performant open-source code for simulation of incompressible and low-Mach fluid flow, heat transfer, and combustion with a particular focus on turbulent flows in complex domains. It is based on rapidly convergent high-order spectral element discretizations that feature minimal numerical dissipation and dispersion. State-of-the-art multilevel preconditioners, efficient high-order time-splitting methods, and runtime-adaptive communication strategies are built on a fast OCCA-based kernel library, libParanumal, to provide scalability and portability across the spectrum of current and future high-performance computing platforms. On Frontier, Nek5000/RS has recently achieved an unprecedented milestone in breaching over 1 billion spectral elements and 350 billion degrees of freedom. Shift has demonstrated the capability to transport upwards of 1 billion particles per second in full core nuclear reactor simulations featuring complete temperature-dependent, continuous-energy physics on Frontier. Shift achieved a weak-scaling efficiency of 97.8% on 8192 nodes of Frontier and calculated 6 reactions in 214,896 fuel pin regions below 1% statistical error yielding first-of-a-kind resolution for a Monte Carlo transport application.

Hamilton, Steven P.↗

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

60 APPLIED LIFE SCIENCES↗

Coil optimization for quasi-helically symmetric stellarator configurations

Filament-based coil optimizations are performed for several quasi-helical stellarator configurations, beginning with the one from Landreman & Paul ( Phys. Rev. Lett. , vol. 128, 2022, 035001), demonstrating that precise quasi-helical symmetry can be achieved with realistic coils. Several constraints are placed on the shape and spacing of the coils, such as low curvature and sufficient plasma–coil distance for neutron shielding. The coils resulting from this optimization have a maximum curvature 0.8 times that of the coils of the Helically Symmetric eXperiment (HSX) and a mean squared curvature 0.4 times that of the HSX coils when scaled to the same plasma minor radius. When scaled up to reactor size and magnetic field strength, no fast particle losses were found in the free-boundary configuration when simulating 5000 alpha particles launched at $3.5\,\mathrm {MeV}$ on the flux surface with a normalized toroidal flux of $s=0.5$ . An analysis of the tolerance of the coils to manufacturing errors is performed using a Gaussian process model, and the coils are found to maintain low particle losses for smooth, large-scale errors up to amplitudes of approximately $0.15\,\mathrm {m}$ . Another coil optimization is performed for the Landreman–Paul configuration with the additional constraint that the coils are purely planar. Visual inspection of the Poincaré plot of the resulting magnetic field-lines reveal that the planar modular coils alone do a poor job of reproducing the target equilibrium. Additional non-planar coil optimizations are performed for the quasi-helical configuration with $5\,\%$ volume-averaged plasma beta from Landreman et al. ( Phys. Plasma , vol. 29, issue 8, 2022, 082501), and a similar configuration also optimized to satisfy the Mercier criterion. The finite beta configurations had larger fast-particle losses, with the free-boundary Mercier-optimized configuration performing the worst, losing approximately $5.5\,\%$ of alpha particles launched at $s=0.5$ .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Adversarial autoencoder ensemble for fast and probabilistic reconstructions of few-shot photon correlation functions for solid-state quantum emitters

Second-order photon correlation measurements [g (2) (τ) functions] are widely used to classify single-photon emission purity in quantum emitters or to measure the multiexciton quantum yield of emitters that can simultaneously host multiple excitations – such as quantum dots – by evaluating the value of g (2) (τ = 0). Accumulating enough photons to accurately calculate this value is time consuming and could be accelerated by fitting of few-shot photon correlations. Here, we develop an uncertainty-aware, deep adversarial autoencoder ensemble (AAE) that reconstructs noise-free g (2) (τ) functions from noise-dominated, few-shot inputs. The model is trained with simulated g (2) (τ) functions that are facilely generated by Poisson sampling time bins. The AAE reconstructions are performed orders-of-magnitude faster, with reconstruction errors and estimates of g (2) (τ = 0) that are lower in variance and similar in accuracy compared to Maximum likelihood estimation and Levenberg-Marquardt least-squares fitting approaches, for simulated and experimentally measured few-shot g (2) (τ) functions (~100 two-photon events) of InP/ZnS/ZnSe and CdS/CdSe/CdS quantum dots. The deep-ensemble model comprises eight individual autoencoders, allowing for probabilistic reconstructions of noise-free g (2) (τ) functions, and we show that the predicted variance scales inversely with number of shots, with comparable uncertainties to computationally intensive Markov chain Monte Carlo sampling. Furthermore, this work demonstrates the advantage of machine learning models to perform uncertainty-aware, fast, and accurate reconstructions of simple Poisson-distributed photon correlation functions, allowing for on-the-fly reconstructions and accelerated materials characterization of solid-state quantum emitters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Model Inputs, Outputs, and Scripts associated with: “Spatial microbial respiration variations in the hyporheic zones within the Columbia River Basin”

This data package is associated with the publication “Spatial microbial respiration variations in the hyporheic zones within the Columbia River Basin” published in the Journal of Geophysical Research: Biogeosciences (Son et al. 2022) available at doi: 10.1029/2021JG006654. This data package includes the key model inputs/outputs of the river corridor model for the Columbia River Basin (CRB) and the model source codes, which were used in the manuscript. The model is a carbon-nitrogen-coupled river corridor model (RCM), and the model is used to quantify hyporheic zone (HZ) aerobic and anaerobic respiration at the NHDPLUS stream reach scales. The RCM used in this study combines empirical substrate models derived from observations and three microbially driven reactions to compute respiration of the HZ for each National Hydrography Dataset (NHD) reach within the CRB. The reactions in HZs of each NHD reach include anaerobic respiration and two-step anaerobic respiration via denitrification. Our HZ respiration estimates are limited to the lotic (or flowing) stream/river systems, and do not account for the respiration process in water column. Note that the RCM only simulates the HZ’s contribution to the dissolved carbon dioxide (CO2) concentrations in the streams, and the CO2 emissions to the atmosphere are not modelled. The model computes at hourly timesteps because of the fast reaction rates. The key input data of the model are exchange flux, residence time, and stream solute (dissolved organic carbon (DOC), dissolved oxygen (DO), and nitrate concentrations). These inputs are constant over time and represent long-term averaged values.This modeling framework successfully quantified HZ respiration components over multiple scales. It revealed key mechanisms driving the spatial variation of HZ aerobic and anaerobic respiration in reaches with varying hydrologic and substrate conditions. Thus, this modeling study offers a testing hypothesis in different river system (e.g., climate and biomes) for the HZ respiration processes, and can be used as a sampling design tool for large-scale HZ experimental studies.This dataset contains five folders: (1) model_inputs, (2) model_outputs, (3) Rscripts, (4) figures, and (5) model_codes. It also contains a readme, file level metadata (FLMD), and data dictionary (dd). Please see the FLMD for a list of all the files contained in this data package and descriptions for each. The model_inputs folder contains the model inputs used to drive the model simulations. The model_outputs folder contains key model output files from the river corridor model. The Rscripts folder contains the Rscripts for pre- and post- processing model results. The figures folder contains the raw figures associated with the manuscript. The model_codes folder includes key model source codes/input files. All files are .jpg, .jpeg, .out, .e, .od, .dat, .sub, .F90, .0, .R, .sbx, .cpg, .sbn, .shx, .shp, .dbf, .prj, .tfw, .tif, .xml, .pdf, or .csv.

54 ENVIRONMENTAL SCIENCES↗

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↗