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User Guide for Compressible Flow Toolbox Version 2.1 for Use With MATLAB(Registered Trademark); Version 7

This report provides a user guide for the Compressible Flow Toolbox, a collection of algorithms that solve almost 300 linear and nonlinear classical compressible flow relations. The algorithms, implemented in the popular MATLAB programming language, are useful for analysis of one-dimensional steady flow with constant entropy, friction, heat transfer, or shock discontinuities. The solutions do not include any gas dissociative effects. The toolbox also contains functions for comparing and validating the equation-solving algorithms against solutions previously published in the open literature. The classical equations solved by the Compressible Flow Toolbox are: isentropic-flow equations, Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section.), normal-shock equations, oblique-shock equations, and Prandtl-Meyer expansion equations. At the time this report was published, the Compressible Flow Toolbox was available without cost from the NASA Software Repository.

Melcher, Kevin J.↗

Quantile Vocoder

Parameters of spectral envelope obtained statistically. Algorithm for digital compression of speech signals encodes power spectral density of each short interval of speech by use of quantiles or order statistics. Purpose to reduce bit rate and bandwidth required for transmission. When fully developed, quantile vocoder - speech-encoding system based on new algorithm - expected moderately complicated compared with other speech-encoding systems and reproduce high-quality speech from code transmitted at relatively low bit rates. Speech signal treated mathematically as though amplitude spectrum stationary during short coding intervals, called "windows". Window duration of 20 or 35 ms, chosen as compromise between frequency resolution and time resolution. During each window, short-time amplitude and power spectra found by sampling at high rate (typically 10 kHz) and taking fast Fourier transforms (FFT's).

Swaminathan, Kumar↗

JPEG 2000 Encoding with Perceptual Distortion Control

An alternative approach has been devised for encoding image data in compliance with JPEG 2000, the most recent still-image data-compression standard of the Joint Photographic Experts Group. Heretofore, JPEG 2000 encoding has been implemented by several related schemes classified as rate-based distortion-minimization encoding. In each of these schemes, the end user specifies a desired bit rate and the encoding algorithm strives to attain that rate while minimizing a mean squared error (MSE). While rate-based distortion minimization is appropriate for transmitting data over a limited-bandwidth channel, it is not the best approach for applications in which the perceptual quality of reconstructed images is a major consideration. A better approach for such applications is the present alternative one, denoted perceptual distortion control, in which the encoding algorithm strives to compress data to the lowest bit rate that yields at least a specified level of perceptual image quality. Some additional background information on JPEG 2000 is prerequisite to a meaningful summary of JPEG encoding with perceptual distortion control. The JPEG 2000 encoding process includes two subprocesses known as tier-1 and tier-2 coding. In order to minimize the MSE for the desired bit rate, a rate-distortion- optimization subprocess is introduced between the tier-1 and tier-2 subprocesses. In tier-1 coding, each coding block is independently bit-plane coded from the most-significant-bit (MSB) plane to the least-significant-bit (LSB) plane, using three coding passes (except for the MSB plane, which is coded using only one "clean up" coding pass). For M bit planes, this subprocess involves a total number of (3M - 2) coding passes. An embedded bit stream is then generated for each coding block. Information on the reduction in distortion and the increase in the bit rate associated with each coding pass is collected. This information is then used in a rate-control procedure to determine the contribution of each coding block to the output compressed bit stream.

Watson, Andrew B.↗

Applications of data compression techniques in modal analysis for on-orbit system identification

Data compression techniques have been investigated for use with modal analysis applications. A redundancy-reduction algorithm was used to compress frequency response functions (FRFs) in order to reduce the amount of disk space necessary to store the data and/or save time in processing it. Tests were performed for both single- and multiple-degree-of-freedom (SDOF and MDOF, respectively) systems, with varying amounts of noise. Analysis was done on both the compressed and uncompressed FRFs using an SDOF Nyquist curve fit as well as the Eigensystem Realization Algorithm. Significant savings were realized with minimal errors incurred by the compression process.

