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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Numerical and experimental investigation of the flame kernel growth in a methane/air mixture near the lean flammability limit

Lean combustion has the potential to improve the thermal efficiency of spark-ignition engines, but it faces the significant challenge of increased cycle-to-cycle variation due to low mixture reactivity and unstable flame dynamics. Computational fluid dynamics (CFD) employing predictive models can guide engine design and optimize operating strategies for lean combustion. However, ignition and combustion models have rarely been validated at fuel-lean conditions, and a fundamental understanding of the early flame kernel growth process is also lacking for a successful sub-model development. Here, the present study develops a numerical simulation framework used to investigate early flame kernel growth in methane/air mixtures. A nanosecond-pulsed discharge (NPD) approach is employed to effectively decouple the flame kernel growth from the electrical discharge due to their difference in timescales, and equivalence ratios near the experimentally measured lean flammability limit (LFL) are selected to focus on challenging mixture conditions. Three numerical investigations, such as the choice of turbulence modeling, grid size, and grid control strategies, are examined to match both LFL and flame kernel structure measured from experiments. It is demonstrated that a quasi-direct numerical simulation (QDNS) with a fixed grid embedding of 10 μm can predict the LFL as φ CFD =0.61 and match the displacement speed of the kernel’s boundary marked in schlieren images. To predict the LFL and flame kernel shape, a fine grid (Δ≤12.5 μm) is needed to capture the consumption of formaldehyde (CH 2 O) in kernel’s reaction branches attached to the anode, and adaptive mesh refinement is replaced with the fixed embedding due to loss of simulation accuracy. Also, it is found that a large-eddy simulation (LES) using the Dynamic Structure model is not suitable for the NPD-induced flame kernel simulation because artificial sub-grid turbulent kinetic energy induced by shock dynamics alters the flow velocity calculation, resulting in divergence of LES from QDNS. Lastly, the simulation well matches the experimental data for the flame kernel evolution in three mixture conditions (φ = 0.7, 0.61, 0.55), showing toroidal flame kernel expansion and flame kernel growth/extinction.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Physical Properties of Moist, Fermented Corn Kernels

A novel approach to producing corn stover biomass feedstock has been investigated. In this approach, corn grain and stover are co-harvested at moisture contents much less than typical corn silage. The grain and stover are conserved together by anaerobic storage and fermentation and then separated before end use. When separated from the stover, the moist, fermented grain had physical characteristics that differ from typical low-moisture, unfermented grain. A comprehensive study was conducted to quantify the physical properties of this moist, fermented grain. Six corn kernel treatments, either fermented or unfermented, having different moisture contents, were used. Moist, fermented kernels (26 and 36% w.b. moisture content) increased in size during storage. The fermented kernels’ widths and thicknesses were 10% and 15% greater, respectively, and their volume was 28% greater than the dry kernels (15% w.b.). Dry basis particle density was 9% less for moist, fermented kernels. Additionally, the dry basis bulk density was 29% less, and the dry basis hopper-discharged mass flow rate was 36% less. Moist, fermented grain had significantly greater kernel-to-kernel coefficients of friction and angles of repose compared to relatively dry grain. The friction coefficient on four different surfaces was also significantly greater for fermented kernels. Fermented corn kernels had lower individual kernel rupture strengths than unfermented kernels. These physical differences must be considered when designing material handling and processing systems for moist, fermented corn grain.

09 BIOMASS FUELS↗
DOE OSTI2018

Microstructure and Fission Product Distribution Examination in the UCO kernel of TRISO Fuel Particles

