Search NASA⌕ Search

SEARCH · Search NASA

Results for “Kernel function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

DRIPS: Dynamic Rebalancing of Pipelined Streaming Applications on CGRAs

Coarse-grained reconfigurable arrays (CGRAs) provide higher flexibility than application-specific integrated circuits (ASICs) and higher efficiency than fine-grained reconfigurable devices such as Field Programmable Gate Arrays (FPGAs). However, CGRAs are generally designed to support offloading of a single kernel. While their design, based on communicating functional units, appears to naturally suit data streaming applications composed of multiple cooperating kernels, current approaches only statically partition the resources across application kernels. However, emerging streaming applications at the edge (scientific instruments, sensor networks, network processing) perform much more than digital signal processing and often are data and input dependent. This leads to extremely variable kernel execution times, severely impacting the throughput of the entire pipeline if resources are only statically allocated. Therefore, in this paper, we propose DRIPS — a coarse-grained, dynamically, and partially reconfigurable array for data-dependent streaming applications. We present a unified compiler framework to facilitate the mapping of a given streaming application onto the DRIPS CGRA architecture. The experimental results show that DRIPS achieves an average throughput improvement of 1.46$\times$ across a set of representative applications over a statically partitioned solution. The additional area overhead to enable dynamic rebalancing consumes 16.34% of the entire area for a 5x5 CGRA prototype.

Tan, Cheng↗

First-principles wave-vector- and frequency-dependent exchange-correlation kernel for jellium at all densities

Here we propose a spatially and temporally nonlocal exchange correlation (XC) kernel for the spin-unpolarized fluid phase of ground-state jellium for use in time-dependent density functional and linear response calculations. The kernel is constructed to satisfy known properties of the exact XC kernel to accurately describe the correlation energies of bulk jellium and to satisfy frequency-moment sum rules at a wide range of bulk jellium densities, including those low densities that display strong correlation and symmetry breaking. These effects are easier to understand in the simple jellium model than in real systems. All exact constraints satisfied by the recent MCP07 kernel are maintained in the revised MCP07 (rMCP07) kernel, while others are added. The revision $f^{rMCP07}_{XC}$ (q, ω) differs from MCP07 only for nonzero frequencies ω. Only at densities much lower than those of real bulk metals is the frequency dependence of the kernel important for the correlation energy of jellium. As the wave vector q tends to zero, the kernel has a -4$πα(ω)/q^2$ divergence whose frequency-dependent ultranonlocality coefficient $α(ω)$ vanishes in jellium, and is predicted by rMCP07 to be extremely small for the real metals Al and Na.

36 MATERIALS SCIENCE↗

IRIS Reimagined: Advancements in Intelligent Runtime System for Task-Based Programming

Task-based programming models are gaining traction in scientific computing. IRIS is a portable runtime system that exploits multiple heterogeneous programming systems and can discover available resources and manage multiple diverse programming systems (e.g., CUDA, Hexagon, HIP, Level Zero, OpenCL, and OpenMP) simultaneously. It accounts for the constraints of task dependencies and provides customizable scheduling policies to map those tasks to heterogeneous devices. In this paper, we present new capabilities added to IRIS to improve its portability for heterogeneous programming, build-friendliness, and performance efficiency. The new additions include vendor-specific kernel support, a runtime system with a foreign function interface to eliminate writing wrapper or boilerplate code for heterogeneous kernels, an easy-to-use and configurable CMake-based build environment, automatic and efficient data transfers and orchestration, and the Hunter and DAGGER toolchains to evaluate IRIS’s task scheduling algorithms.

Miniskar, Narasinga Rao↗

Bayesian Active Learning for Scanning Probe Microscopy: From Gaussian Processes to Hypothesis Learning

Recent progress in machine learning methods and the emerging availability of programmable interfaces for scanning probe microscopes (SPMs) have propelled automated and autonomous microscopies to the forefront of attention of the scientific community. However, enabling automated microscopy requires the development of task-specific machine learning methods, understanding the interplay between physics discovery and machine learning, and fully defined discovery workflows. This, in turn, requires balancing the physical intuition and prior knowledge of the domain scientist with rewards that define experimental goals and machine learning algorithms that can translate these to specific experimental protocols. Here, we discuss the basic principles of Bayesian active learning and illustrate its applications for SPM. We progress from the Gaussian process as a simple data-driven method and Bayesian inference for physical models as an extension of physics-based functional fits to more complex deep kernel learning methods, structured Gaussian processes, and hypothesis learning. These frameworks allow for the use of prior data, the discovery of specific functionalities as encoded in spectral data, and exploration of physical laws manifesting during the experiment. Here, the discussed framework can be universally applied to all techniques combining imaging and spectroscopy, SPM methods, nanoindentation, electron microscopy and spectroscopy, and chemical imaging methods and can be particularly impactful for destructive or irreversible measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nonlinear Integral Equations with Potential-Type Kernels on a Segment

