Measurement of the kernels of a non-linear system of finite order.
Measurement of Volterra kernels of finite order nonlinear system
VOLTERRA EQUATION↗
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Kernel polynomial method for linear spin wave theory
Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially in systems with large magnetic unit cells, such as those with incommensurate magnetic structures or quenched disorder. In this paper, we demonstrate an efficient scheme based on the kernel polynomial method for calculating dynamical correlations of relevance to inelastic neutron scattering experiments. This method reduces the scaling of numerical cost from cubic to linear in the magnetic unit cell size.
97 MATHEMATICS AND COMPUTING↗
Exploring Causal Physical Mechanisms via Non-Gaussian Linear Models and Deep Kernel Learning: Applications for Ferroelectric Domain Structures
Rapid emergence of multimodal imaging in scanning probe, electron, and optical microscopies has brought forth the challenge of understanding the information contained in these complex data sets, targeting the intrinsic correlations between different channels, and further exploring the underpinning causal physical mechanisms. Here, we develop such an analysis framework for Piezoresponse Force Microscopy. We argue that under certain conditions, we can bootstrap experimental observations with the prior knowledge of materials structure to get information on certain nonobserved properties, and demonstrate linear causal analysis for PFM observables. We further demonstrate that the strength of individual causal links between complex descriptors can be ascertained using the deep kernel learning (DKL) model. In this DKL analysis, we use the prior information on domain structure within the image to predict the physical properties. This analysis demonstrates the correlative relationships between morphology, piezoresponse, elastic property, etc., at nanoscale. The prediction of morphology and other physical parameters illustrates a mutual interaction between surface condition and physical properties in ferroelectric materials. Overall, this analysis is universal and can be extended to explore the correlative relationships of other multichannel data sets, and allow for high-fidelity reconstruction of underpinning functionalities and physical mechanisms.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Performance portable batched sparse linear solvers in Kokkos kernels.
Abstract not provided.
Liegeois, Kim↗
Performance portable batched sparse linear solvers in Kokkos Kernels.
Abstract not provided.
Liegeois, Kim↗
Kernel PLS-SVC for Linear and Nonlinear Discrimination
A new methodology for discrimination is proposed. This is based on kernel orthonormalized partial least squares (PLS) dimensionality reduction of the original data space followed by support vector machines for classification. Close connection of orthonormalized PLS and Fisher's approach to linear discrimination or equivalently with canonical correlation analysis is described. This gives preference to use orthonormalized PLS over principal component analysis. Good behavior of the proposed method is demonstrated on 13 different benchmark data sets and on the real world problem of the classification finger movement periods versus non-movement periods based on electroencephalogram.
Rosipal, Roman↗
Renormalon cancellation and linear power correction to threshold-like asymptotics of space-like parton correlators
Abstract In this paper, we show that the common hard kernel of double-log-type or threshold-type factorization for certain space-like parton correlators that arise in the context of lattice parton distributions, theheavy-light Sudakov hard kernel, has linear infrared (IR) renormalon. We explicitly demonstrate how this IR renormalon correlates with ultraviolet (UV) renormalons of next-to-leading power operators in two explicit examples: threshold asymptotics of space-like quark-bilinear coefficient functions and transverse momentum dependent (TMD) factorization of quasi wave function amplitude. Theoretically, the pattern of renormalon cancellation complies with general expectations to marginal asymptotics in the UV limit. Practically, this linear renormalon explains the slow convergence of imaginary parts observed in lattice extraction of the Collins-Soper kernel and signals the relevance of next-to-leading power contributions. Fully factorized, fully controlled threshold asymptotic expansion for space-like quark-bilinear coefficient functions in coordinate and moment space has also been proposed.