Carlin, Robert A.↗

Reconstructing three-dimensional protein crystal intensities from sparse unoriented two-axis X-ray diffraction patterns

Recently, there has been a growing interest in adapting serial microcrystallography (SMX) experiments to existing storage ring (SR) sources. For very small crystals, however, radiation damage occurs before sufficient numbers of photons are diffracted to determine the orientation of the crystal. The challenge is to merge data from a large number of such `sparse' frames in order to measure the full reciprocal space intensity. To simulate sparse frames, a dataset was collected from a large lysozyme crystal illuminated by a dim X-ray source. The crystal was continuously rotated about two orthogonal axes to sample a subset of the rotation space. With the EMC algorithm [expand–maximize–compress; Loh & Elser (2009). Phys. Rev. E , 80 , 026705], it is shown that the diffracted intensity of the crystal can still be reconstructed even without knowledge of the orientation of the crystal in any sparse frame. Moreover, parallel computation implementations were designed to considerably improve the time and memory scaling of the algorithm. The results show that EMC-based SMX experiments should be feasible at SR sources.

Chemistry↗

Revisiting Huffman Coding: Toward Extreme Performance on Modern GPU Architectures

Today's high-performance computing (HPC) applications are producing vast volumes of data, which are challenging to store and transfer efficiently during the execution, such that data compression is becoming a critical technique to mitigate the storage burden and data movement cost. Huffman coding is arguably the most efficient Entropy coding algorithm in information theory, such that it could be found as a fundamental step in many modern compression algorithms such as DEFLATE. On the other hand, today's HPC applications are more and more relying on the accelerators such as GPU on supercomputers, while Huffman encoding suffers from low throughput on GPUs, resulting in a significant bottleneck in the entire data processing. In this paper, we propose and implement an efficient Huffman encoding approach based on modern GPU architectures, which addresses two key challenges: (1) how to parallelize the entire Huffman encoding algorithm, including codebook construction, and (2) how to fully utilize the high memory-bandwidth feature of modern GPU architectures. The detailed contribution is fourfold. (1) We develop an efficient parallel codebook construction on GPUs that scales effectively with the number of input symbols. (2) We propose a novel reduction based encoding scheme that can efficiently merge the codewords on GPUs. (3) We optimize the overall GPU performance by leveraging the state-of-the-art CUDA APIs such as Cooperative Groups. (4) We evaluate our Huffman encoder thoroughly using six real-world application datasets on two advanced GPUs and compare with our implemented multi-threaded Huffman encoder. Experiments show that our solution can improve the encoding throughput by up to 5.0x and 6.8x on NVIDIA RTX 5000 and V100, respectively, over the state-of-the-art GPU Huffman encoder, and by up to 3.3x over the multi-thread encoder on two 28-core Xeon Platinum 8280 CPUs.

Tian, Jiannan↗

Revisiting Huffman Coding: Toward Extreme Performance on Modern GPU Architectures

Today's high-performance computing (HPC) applications are producing vast volumes of data, which are challenging to store and transfer efficiently during the execution, such that data compression is becoming a critical technique to mitigate the storage burden and data movement cost. Huffman coding is arguably the most efficient Entropy coding algorithm in information theory, such that it could be found as a fundamental step in many modern compression algorithms such as DEFLATE. On the other hand, today's HPC applications are more and more relying on the accelerators such as GPU on supercomputers, while Huffman encoding suffers from low throughput on GPUs, resulting in a significant bottleneck in the entire data processing. In this paper, we propose and implement an efficient Huffman encoding approach based on modern GPU architectures, which addresses two key challenges: (1) how to parallelize the entire Huffman encoding algorithm, including codebook construction, and (2) how to fully utilize the high memory-bandwidth feature of modern GPU architectures. The detailed contribution is fourfold. (1) We develop an efficient parallel codebook construction on GPUs that scales effectively with the number of input symbols. (2) We propose a novel reduction based encoding scheme that can efficiently merge the codewords on GPUs. (3) We optimize the overall GPU performance by leveraging the state-of-the-art CUDA APIs such as Cooperative Groups. (4) We evaluate our Huffman encoder thoroughly using six real-world application datasets on two advanced GPUs and compare with our implemented multithreaded Huffman encoder. Experiments show that our solution can improve the encoding throughput by up to 5.0× and 6.8× on NVIDIA RTX 5000 and V100, respectively, over the state-of-the-art GPU Huffman encoder, and by up to 3.3× over the multithread encoder on two 28-core Xeon Platinum 8280 CPUs.