We study various classes of nonlinear equations containing operators of potential type (Riesz potential). By the method of monotone operators in the Lebesgue spaces of real-valued functions L{sub p}(a, b) we prove global theorems on the existence, uniqueness, estimates, and methods of construction of their solutions. We present applications that illustrate the results obtained.

97 MATHEMATICS AND COMPUTING↗

Overdestabilization vs Overstabilization in the Theoretical Analysis of f-Orbital Covalency

The complex nature of the f-orbital electronic structures and their interaction with the chemical environment pose significant computational challenges. Advanced computational techniques that variationally include scalar relativities and spin–orbit coupling directly at the molecular orbital level have been developed to address this complexity. Among these, variational relativistic multiconfigurational multireference methods stand out for their high accuracy and systematic improvement in studies of f-block complexes. Additionally, these advanced methods offer the potential for calibrating low-scaling electronic structure methods such as density functional theory. However, studies on the Cl K-edge X-ray absorption spectra of the [Ce(III)Cl 6 ] 3– and [Ce(IV)Cl 6 ] 2– complexes show that time-dependent density functional theory with approximate exchange–correlation kernels can lead to inaccuracies, resulting in an overstabilization of 4f orbitals and incorrect assessments of covalency. In contrast, approaches utilizing small active space wave function methods may understate the stability of these orbitals. The results herein demonstrate the need for large active space, multireference, and variational relativistic methods in studying f-block complexes.

chemical calculations↗

Continuum electromagnetic gyrokinetic simulations of turbulence in the tokamak scrape-off layer and laboratory devices

Here, we present algorithms and results from Gkeyll, a full-f continuum, electromagnetic gyrokinetic code, designed to study turbulence in the edge region of fusion devices. The edge is computationally very challenging, requiring robust algorithms that can handle large-amplitude fluctuations and stable interactions with plasma sheaths. We present an energy-conserving high-order discontinuous Galerkin scheme that solves gyrokinetic equations in Hamiltonian form. Efficiency is improved by a careful choice of basis functions and automatically generated computation kernels. Previous verification tests were performed in the straight-field-line large plasma device [Shi et al., J. Plasma Phys. 83, 905830304 (2017)] and the Texas Helimak, a simple magnetized torus [Bernard et al., Phys. Plasmas 26, 042301 (2019)], including the effect of end-plate biasing on turbulence. Results for the scrape-off layer for NSTX parameters with a model helical magnetic geometry with bad curvature have been obtained [Shi et al., Phys. Plasmas 26, 012307 (2019)]. In this paper, we present algorithms for the two formulations of electromagnetic gyrokinetics: the Hamiltonian and the symplectic. We describe each formulation and show results of benchmark tests. Although our scheme works for the Hamiltonian formulation, the presence of spurious numerical modes for high-β and large $k^2_⊥ρ^2_s$ regimes shows that the symplectic formulation is more robust. We then review our recent algorithm for the symplectic formulation [Mandell et al., J. Plasma Phys. 86, 905860109 (2020)], along with example application of this new capability. Maintaining positivity of the distribution function can be challenging, and we describe a new and novel exponential recovery based algorithm to address this.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

MICCO: An Enhanced Multi-GPU Scheduling Framework for Many-Body Correlation Functions