Physics↗
The HadGEM3-GA7.1 radiative kernel: the importance of a well-resolved stratosphere
We present top-of-atmosphere and surface radiative kernels based on the atmospheric component (GA7.1) of the HadGEM3 general circulation model developed by the UK Met Office. We show that the utility of radiative kernels for forcing adjustments in idealised CO2 perturbation experiments is greatest where there is sufficiently high resolution in the stratosphere in both the target climate model and the radiative kernel. This is because stratospheric cooling to a CO2 perturbation continues to increase with height, and low-resolution or low-top kernels or climate model output are unable to fully resolve the full stratospheric temperature adjustment. In the sixth phase of the Coupled Model Intercomparison Project (CMIP6), standard atmospheric model data are available up to 1 hPa on 19 pressure levels, which is a substantial advantage compared to CMIP5. We show in the IPSL-CM6A-LR model where a full set of climate diagnostics are available that the HadGEM3-GA7.1 kernel exhibits linear behaviour and the residual error term is small, as well as from a survey of kernels available in the literature that in general low-top radiative kernels underestimate the stratospheric temperature response. The HadGEM3-GA7.1 radiative kernels are available at https://doi.org/10.5281/zenodo.3594673 (Smith, 2019).
radiative kernels↗
A Method for Improving Hotspot Directional Signatures in BRDF Models Used for MODIS
The semi-empirical, kernel-driven, linear RossThick-LiSparseReciprocal (RTLSR) Bidirectional Reflectance Distribution Function (BRDF) model is used to generate the routine MODIS BRDFAlbedo product due to its global applicability and the underlying physics. A challenge of this model in regard to surface reflectance anisotropy effects comes from its underestimation of the directional reflectance signatures near the Sun illumination direction; also known as the hotspot effect. In this study, a method has been developed for improving the ability of the RTLSR model to simulate the magnitude and width of the hotspot effect. The method corrects the volumetric scattering component of the RTLSR model using an exponential approximation of a physical hotspot kernel, which recreates the hotspot magnitude and width using two free parameters (C(sub 1) and C(sub 2), respectively). The approach allows one to reconstruct, with reasonable accuracy, the hotspot effect by adjusting or using the prior values of these two hotspot variables. Our results demonstrate that: (1) significant improvements in capturing hotspot effect can be made to this method by using the inverted hotspot parameters; (2) the reciprocal nature allow this method to be more adaptive for simulating the hotspot height and width with high accuracy, especially in cases where hotspot signatures are available; and (3) while the new approach is consistent with the heritage RTLSR model inversion used to estimate intrinsic narrowband and broadband albedos, it presents some differences for vegetation clumping index (CI) retrievals. With the hotspot-related model parameters determined a priori, this method offers improved performance for various ecological remote sensing applications; including the estimation of canopy structure parameters.
airborne measurements↗
Nonlinear analog processing with anisotropic nonlinear films
Digital signal processing is the cornerstone of several modern-day technologies, yet in multiple applications it faces critical bottlenecks related to memory and speed constraints. Thanks to recent advances in metasurface design and fabrication, light-based analog computing has emerged as a viable option to partially replace or augment digital approaches. Several light-based analog computing functionalities have been demonstrated using patterned flat optical elements, with great opportunities for integration in compact nanophotonic systems. So far, however, the available operations have been restricted to the linear regime, limiting the impact of this technology to a compactification of Fourier optics systems. In this paper, we introduce nonlinear operations to the field of metasurface-based analog optical processing, demonstrating that nonlinear optical phenomena, combined with nonlocality in flat optics, can be leveraged to synthesize kernels beyond linear Fourier optics, paving the way to a broad range of new opportunities. As a practical demonstration, we report the experimental synthesis of a class of nonlinear operations that can be used to realize broadband, polarization-selective analog-domain edge detection.
analog image processing↗
FSISPH: An SPH formulation for impacts between dissimilar materials
Here, we present an SPH formulation with several new features designed to better model the fully-compressible interaction of dissimilar materials. We developed the new method to simulate the atmospheric entry and break-up of small celestial bodies in planetary atmospheres. The formulation uses a unity-based, density-energy discretization of the hydrodynamic conservation laws with linear-corrected kernel gradients. To account for variations in compressibility, we use an HLLC approximate Riemann solver to adjust the velocity gradient at material interfaces. To handle large transverse velocity discontinuities, we introduce a simple slip interface model that limits the artificial viscosity at material interfaces. Diffusion is optionally applied through the velocity gradient and this allows the density and specific thermal energy to evolve in a manner more consistent with the first law of thermodynamics in comparison to other more direct diffusion schemes. We also introduce a material-local second-order artificial conduction scheme used to smooth the specific thermal energy field. Material damage fits neatly under this framework by treating the damage front as a material interface. The method has been implemented as a solver, FSISPH, within the code, Spheral++, and is publicly available on github. We test our new solver on a number of classic shock, mixing, and multi-material problem. The components we outline can significantly improve accuracy of SPH for problems with sharp contact discontinuities.
