Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Kernel methods”

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 127 records · Page 7

Unsteady Subsonic Loadings Due to Control-Surface Motion

RHOIV computer program predicts unsteady lifting-surface loadings caused by motions of leading edge and trailing-edge control surfaces having sealed gaps at hinge lines and side edges. Analysis is based on linear, subsonic, potential-flow theory using kernel function method. Linear combinations of pressure distributions are used that are continuous except at planform edges and hinge lines. Loading solution is obtained by downwash collocation for deflection or motion of main wing and control surfaces.

Rowe, W. S.↗

The Updated Umkehr Ozone Retrieval Algorithm and its Validation against Satellite Data

Improvements to the Umkehr ozone profile retrieval algorithm have been developed and are now being evaluated. The updated algorithm is able to simulate observations more accurately and provides data output that is easier to analyze. Among the new diagnostic capabilities that the updated algorithm provides is the averaging kernel (AK) method. The AK approach allows studying how the algorithm responds when a small perturbation is made in a particular layer of the atmosphere [Rodgers 1976, 1990]. We will use the AK method to define precisely what Umkehr should measure given a set of profiles measured by other platforms. This method allows us to compare trends and offsets in data more accurately than it has been done in the past. The updated Umkehr retrievals will be validated against SAGE II ozone profiles as well as SSBUV ozone profile data. We will discuss possible reasons for offset between data and differences in derived ozone profile trends. Considerable variability of the ozone profile within the 10-degree latitude envelope creates noise in the SAGE matching dataset and makes comparisons difficult. To eliminate this problem, the SAGE and Umkehr data had been previously de-seasonalized by subtracting the latitude/season dependent ozone climatology. However, the remaining noise in the ozone residuals was still considerably high for trend analysis and was attributed to longitude variability of SAGE sampling. The new ozone climatology (Labow, NASA) that has longitude dependent ozone variability will be used to minimize contribution of sampling noise in comparisons of satellite and ground station. The comparison of zenith-sky radiances (Umkehr N-value measurements) synthesized for a given set of SAGE profiles will be used to determine whether SAGE-derived N-values agree with the Umkehr-measured N-values. The instrumental effects will be discussed. Both the Umkehr data and SAGE II measurements will be analyzed for their information about ozone variability and loss and recovery rates at the mid- and upper (40 km) levels. The updated long-term Umkehr dataset can be used to provide high quality information for identifying signs of ozone recovery. The long Umkehr historical record can provide additional information for separating the dynamic and chemical mechanisms of depletion, and can help the community better understand climate change effects.

Petropavlovskikh, I.↗

Active Learning for Directed Exploration of Complex Systems

Physics-based simulation codes are widely used in science and engineering to model complex systems that would be infeasible to study otherwise. Such codes provide the highest-fidelity representation of system behavior, but are often so slow to run that insight into the system is limited. For example, conducting an exhaustive sweep over a d-dimensional input parameter space with k-steps along each dimension requires k(sup d) simulation trials (translating into k(sup d) CPU-days for one of our current simulations). An alternative is directed exploration in which the next simulation trials are cleverly chosen at each step. Given the results of previous trials, supervised learning techniques (SVM, KDE, GP) are applied to build up simplified predictive models of system behavior. These models are then used within an active learning framework to identify the most valuable trials to run next. Several active learning strategies are examined including a recently-proposed information-theoretic approach. Performance is evaluated on a set of thirteen synthetic oracles, which serve as surrogates for the more expensive simulations and enable the experiments to be replicated by other researchers.

oracles↗

Measurement of the muon anomalous precession frequency in runs 2 \& 3 of the Muon $g-2$ Experiment at Fermilab