Tian, Jiannan↗

Ghost imaging second harmonic generation microscopy

Second harmonic generation (SHG) microscopy is useful for visualizing interfaces and sub-structures within a wide range of materials due to the propensity for SHG to occur in non-centrosymmetric environments. However, since SHG is a nonlinear process generally necessitating small focal sizes for higher peak powers, a raster scanning approach is usually needed to build an SHG image over a significant sample size. While raster scanning is effective, there is a cost in terms of the time needed to acquire the image and, also, some materials cannot withstand the higher optical intensities within the small focal volume. As such, we describe a SHG microscopy approach based on ghost imaging (GI), which enables imaging data to be collected in parallel rather than sequentially as in raster scanning techniques. We experimentally demonstrate the approach and combine GI-SHG with compressive sensing to make further substantial gains in reducing the amount of sampling required for image reconstruction. Furthermore, GI-SHG is shown to have significant advantages for imaging in highly scattering environments, partly because GI is a background-free approach requiring spatial correlations between photons that travel two paths, with one path entirely devoid of sample interaction. This basic property of GI means that only the photons that travel unimpeded through the sample preserve the spatial correlations needed to reconstruct the image, while more scattered photons do not contribute to the overall GI signal. Finally, we compare the image quality and sampling properties of three different reconstruction algorithms used for compressive sensing.

47 OTHER INSTRUMENTATION↗

A hybrid finite volume method and smoothed particle hydrodynamics approach for efficient and accurate blast simulations

Modeling strong shock waves in fluids remains a persistent challenge in computational physics. Essential to research efforts in industry and defense, numerous methods have been devised to improve the accuracy and efficiency of shock simulations. A novel, hybrid Finite Volume Method (FVM)-Smoothed Particle Hydrodynamics (SPH) approach is capable of further improving efficiency and retaining accuracy by exploiting the favorable characteristics of each respective method. This hybrid approach is presented for shock capturing in compressible fluids. The Python framework Pyro2 is employed to simulate a coarse FVM mesh, while the Python framework PySPH is utilized to model the fluid in regions with high gradients through SPH particles. The performance of the hybrid FVM-SPH scheme, compared to the individual FVM and SPH methods, is assessed in 1 kt and 10 kt blast simulations. Our results indicate that the hybrid approach offers higher computational efficiency than SPH while preserving its accuracy and characteristics. The hybrid approach had a relative speedup of 11.3x and 22.3x over the FVM and SPH approaches for the 1 kt simulation and a relative speedup of 14.7x and 20.9x over the FVM and SPH approaches for the 10 kt simulation. The hybrid SPH algorithm enables future compressible fluid simulations with more extensive capabilities than grid-based methods alone, presenting potential applications in modeling fluid-structure interactions and solid deformation and fracturing in blast simulations.

Myers, Conner↗

A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux-difference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3-5 percent of the standard Roe flux-difference splitting dissipation is needed.

Bui, Trong T.↗

Online adaptive basis refinement and compression for reduced-order models via vector-space sieving

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these approximate solutions are accurate; their accuracy depends on the ability of the low-dimensional trial basis to represent the FOM solution. As a result, ROMs can generate inaccurate approximate solutions, e.g., when the FOM solution at the online prediction point is not well represented by training data used to construct the trial basis. To address this fundamental deficiency of standard model-reduction approaches, this work proposes a novel online-adaptive mechanism for efficiently enriching the trial basis in a manner that ensures convergence of the ROM to the FOM, yet does not incur any FOM solves. The mechanism is based on the previously proposed adaptive $h$-refinement method for ROMs, but improves upon this work in two crucial ways. First, the proposed method enables basis refinement with respect to any orthogonal basis (not just the Kronecker basis), thereby generalizing the refinement mechanism and enabling it to be tailored to the physics characterizing the problem at hand. Second, the proposed method provides a fast online algorithm for periodically compressing the enriched basis via an efficient proper orthogonal decomposition (POD) method, which does not incur any operations that scale with the FOM dimension. We report these two features allow the proposed method to serve as (1) a failsafe mechanism for ROMs, as the method enables the ROM to satisfy any prescribed error tolerance online (even in the case of inadequate training), and (2) an efficient online basis-adaptation mechanism, as the combination of basis enrichment and compression enables the basis to adapt online while controlling its dimension.