Calculation of many-body correlation functions is one of the critical kernels utilized in many scientific computing areas, especially in Lattice Quantum Chromodynamics (Lattice QCD). It is formalized as a sum of a large number of contraction terms each of which can be represented by a graph consisting of vertices describing quarks inside a hadron node and edges designating quark propagations at specific time intervals. Due to its computation- and memory-intensive nature, real-world physics systems (e.g., multi-meson or multi-baryon systems) explored by Lattice QCD prefer to leverage multi-GPUs. Different from general graph processing, many-body correlation function calculations show two specific features: a large number of computation-/data-intensive kernels and frequently repeated appearances of original and intermediate data. The former results in expensive memory operations such as tensor movements and evictions. The latter offers data reuse opportunities to mitigate the data-intensive nature of many-body correlation function calculations. However, existing graph-based multi-GPU schedulers cannot capture these data-centric features, thus resulting in a sub-optimal performance for many-body correlation function calculations. To address this issue, this paper presents a multi-GPU scheduling framework, MICCO, to accelerate contractions for correlation functions particularly by taking the data dimension (e.g., data reuse and data eviction) into account. This work first performs a comprehensive study on the interplay of data reuse and load balance, and designs two new concepts: local reuse pattern and reuse bound to study the opportunity of achieving the optimal trade-off between them. Based on this study, MICCO proposes a heuristic scheduling algorithm and a machine-learning-based regression model to generate the optimal setting of reuse bounds. Specifically, MICCO is integrated into a real-world Lattice QCD system, Redstar, for the first time running on multiple GPUs. The evaluation demonstrates MICCO outperforms other state-of-art works, achieving up to 2.25× speedup in synthesized datasets, and 1.49× speedup in real-world correlation functions.

Wang, Qihan↗

The Arrow of Time in the Collapse of Collisionless Self-gravitating Systems: Non-validity of the Vlasov–Poisson Equation during Violent Relaxation

The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is traditionally assumed that this evolution is governed by the Vlasov–Poisson equation, in which case entropy must be conserved. We run N-body simulations of isolated self-gravitating systems, using three simulation codes, NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening), and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. At each snapshot, we estimate the Shannon entropy of the distribution function with three different techniques: Kernel, Nearest Neighbor, and EnBiD. For all simulation codes and estimators, the entropy evolution converges to the same limit as N increases. During violent relaxation, the entropy has a fast increase followed by damping oscillations, indicating that violent relaxation must be described by a kinetic equation other than the Vlasov–Poisson equation, even for N as large as that of astronomical structures. This indicates that violent relaxation cannot be described by a time-reversible equation, shedding some light on the so-called “fundamental paradox of stellar dynamics.” The long-term evolution is well-described by the orbit-averaged Fokker–Planck model, with Coulomb logarithm values in the expected range 10--12. By means of NBODY-2, we also study the dependence of the two-body relaxation timescale on the softening length. The approach presented in the current work can potentially provide a general method for testing any kinetic equation intended to describe the macroscopic evolution of N-body systems.

79 ASTRONOMY AND ASTROPHYSICS↗

Global adjoint tomography: first-generation model

We present the first-generation global tomographic model constructed based on adjoint tomography, an iterative full-waveform inversion technique. Synthetic seismograms were calculated using GPU-accelerated spectral-element simulations of global seismic wave propagation, accommodating effects due to 3-D anelastic crust & mantle structure, topography & bathymetry, the ocean load, ellipticity, rotation, and self-gravitation. Fréchet derivatives were calculated in 3-D anelastic models based on an adjoint-state method. The simulations were performed on the Cray XK7 named ‘Titan’, a computer with 18 688 GPU accelerators housed at Oak Ridge National Laboratory. The transversely isotropic global model is the result of 15 tomographic iterations, which systematically reduced differences between observed and simulated three-component seismograms. Our starting model combined 3-D mantle model S362ANI with 3-D crustal model Crust2.0. We simultaneously inverted for structure in the crust and mantle, thereby eliminating the need for widely used ‘crustal corrections’. We used data from 253 earthquakes in the magnitude range 5.8 ≤ M w ≤ 7.0. We started inversions by combining ~30 s body-wave data with ~60 s surface-wave data. The shortest period of the surface waves was gradually decreased, and in the last three iterations we combined ~17 s body waves with ~45 s surface waves. We started using 180 min long seismograms after the 12th iteration and assimilated minor- and major-arc body and surface waves. The 15th iteration model features enhancements of well-known slabs, an enhanced image of the Samoa/Tahiti plume, as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone and Erebus. Furthermore, we see clear improvements in slab resolution along the Hellenic and Japan Arcs, as well as subduction along the East of Scotia Plate, which does not exist in the starting model. Point-spread function tests demonstrate that we are approaching the resolution of continental-scale studies in some areas, for example, underneath Yellowstone. Here, this is a consequence of our multiscale smoothing strategy in which we define our smoothing operator as a function of the approximate Hessian kernel, thereby smoothing gradients less wherever we have good ray coverage, such as underneath North America.