The effect of irradiation and fabrication process on the UCO fuel kernel, kernel-buffer interlayer and fission products, has not been fully studied for UCO fuel kernels of TRISO coated particles. Specifically, the potential correlation(s) with fission product retention, composition and distribution within these structures for the tristructural isotropic (TRISO) fuel performance at normal and accident conditions, are not well reported in literature. Structural and chemical information in the irradiated UCO fuel kernel, e.g., the stoichiometry variations, may further contribute to fuel performance modeling under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. The microstructural and micro-chemical evolution of selected irradiated UCO fuel kernels, kernel buffer interfaces and recoil zones were characterized using Scanning Transmission Electron Microscopy (STEM) and Energy Dispersive Spectroscopy (EDS) elemental mapping. The fuel kernel of particles from Advanced Gas Reactor (AGR)-2 irradiated to 10.8% fissions per initial metal atom (FIMA), were examined with the following main findings: (1) large fission gas bubbles were mainly identified in the zirconium and molybdenum enriched but oxygen depleted phases in the center of fuel kernel, (2) significant inter-diffusion between the UCO fuel kernel and pyro-carbon buffer layer was observed as a high density of sub-micron sized carbon inclusions was identified at near the interface in the kernel side and some isolated UCO particles were located in the buffer layer, (3) pores filled with free carbon were also observed in the recoil zone specimen. Fuel kernels from two AGR-1 compacts irradiated to 11.4 and 17.4% FIMA respectively, were examined with the following main findings: (1) two primary phases consisting of a “high-Z (atomic mass)” UC(O) phase (rocksalt; a=0.496 nm) that also contained Zr, Mo, and/or Ru and a “low-Z” UO2(C) phase (fluorite structure; a = 0.547nm) in which trace amounts of I, Nd, Pr, and/or Er could be detected. This latter phase contained many precipitates of the “high-Z” phase. Conversely, this latter phase did not contain precipitates of the UO2-type material, (2) Xe bubbles were found almost exclusively in the “high-Z” phase and in the particular example shown, the Zr-containing variant. Further work in this area should address whether this potential Xe preference for just one of the high-Z phases is indeed a real effect.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Exponential concentration in quantum kernel methods

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Numerical study of the ignition behavior of a post-discharge kernel in a turbulent stratified crossflow

Ensuring robust ignition is critical for the operability of aeronautical gas-turbine combustors. For ignition to be successful, an important aspect is the ability of the hot gas generated by the spark discharge to initiate combustion reactions, leading to the formation of a self-sustained ignition kernel. This study focuses on this phenomena by performing simulations of kernel ignition in a crossflow configuration that was characterized experimentally. First, inert simulations are performed to identify numerical parameters correctly reproducing the kernel ejection from the ignition cavity, which is here modeled as a pulsed jet. In particular, the kernel diameter and the transit time of the kernel to the reacting mixture are matched with measurements. Considering stochastic perturbations of the ejection velocity of the ignition kernel, the variability of the kernel transit time is also reproduced by the simulations. Subsequently, simulations of a series of ignition sequences are performed with varying equivalence ratio of the fuel-air mixture in the crossflow. The numerical results are shown to reproduce the ignition failure that occurs for the leanest equivalence ratio ($φ = 0.6$). For higher equivalence ratios, the simulations are shown to capture the sensitivity of the ignition to the equivalence ratio, and the kernel successfully transitions into a propagating flame. Significant stochastic dispersion of the ignition strength is observed, which relates to the variability of the transit time of the kernel to the re- active mixture. An analysis of the structure of the ignition kernel also highlights the transition towards a self-propagating flame for successful ignition conditions.

42 ENGINEERING↗
DOE OSTI2018

Evaluating and Optimizing OpenCL Base64 Data Unpacking Kernel with FPGA

Development of applications using OpenCL targeting FPGAs is an emerging approach on heterogeneous computing systems. This paper uses the data unpacking algorithm in Base64 encoding as a case study to present programming and optimization techniques, and experimental results of the OpenCL-based implementations on an FPGA. We explain the algorithm and evaluate the performance of the kernel implementations with Intel's FPGA OpenCL SDK. The experimental results show kernel vectorization and duplication are two optimization techniques that can improve the kernel performance. The performance of kernel duplication is also closely related to the local work size. Our experiment shows 16-lane vectorization increases the bandwidth by a factor of 2 to 10 for large input data sizes. Moreover, the performance of kernel duplication using 16 compute units is 40% to 1.5% less than that of kernel vectorization depending on the input size. Tuning the local work size can improve the kernel performance by a factor of 3 to 23. For this kernel, using local memory is not an effective technique to improve the kernel performance because input data is not reused. A combination of vectorization and duplication achieves the highest performance of 12.3 GiB/s. Compared to an Intel Xeon E5 CPU and an Nvidia Tesla K80 GPU, the performance of the kernel on the Arria 10 FPGA is 6.7X faster than the CPU and 3X slower than the GPU. The performance per watt on the FPGA is 20.5X higher than the CPU and 1.19X lower than the GPU.