79 ASTRONOMY AND ASTROPHYSICS↗
A High-Throughput Solver for Marginalized Graph Kernels on GPU
Here, we present the design and optimization of a solver for efficient and high-throughput computation of the marginalized graph kernel on General Purpose GPUs. The graph kernel is computed using the conjugate gradient method to solve a generalized Laplacian of the tensor product between a pair of graphs. To cope with the large gap between the instruction throughput and the memory bandwidth of the GPUs, our solver forms the graph tensor product on-the-fly without storing it in memory. This is achieved by using threads in a warp cooperatively to stream the adjacency and edge label matrices of individual graphs by small square matrix blocks called tiles, which are then staged in registers and the shared memory for later reuse. Warps across a thread block can further share tiles via the shared memory to increase data reuse. We exploit the sparsity of the graphs hierarchically by storing only non-empty tiles using a coordinate format and nonzero elements within each tile using bitmaps. We propose a new partition-based reordering algorithm for aggregating nonzero elements of the graphs into fewer but denser tiles to further exploit sparsity. We carry out extensive theoretical analyses on the graph tensor product primitives for tiles of various density and evaluate their performance on synthetic and real-world datasets. Our solver delivers three to four orders of magnitude speedup over existing CPU-based solvers such as GraKeL and GraphKernels. The capability of the solver enables kernel-based learning tasks at unprecedented scales.
97 MATHEMATICS AND COMPUTING↗
Fast and Scalable Sparse Triangular Solver for Multi-GPU Based HPC Architectures
Designing efficient and scalable sparse linear algebra kernels on modern multi-GPU based HPC systems is a daunting task due to significant irregular memory references and workload imbalance across the GPUs. This is particularly the case for \textit{Sparse Triangular Solver (SpTRSV)} which introduces additional two-dimensional computation dependencies among subsequent computation steps. Dependency information is exchanged and shared among GPUs, thus warrant for efficient memory allocation, data partitioning, and workload distribution as well as fine-grained communication and synchronization support. In this work, we demonstrate that directly adopting unified memory can adversely affect the performance of SpTRSV on multi-GPU architectures, despite linking via fast interconnect like NVLinks and NVSwitches. Alternatively, we employ the latest NVSHMEM technology based on Partitioned Global Address Space programming model to enable efficient fine-grained communication and drastic synchronization overhead reduction. Furthermore, to handle workload imbalance, we propose a malleable task-pool execution model which can further enhance the utilization of GPUs. By applying these techniques, our experiments on the NVIDIA multi-GPU supernode V100-DGX-1 and DGX-2 systems demonstrate that our design can achieve on average 3.53x (up to 9.86x) speedup on a DGX-1 system and 3.66x (up to 9.64x) speedup on a DGX-2 system with 4-GPUs over the Unified-Memory design. The comprehensive sensitivity and scalability studies also show that the proposed zero-copy SpTRSV is able to fully utilize the computing and communication resources of the multi-GPU system.
Xie, Chenhao↗
s-blas
This package includes the implementation for four sparse linear algebra kernels: Sparse-Matrix-Vector-Multiplication (SpMV), Sparse-Triangular-Solve (SpTRSV), Sparse-Matrix-Transposition (SpTrans) and Sparse-Matrix-Matrix-Multiplication (SpMM) for Single-node Multi-GPU (scale-up) platforms such as NVIDIA DGX-1 and DGX-2.