42 ENGINEERING↗

Transonic Navier-Stokes solutions about a generic hypersonic configuration

Three-dimensional transonic viscous flow computations are presented for a generic high-speed accelerator model that includes wing, body, fillets, and a no-flow-through engine nacelle. Solutions are obtained from an algorithm for the compressible Navier-Stokes equations that incorporates an upwind-biased, flux-vector-splitting approach along with longitudinally patched grids. Results are presented for fully turbulent flow assumptions and include correlations with wind-tunnel data. A good quantitative agreement for the forebody surface pressure distribution is achieved between computations and the available wind-tunnel measurements at M∞ = 0.9. Furthermore, it is demonstrated that the flow is stagnating around the boattail region due to separation from the aft-engine cowl lip.

Hypersonic flows↗

NASA's Robotic Lunar Lander Development Project

Since early 2005, NASA's Robotic Lunar Lander Development (RLLD) office at NASA MSFC, in partnership with the Applied Physics Laboratory (APL), has developed mission concepts and preformed risk-reduction activities to address planetary science and exploration objectives uniquely met with landed missions. The RLLD team developed several concepts for lunar human-exploration precursor missions to demonstrate precision landing and in-situ resource utilization, a multi-node lunar geophysical network mission, either as a stand-alone mission, or as part of the International Lunar Network (ILN), a Lunar Polar Volatiles Explorer and a Mercury lander mission for the Planetary Science decadal survey, and an asteroid rendezvous and landing mission for the Exploration Precursor Robotics Mission (xPRM) office. The RLLD team has conducted an extensive number of risk-reduction activities in areas common to all lander concepts, including thruster testing, propulsion thermal control demonstration, composite deck design and fabrication, and landing leg stability and vibration. In parallel, the team has developed two robotic lander testbeds providing closed-loop, autonomous hover and descent activities for integration and testing of flight-like components and algorithms. A compressed-air test article had its first flight in September 2009 and completed over 150 successful flights. This small test article (107 kg dry/146 kg wet) uses a central throttleable thruster to offset gravity, plus 3 descent thrusters (~37lbf ea) and 6 attitude-control thrusters (~12lbf ea) to emulate the flight system with pulsed operation over approximately 10s of flight time. The test article uses carbon composite honeycomb decks, custom avionics (COTS components assembled in-house), and custom flight and ground software. A larger (206 kg dry/322 kg wet), hydrogen peroxide-propelled vehicle began flight tests in spring 2011 and fly over 30 successful flights to a maximum altitude of 30m. The monoprop testbed also uses a central gravity-canceling thruster and 3 descent thrusters, but has 12 attitude-control thrusters and a maximum flight time of over a minute. The testbed uses aluminum ortho-grid decks, an LN200-1 IMU, Roke Manor Radar Altimeter, Illunis optical cameras, Novatel Pro-Pak GPS truth data system, Pressure transducers & thermocouples for housekeeping, "In-Control" ground system software, and the core Flight Executive (cFE) modular software environment. The peroxide lander testbed is able to accept other sensors and algorithms for testing, both from within NASA and from other customers. Through these activities, the RLLD team has significantly reduced technical risks for all small and medium class robotic landers for the Moon and other airless planetary bodies.

Cohen, Barbara A.↗

Simultaneous Retrieval of Temperature, Water Vapor and Ozone Atmospheric Profiles from IASI: Compression, De-noising, First Guess Retrieval and Inversion Algorithms

A fast temperature water vapor and ozone atmospheric profile retrieval algorithm is developed for the high spectral resolution Infrared Atmospheric Sounding Interferometer (IASI) space-borne instrument. Compression and de-noising of IASI observations are performed using Principal Component Analysis. This preprocessing methodology also allows, for a fast pattern recognition in a climatological data set to obtain a first guess. Then, a neural network using first guess information is developed to retrieve simultaneously temperature, water vapor and ozone atmospheric profiles. The performance of the resulting fast and accurate inverse model is evaluated with a large diversified data set of radiosondes atmospheres including rare events.

Aires, F.↗

Scientific data interpolation with low dimensional manifold model

Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.