Base64 Encoding↗
DOE OSTI2025

Multiphysics Meshfree Degradation Modeling of Energy Storage Materials with Kernel Enrichment

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. Reference: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

25 ENERGY STORAGE↗
DOE OSTI2026

Kernel Enriched Meshfree Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Laboratory of the Rockies (NLR), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. References: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Comparison of Zn accumulation and speciation in kernels of sweetcorn and maize differing in maturity

Abstract Background and Aims Understanding the speciation of Zn in edible portions of crops helps identify the most effective biofortification strategies to increase the supply of nutrients for improving the health and nutrition of consumers. Methods Kernels of 12 sweetcorn and three maize (Zea mays) varieties were analysed for Zn concentration and content. The speciation of the Zn in the embryos, endosperms and whole kernels at 21, 28 and 56 days after pollination (DAP) was then examined for one maize and one sweetcorn variety using synchrotron-based X-ray absorption spectroscopy (XAS). Key Results Averaged across all sweetcorn and maize varieties at 21 DAP, the embryo contributed 27–29% of the whole kernel Zn whilst the endosperm contributed 71–73 %. While sweetcorn embryos contributed a lower proportion to the total kernel Zn than those of maize, the proportion of total Zn in the embryo increased as kernels aged for both varieties, reaching 33 % for sweetcorn and 49% for maize at 28 DAP. Using XAS, it was predicted that an average of 90 % of the Zn in the embryos was present as Zn-phytate, while in the endosperm the Zn was primarily complexed with an N-containing ligand such as histidine and to a lesser extent with phytate. However, in maize endosperms, it was also observed that the proportion of Zn present as Zn-phytate increased as the kernel matured, thereby also probably decreasing its bioavailability in these mature maize kernels. Conclusions The apparent low bioavailability of Zn supplied in maize at its consumption stage (i.e. mature kernels) probably undermines the effectiveness of biofortification of this crop. Conversely, successful biofortification of Zn in sweetcorn and green maize consumed as immature kernels could potentially provide a good source of bioavailable Zn in human diets.

Cheah, Zhong Xiang↗
DOE OSTI2018

Optimizing Kernel Machines Using Deep Learning

Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring non-linear models through the construction of similarity functions from data. These methods are particularly preferred in cases where the training data sizes are limited and when prior knowledge of the data similarities is available. Despite their usefulness, they are limited by the computational complexity and their inability to support end-to-end learning with a task specific objective. On the other hand, deep neural networks have become the de facto solution for end-to-end inference in several learning paradigms. In this article, we explore the idea of using deep architectures to perform kernel machine optimization, for both computational efficiency and end-to-end inferencing. To this end, we develop the DKMO (Deep Kernel Machine Optimization) framework, that creates an ensemble of dense embeddings using Nystrõm kernel approximations and utilizes deep learning to generate task-specific representations through the fusion of the embeddings. Intuitively, the filters of the network are trained to fuse information from an ensemble of linear subspaces in the RKHS. Furthermore, we introduce the kernel dropout regularization to enable improved training convergence. Finally, we extend this framework to the multiple kernel case, by coupling a global fusion layer with pre-trained deep kernel machines for each of the constituent kernels. Using case studies with limited training data, and lack of explicit feature sources, we demonstrate the effectiveness of our framework over conventional model inferencing techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

MONTE CARLO CROSS SECTION LOOKUP KERNEL FOR THE CEREBRAS WSE-2 IN CSL

This is a small kernel that was used to collect data for an upcoming paper. We would like to have the code be open source so that the reviewers (and then readers) of the paper can see the whole code, and can reproduce/verify our results. This is not a fully featured application, it cannot produce any useful simulation results, it just executes a small abstracted kernel using synthetic data. The purpose of the kernel is to understand the basic performance characteristics of an HPC kernel on novel AI accelerator architectures. The main kernel is written in the CSL coding language for use with the Cerebras WSE-2 AI accelerator. The kernel represented is the Monte Carlo cross section lookup kernel, which is a small kernel used by the Monte Carlo neutral particle transport algorithm. There is also a baseline kernel written in CUDA that we will include in the repository to form a basis for comparing the WSE-2 to GPU.