58 GEOSCIENCES↗

MemHC: An Optimized GPU Memory Management Framework for Accelerating Many-body Correlation

The many-body correlation function is a fundamental computation kernel in modern physics computing applications, e.g., Hadron Contractions in Lattice quantum chromodynamics (QCD). This kernel is both computation and memory intensive, involving a series of tensor contractions, and thus usually runs on accelerators like GPUs. Existing optimizations on many-body correlation mainly focus on individual tensor contractions (e.g., cuBLAS libraries and others). In contrast, this work discovers a new optimization dimension for many-body correlation by exploring the optimization opportunities among tensor contractions. More specifically, it targets general GPU architectures (both NVIDIA and AMD) and optimizes many-body correlation’s memory management by exploiting a set of memory allocation and communication redundancy elimination opportunities: first, GPU memory allocation redundancy: the intermediate output frequently occurs as input in the subsequent calculations; second, CPU-GPU communication redundancy: although all tensors are allocated on both CPU and GPU, many of them are used (and reused) on the GPU side only, and thus, many CPU/GPU communications (like that in existing Unified Memory designs) are unnecessary; third, GPU oversubscription: limited GPU memory size causes oversubscription issues, and existing memory management usually results in near-reuse data eviction, thus incurring extra CPU/GPU memory communications.

97 MATHEMATICS AND COMPUTING↗

Compadre Toolkit

The Compadre Toolkit solves a minimization problem, that once solved allows a user to reconstruct a function from sample data collected from a cloud of data sites. The solution to this minimization can also be used to assemble a linear system that can be solved numerically using some other software. The minimization problem the toolkit solves is to find the optimal finite polynomial in a user specified finite dimensional space with regards to minimizing an objective function which measures a linear sampling functional applied to the polynomial, compared to the same sampling functional applied to the source function, weighted by a positive kernel that has compact support.

SciDAC↗

LaplaceInterpolation.jl: A Julia package for fast interpolation on a grid

We implement a linear-time algorithm for interpolation on a regular multidimensional grid in the Julia language. The algorithm is an approximate Laplace interpolation (Press, 1992) when no parameters are given; and when parameters m ∈ Z and ϵ > 0 are set, the interpolant approximates a Matérn kernel, of which radial basis functions and polyharmonic splines are a special case. We implement, in addition, Neumann, Dirichlet (trivial), and average boundary conditions with potentially different aspect ratios in the different dimensions. The interpolant functions in arbitrary dimensions.

97 MATHEMATICS AND COMPUTING↗

Advanced Finite-Volume Numerics and Source Term Assumptions for Kernel and G-Equation Modelling of Propane/Air Flames

Here G-Equation models represent propagating flame fronts with an implicit two-dimensional surface representation (level-set). Level-set methods are fast, as transport source terms for the implicit surface can be solved with finite-volume operators on the finite-volume domain, without having to build the actual surface. However, they include approximations whose practical effects are not properly understood. In this study, we improved the numerics of the FRESCO CFD code’s G-Equation solver and developed a new method to simulate kernel growth using signed distance functions and the analytical sphere-mesh overlap. We analyzed their role for simulating propane/air flames, using three well-established constant-volume configurations: a one-dimensional, freely propagating laminar flame; a disc-shaped, constant-volume swirl combustor; and torch-jet flame development through an orifice from a two-chamber device. We tested the explicit (sub-cycled) vs. implicit formulation for the standard transport operators (advection, diffusion, compressibility). In addition to the accurate flame swept-volume method for chemistry and species source term, we developed a more accurate estimator for the burnt/unburnt split cell composition. Then, we developed a signed-distance-function (SDF) based method which provides a more stable reinitialization of the level-set field at every time-step. We found that simplifying assumptions common to several G-Equation implementations, for straightforward terms such as compressibility and advection, lead to large errors in predicting the propagation of even laminar flames, with deviations up to ~300% in simulated vs. formulated flame speed. Conversely, the enhanced numerics enabled through the SDF field reinitialization and improved chemistry source term improve simulation stability and smooth flame propagation even with significantly larger solver time-steps.