97 MATHEMATICS AND COMPUTING↗

Cryo-STEM Tomography with Inpainting

Traditionally, microscopists have worked with the Nyquist-Shannon theory of sampling, which states that to be able to reconstruct the image fully it needs to be sampled at a rate of at least twice the highest spatial frequency in the image. This sampling rate assumes that the image is sampled at regular intervals and that every pixel contains information that is crucial for the image (it even assumes that noise is important). Images in general, and especially low dose S/TEM images, contain significantly less information than can be encoded by a grid of pixels (which is why image compression works). Mathematically speaking, the image data has a low dimensional or sparse representation. Through the application of compressive sensing methods [1,2,3] this representation can be found using pre-designed measurements that are usually random for implementation simplicity. These measurements and the compressive sensing reconstruction algorithms have the added benefit of reducing noise. This reconstruction approach can be extended into higher dimensions, whereby the random sampling in each 2-D image can be extended into: a sequence of tomographic projections (i.e. tilt images); a sequence of video frames (i.e. incorporating temporal resolution and dynamics); spectral resolution (i.e. energy filtering an image to see the distribution of elements); and ptychography (i.e. sampling a full diffraction image at each location in a 2-D grid across the sample). This approach has been employed experimentally for materials science samples requiring low-dose imaging [2], and can be readily applied to biological samples. Figure 1 shows the resolution possible in a complex biological system, mouse pancreatic islet beta cells [4], when tomogram slices are reconstructed using subsampling. Reducing the number of pixels (1/6 pix and 1/3*1/3) shows minimal degradation compared to the reconstructions using all pixels (all data and 1/3 tilt). Although subsampling 1/6 of the tilts (1/6 of overall dose) degrades the reconstruction to the point that the cellular structures cannot be identified. Using 1/3 of both the pixels and the tilts provides a high quality image at 1/9 the overall dose even for this most basic and rapid demonstration of the CS methods. Figure 2 demonstrates the theoretical tomogram reconstruction quality (vertical axis) as undersampling (horizontal axis) is increased; we examined subsampling pixels and tilt-angles individually and a combined approach in which both pixels and tilts are sub-sampled. Note that subsampling pixels maintains high quality reconstructions (solid lines). Using the inpainting algorithm to obtain tomograms can automatically reduce the dose applied to the system by an order of magnitude. Perhaps the best way to understand the impact is to consider that by using inpainting (and with minimal hardware changes), a sample that can normally withstand a dose of ~10 e/Å2 can potentially be imaged with an “equivalent quality” to a dose level of 103 e/Å2. To put this in perspective, this is approaching the dose level used for the most advanced images, in terms of spatial resolution, for inorganic systems. While there are issues for biological specimens beyond dose (structural complexity being the most important one), this sampling approach allows the methods that are traditionally used for materials science to be applied to biological systems [5]. References: [1] A Stevens, H Yang, L Carin et al. Microscopy 63(1), (2014), pp. 41. [2] L Kovarik, A Stevens, A Liyu et al. Appl. Phys. Lett. 109, 164102 (2016) [3] A Stevens, L Kovarik, P Abellan et al. Adv. Structural and Chemical Imaging 1(10), (2015), pp. 1. [4] MD Guay, W Czaja, MA Aronova et al. Scientific Reports 6, 27614 (2016) [5] Supported by the Chemical Imaging, Signature Discovery, and Analytics in Motion Initiatives at PNNL. PNNL is operated by Battelle Memorial Inst. for the US DOE; contract DE-AC05-76RL01830.

Stevens, Andrew↗

Equation of State of a Natural Chromian Spinel at Ambient Temperature

A natural chromian spinel with the composition (Mg0.48(3)Fe0.52(3))(Fe0.06(1)Al0.28(1)Cr0.66(2))2O4 was investigated up to 15 GPa via synchrotron X-ray diffraction with a diamond-anvil cell at room temperature. No phase transition was clearly observed up to the maximum experimental pressure. The pressure–volume data fitted to the third-order Birch–Murnaghan equation of state yielded an isothermal bulk modulus ( K T 0 ) of 207(5) GPa and its first pressure derivative ( K T 0 ' ) of 3.2(7), or K T 0 = 202(2) GPa with K T 0 ' fixed as 4. With this new experimental result and the results on some natural chromian spinels in the literature, a simple algorithm describing the relation between the K T 0 and the compositions of the natural chromian spinels was proposed. To examine this algorithm further, more compression experiments should be performed on natural chromian spinels with different chemical compositions.

Mi, Zhongying↗