Tramm, John↗
DOE OSTI2019

Measurement of kernel swelling and buffer densification in irradiated UCO and UO 2 TRISO fuel particles from AGR-2

The second Advanced Gas Reactor irradiation (AGR-2) featured UCO tristructural isotropic (TRISO)-coated particle fuel and, for comparison purposes, UO2 TRISO fuel. Particles from three UCO fuel compacts and one UO2 fuel compact were chosen for analysis of kernel swelling and buffer shrinkage. Both kernel swelling and buffer shrinkage are common elements of TRISO fuel performance models. More recently, the AGR program has determined that buffer shrinkage may impact the integrity of the inner pyrolytic carbon (IPyC) layer, which may impact SiC layer integrity (particularly during high-temperature heating tests). Therefore, measurements of buffer irradiation-induced shrinkage may be useful in improving existing models and developing new models that capture buffer-IPyC-SiC-fission product interactions observed in recent AGR post-irradiation examination (PIE). TRISO particles were mounted in epoxy, ground, polished, and imaged via optical microscopy in four separate iterations. Each of the four iterations revealed progressively deeper cross sections within the particles. Images collected from each iteration were analyzed for the circumferences/radii of the kernel, buffer, IPyC, and SiC. Spheres were fit to each set of measurements to generate spherical radii representative of the components of the fuel particle. From these radii, volumes were computed and compared to the as-fabricated volumes. UCO kernel swelling was similar among the three AGR-2 compacts ranging from approximately 28 to 32%. This is only slightly higher swelling than was measured in an earlier study of an AGR-1 compact. However, the burnup at which this swelling occurred in AGR-2 was lower than in AGR-1, indicating a faster swelling rate for the AGR-2 kernels for the irradiation conditions covered by these compacts. The AGR-2 UO2 kernel swelling was less, at 9.9%, comparable to other studies of UO2 kernel swelling. While AGR-2 UCO and UO2 kernels demonstrated different rates of swelling, the extent of buffer shrinkage was similar among the two fuel types, ranging from 24-28%. For comparison, a prior study showed that AGR-1 Compact 1-3-1 experienced 39% buffer shrinkage. A commonly-observed post-irradiation particle morphology is where the buffer pulls away from the IPyC (at least in some regions of the particle). Besides the possibility of the buffer degrading the IPyC when it pulls away from the IPyC, this gap is significant because it may also reduce heat transfer within the particle. Average AGR-2 buffer-IPyC gaps were similar for the UCO and UO2 particles, ranging from 22.2 to 26.0 µm. This is similar to what was measured for AGR-1 Compact 1-3-1.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2020

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↗
DOE OSTI2026

Irradiation of UC1+x kernels using the MiniFuel vehicle: Microstructure, phase analysis, and initial post-irradiation examination

Uranium carbide is a candidate fuel form for a wide range of advanced reactors, including larger Generation IV reactors as well as small modular reactors and microreactors. However, its commercial deployment timeline faces challenges via traditional qualification approaches. To address this issue, an accelerated fission rate irradiation test was performed to collect basic fuel performance data to inform fuel performance models and potential future integral tests. Hyperstoichiometric UC (UC1+x) kernels were irradiated in the High Flux Isotope Reactor using the MiniFuel irradiation vehicle. The test matrix spanned two temperature regimes (700 °C and 800 °C) and burnup levels (1.8 % FIMA and 2.8 % FIMA). Between 21 and 63 kernels were tested at each unique temperature and burnup condition. As-fabricated microstructural analysis revealed a multiphase composition with UC, UC2, UC2−y, and U-C-O bearing phases for the irradiated kernels. Following irradiation, fission gas release, swelling, and microstructures were analyzed. Measured fission gas release was below 5 % for all irradiation conditions, reaching a maximum at the highest temperature and burnup condition. A binary swelling response was observed; the lower burnup and temperature conditions resulted in negligible swelling, but the higher burnup and temperature conditions produced significant anisotropic swelling and densification in a subset of kernels. The basic microstructural exams of kernels following irradiation were not capable of showing a correlation between kernels that exhibited excessive swelling and those that did not. Characterization of a subset of samples using the Advanced Photon Source and more detailed microstructural examination of unirradiated kernels revealed that a subset of kernels contained very high UC2 phase fractions. The anomalous swelling response is hypothesized to have been driven by this chemical variation. The results of this irradiation highlight the potential of accelerated fission rate irradiation testing to explore such behaviors and inform the development of fuel specifications.