Li, Ang↗
Domain decomposition methods in aerodynamics
Compressible Euler equations are solved for two-dimensional problems by a preconditioned conjugate gradient-like technique. An approximate Riemann solver is used to compute the numerical fluxes to second order accuracy in space. Two ways to achieve parallelism are tested, one which makes use of parallelism inherent in triangular solves and the other which employs domain decomposition techniques. The vectorization/parallelism in triangular solves is realized by the use of a recording technique called wavefront ordering. This process involves the interpretation of the triangular matrix as a directed graph and the analysis of the data dependencies. It is noted that the factorization can also be done in parallel with the wave front ordering. The performances of two ways of partitioning the domain, strips and slabs, are compared. Results on Cray YMP are reported for an inviscid transonic test case. The performances of linear algebra kernels are also reported.
Venkatakrishnan, V.↗
Performance and Portability of a Linear Solver Across Emerging Architectures
A linear solver algorithm used by a large-scale unstructured-grid computational fluid dynamics application is examined for a broad range of familiar and emerging architectures. Efficient implementation of a linear solver is challenging on recent CPUs offering vector architectures. Vector loads and stores are essential to effectively utilize available memory bandwidth on CPUs, and maintaining performance across different CPUs can be difficult in the face of varying vector lengths offered by each. A similar challenge occurs on GPU architectures, where it is essential to have coalesced memory accesses to utilize memory bandwidth effectively. In this work, we demonstrate that restructuring a computation, and possibly data layout, with regard to architecture is essential to achieve optimal performance by establishing a performance benchmark for each target architecture in a low level language such as vector intrinsics or CUDA. In doing so, we demonstrate how a linear solver kernel can be mapped to Intel® Xeon™ and Xeon Phi™, Marvell® ThunderX2®, NEC® SX-Aurora™ TSUBASA Vector Engine, and NVIDIA® and AMD® GPUs. We further demonstrate that the required code restructuring can be achieved in higher level programming environments such as OpenACC, OCCA, and Intel® OneAPI™/SYCL, and that each generally results in optimal performance on the target architecture. Relative performance metrics for all implementations are shown, and subjective ratings for ease of implementation and optimization are suggested.
Programming models↗
Memory Optimizations for Sparse Linear Algebra on GPU Hardware
An effort to maximize memory bandwidth utilization for a sparse linear algebra kernel executing on NVIDIA® Tesla V100 and A100 Graphics Processing Units (GPUs) is described. The kernel consists of a block-sparse matrix-vector product and a series of forward/backward triangular solves. The computation is memory-bound and exhibits low arithmetic intensity. Along with a relatively small block size, the data layout poses a challenge to effectively utilize the available memory bandwidth on common GPU architectures. An earlier implementation using a warp to process a single row of the matrix was found to yield good memory performance on the V100 architecture. However, anew approach, which assigns a warp to six rows of the matrix, is proposed for the A100. In addition, two new features offered by the A100 architecture are explored.L2residency control enables a portion of theL2cache to be used for persistent data access, and the asynchronous copy instruction allows data to be loaded directly from main memory into shared memory. Demonstrations show that the new implementation improves memory bandwidth utilization from 71.5% to 81.2% of the peak available on theA100 architecture.
GPU↗
Hyperspectral Sounder Spectral Fingerprinting: Using Machine Learning Techniques to Enhance Model-Based Physical Inversion
Different retrieval algorithms have been developed to process top-of-atmosphere (TOA) spectral radiance data provided by hyperspectral infrared sounder missions. Those algorithms are either optimal estimation method (OEM) based schemes with radiative transfer calculation involved in the retrieval process, or machine learning based methods that allow ultra-efficient data procession but lack of radiometric consistency validation based on the directly measured information. Combining both approaches leverages their respective technical advantages, leading to more accurate results. This study introduces a hyperspectral sounder fingerprinting algorithm to explore this hybrid approach. This approach involves the use of a spectral information-based classification method to identify an reference geophysical state and the corresponding radiative kernel. This enables the efficient retrieval of geophysical variables of interest through a radiative kernel-based linear inversion procedure. The fingerprinting method has been applied to analyze a decade-long hyperspectral sounder data record.
Wan Wu↗