42 ENGINEERING↗

Exact Gaussian processes for massive datasets via non-stationary sparsity-discovering kernels

Abstract A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. Its success is largely attributed to the GP’s analytical tractability, robustness, and natural inclusion of uncertainty quantification. Unfortunately, the use of exact GPs is prohibitively expensive for large datasets due to their unfavorable numerical complexity of $$O(N^3)$$ O ( N 3 ) in computation and $$O(N^2)$$ O ( N 2 ) in storage. All existing methods addressing this issue utilize some form of approximation—usually considering subsets of the full dataset or finding representative pseudo-points that render the covariance matrix well-structured and sparse. These approximate methods can lead to inaccuracies in function approximations and often limit the user’s flexibility in designing expressive kernels. Instead of inducing sparsity via data-point geometry and structure, we propose to take advantage of naturally-occurring sparsity by allowing the kernel to discover—instead of induce—sparse structure. The premise of this paper is that the data sets and physical processes modeled by GPs often exhibit natural or implicit sparsities, but commonly-used kernels do not allow us to exploit such sparsity. The core concept of exact, and at the same time sparse GPs relies on kernel definitions that provide enough flexibility to learn and encode not only non-zero but also zero covariances. This principle of ultra-flexible, compactly-supported, and non-stationary kernels, combined with HPC and constrained optimization, lets us scale exact GPs well beyond 5 million data points.

97 MATHEMATICS AND COMPUTING↗

SU-F-SPS-06: Implementation of a Back-Projection Algorithm for 2D in Vivo Dosimetry with An EPID System

Purpose: To implement a back-projection algorithm for 2D dose reconstructions for in vivo dosimetry in radiation therapy using an Electronic Portal Imaging Device (EPID) based on amorphous silicon. Methods: An EPID system was used to calculate dose-response function, pixel sensitivity map, exponential scatter kernels and beam hardenig correction for the back-projection algorithm. All measurements were done with a 6 MV beam. A 2D dose reconstruction for an irradiated water phantom (30×30×30 cm{sup 3}) was done to verify the algorithm implementation. Gamma index evaluation between the 2D reconstructed dose and the calculated with a treatment planning system (TPS) was done. Results: A linear fit was found for the dose-response function. The pixel sensitivity map has a radial symmetry and was calculated with a profile of the pixel sensitivity variation. The parameters for the scatter kernels were determined only for a 6 MV beam. The primary dose was estimated applying the scatter kernel within EPID and scatter kernel within the patient. The beam hardening coefficient is σBH= 3.788×10{sup −4} cm{sup 2} and the effective linear attenuation coefficient is µAC= 0.06084 cm{sup −1}. The 95% of points evaluated had γ values not longer than the unity, with gamma criteria of ΔD = 3% and Δd = 3 mm, and within the 50% isodose surface. Conclusion: The use of EPID systems proved to be a fast tool for in vivo dosimetry, but the implementation is more complex that the elaborated for pre-treatment dose verification, therefore, a simplest method must be investigated. The accuracy of this method should be improved modifying the algorithm in order to compare lower isodose curves.

60 APPLIED LIFE SCIENCES↗

Transverse-momentum-dependent pion structures from lattice QCD: Collins-Soper kernel, soft factor, TMDWF, and TMDPDF

We present the first lattice quantum chromodynamics (QCD) calculation of the pion valence-quark transverse-momentum-dependent parton distribution function (TMDPDF) within the framework of large-momentum effective theory (LaMET). Using correlators fixed in the Coulomb gauge (CG), we computed the quasi-TMD beam function for a pion with a mass of 300 MeV, a fine lattice spacing of 𝑎 =0.06 fm, and multiple large momenta up to 3 GeV. The intrinsic soft functions in the CG approach are extracted from form factors with large momentum transfer, and as a byproduct, we also obtain the corresponding Collins-Soper (CS) kernel. Our determinations of both the soft function and the CS kernel agree with perturbation theory at small transverse separations (𝑏 ⊥ ) between the quarks. At larger 𝑏 ⊥ , the CS kernel remains consistent with recent results obtained using both CG and gauge-invariant TMD correlators in the literature. By combining next-to-leading logarithmic factorization of the quasi-TMD beam function and the soft function, we obtain an 𝑥-dependent pion valence-quark TMDPDF for transverse separations 𝑏 ⊥ ≳1 fm. Interestingly, we find that the 𝑏 ⊥ dependence of the phenomenological parametrizations of TMDPDF for moderate values of 𝑥 are in reasonable agreement with our QCD determinations. In addition, we present results for the transverse-momentum-dependent wave function for a heavier pion with 670 MeV mass.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