Adorno Lopes, Denise [ORNL] (ORCID:000900023705987↗
DOE OSTI2020

Reinforcement Learning via Gaussian Processes with Neural Network Dual Kernels

While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex non-linear embeddings, but do not naturally quantify uncertainty and are often data-inefficient to train. GPs infer posterior distributions over functions, but popular kernels exhibit limited expressivity on complex and high-dimensional data. Fortunately, recently discovered conjugate and neural tangent kernel functions encode the behavior of overparameterized neural networks in the kernel domain. We demonstrate that these kernels can be efficiently applied to regression and reinforcement learning problems by analyzing a baseline case study.We apply GPs with neural network dual kernels to solve reinforcement learning tasks for the first time. We demonstrate, using the well understood mountain-car problem, that GPs empowered with dual kernels perform at least as well as those using the conventional radial basis function kernel. Finally, we conjecture that by inheriting the probabilistic rigor of GPs and the powerful embedding properties of DNNs, GPs using NN dual kernels will empower future reinforcement learning models on difficult domains.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1955

On the Kernel function of the integral equation relating the lift and downwash distributions of oscillating finite wings in subsonic flow

This report treats the Kernel function of an integral equation that relates a known prescribed downwash distribution to an unknown lift distribution for a harmonically oscillating finite wing in compressible subsonic flow. The Kernel function is reduced to a form that can be accurately evaluated by separating the Kernel function into two parts: a part in which the singularities are isolated and analytically expressed and a nonsingular part which may be tabulated. The form of the Kernel function for the sonic case (Mach number 1) is treated separately. In addition, results for the special cases of Mach number of 0 (incompressible case) and frequency of 0 (steady case) are given. The derivation of the integral equation which involves this Kernel function is reproduced as an appendix. Another appendix gives the reduction of the form of the Kernel function obtained herein for the three-dimensional case to a known result of Possio for two-dimensional flow. A third appendix contains some remarks on the evaluation of the Kernel function, and a fourth appendix presents an alternate form of expression for the Kernel function.

Watkins, Charles E↗
NASA NTRS2008

Integrating the Gradient of the Thin Wire Kernel

A formulation for integrating the gradient of the thin wire kernel is presented. This approach employs a new expression for the gradient of the thin wire kernel derived from a recent technique for numerically evaluating the exact thin wire kernel. This approach should provide essentially arbitrary accuracy and may be used with higher-order elements and basis functions using the procedure described in [4].When the source and observation points are close, the potential integrals over wire segments involving the wire kernel are split into parts to handle the singular behavior of the integrand [1]. The singularity characteristics of the gradient of the wire kernel are different than those of the wire kernel, and the axial and radial components have different singularities. The characteristics of the gradient of the wire kernel are discussed in [2]. To evaluate the near electric and magnetic fields of a wire, the integration of the gradient of the wire kernel needs to be calculated over the source wire. Since the vector bases for current have constant direction on linear wire segments, these integrals reduce to integrals of the form

Champagne, Nathan J.↗
NASA NTRS2011

Spectral Kernel Approach to Study Radiative Response of Climate Variables and Interannual Variability of Reflected Solar Spectrum

The radiative kernel approach provides a simple way to separate the radiative response to different climate parameters and to decompose the feedback into radiative and climate response components. Using CERES/MODIS/Geostationary data, we calculated and analyzed the solar spectral reflectance kernels for various climate parameters on zonal, regional, and global spatial scales. The kernel linearity is tested. Errors in the kernel due to nonlinearity can vary strongly depending on climate parameter, wavelength, surface, and solar elevation; they are large in some absorption bands for some parameters but are negligible in most conditions. The spectral kernels are used to calculate the radiative responses to different climate parameter changes in different latitudes. The results show that the radiative response in high latitudes is sensitive to the coverage of snow and sea ice. The radiative response in low latitudes is contributed mainly by cloud property changes, especially cloud fraction and optical depth. The large cloud height effect is confined to absorption bands, while the cloud particle size effect is found mainly in the near infrared. The kernel approach, which is based on calculations using CERES retrievals, is then tested by direct comparison with spectral measurements from Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY) (a different instrument on a different spacecraft). The monthly mean interannual variability of spectral reflectance based on the kernel technique is consistent with satellite observations over the ocean, but not over land, where both model and data have large uncertainty. RMS errors in kernel ]derived monthly global mean reflectance over the ocean compared to observations are about 0.001, and the sampling error is likely a major component.

Jin, Zhonghai↗