This dissertation presents a measurement of the muon anomalous precession frequency for the Runs 2 \& 3 data of the E989 Muon $g-2$ Experiment at Fermilab. The muon anomalous precession frequency is one of two key inputs, the other being the magnetic field, used to precisely determine the muon magnetic anomaly, $a_{\mu}$. In April 2021, the E989 collaboration reported its first measurement of $a_{\mu}$ to an unprecedented precision of 460 parts-per-billion (ppb). This result is in agreement with the previous measurement performed by the E821 collaboration at Brookhaven National Laboratory, and the combined experimental value is in tension with the Standard Model prediction at 4.2$\sigma$, a possible hint of new physics. The first result from E989 was based on the Run-1 data, which was collected in 2018 and comprises 6\% of the experiment’s target statistics; the Run-1 result was statistics-limited. The Runs 2 \& 3 data were collected in 2019-2020 and constitute a four-fold increase i n statistics compared to Run-1 and consequently, a factor of two reduction in the measurement’s statistical uncertainty. This reduced statistical uncertainty, as well as continued understanding of systematic effects, will result in an even more precise measurement of $a_{\mu}$ and will help clarify the observed tension between theory and experiment. The precession frequency analysis presented in this dissertation includes a number of improvements compared to Boston University's Run-1 analysis: the implementation of a more robust pileup-subtraction procedure, the implementation of a kernel ratio method, the adoption of the statistically optimal asymmetry-weighted method, and investigations that led to an improved understanding of an outstanding residual slow effect. This dissertation motivates a measurement of the muon magnetic anomaly, describes the experimental principle, gives an overview of the E989 experiment, and presents a precession frequency analysis with full systematic unc ertainty evaluation for the Runs 2 \& 3 data. The combined precession frequency measurement, using the ratio asymmetry-weighted method, has a statistical uncertainty of 201 ppb and a systematic uncertainty of 25 ppb, constituting the most precise determination of the muon anomalous precision frequency to date.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reduce-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which usually consists of a database of tabulated values, used to calculate the cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of micro cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. To address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multi-group cross section data across isotopes, reaction types and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs for have been trained for all isotopes in this work and systematic Griffin testing is ongoing at this moment to ensure the feasibility of this ROM technique for cross section predictions.

42 - ENGINEERING↗

Reduced-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Abstract – Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which consist of databases of tabulated values, used to calculate the neutron cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of microscopic cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. In order to address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multigroup cross section data across isotopes, reaction types, and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs have been trained for all isotopes in this work and systematic Griffin testing is ongoing to ensure the feasibility of this ROM technique for predicting cross section and reducing memory requirements without a significant sacrifice in computational performance.

42 - ENGINEERING↗

Advanced Cross Section Library Generation using Reduced Order Models

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which consist of databases of tabulated values, used to calculate the neutron cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of microscopic cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. In order to address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multigroup cross section data across isotopes, reaction types, and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs have been trained for all isotopes in this work and systematic Griffin testing is ongoing to ensure the feasibility of this ROM technique for predicting cross section and reducing memory requirements without a significant sacrifice in computational performance.

42 - ENGINEERING↗

The Top-of-Atmosphere, Surface and Atmospheric Cloud Radiative Kernels Based on ISCCP-H Datasets: Method and Evaluation

This study aims to create observation-based cloud radiative kernel (CRK) datasets and evaluate them by direct comparison of CRK and the CRK-derived cloud feedback datasets. Based on the International Satellite Cloud Climatology Project (ISCCP) H datasets, we calculate CRKs (called ISCCP-FH or FH CRKs) as 2D joint function/histogram of cloud optical depth and cloud top pressure for shortwave (SW), longwave (LW), and their sum, Net, at the top of atmosphere (TOA), as well as, for the first time, at the surface (SFC) and in the atmosphere (ATM). With cloud fraction change (CFC) datasets from doubled-CO2 simulation and short-term observational anomalies, we derive all the TOA, SFC and ATM cloud feedback for SW, LW and Net using our CRKs.The direct comparison with modeled and observed CRKs (or cloud radiative effects), cloud feedback from previous model results and the Clouds and the Earth's Radiant Energy System products show that our CRKs and CRK-derived cloud feedback are reasonably well validated. We estimate the uncertainty for the CRK-derived cloud feedback and show that the CFC-associated uncertainty contributes >98.5% of the total cloud feedback uncertainty while CRK's is very small. Our preliminary evaluation also shows that some near-zero/small cloud feedback in the TOA-alone feedback indeed results from the compensation of sizable cloud feedback of the SFC and ATM feedback and reveals some significant surface and atmospheric cloud feedback whose sum appears insignificant in TOA-alone feedback. In addition, the atmospheric longwave cloud feedback seems to play a role in enhancing meridional atmospheric energy transport.

cloud radiative kernel↗

A group finder algorithm optimised for the study of local galaxy environments

Context. The majority of galaxy group catalogues available in the literature use the popular friends-of-friends algorithm which links galaxies using a linking length. One potential drawback to this approach is that clusters of points can be linked with thin bridges which may not be desirable. In order to study galaxy groups, it is important to obtain realistic group structures. Aim. Here, in this study, we present a new simple group finder algorithm, TD-ENCLOSER, that finds the group that encloses a target galaxy of interest. Methods. TD-ENCLOSER is based on the kernel density estimation method which treats each galaxy, represented by a zero-dimensional particle, as a two-dimensional circular Gaussian. The algorithm assigns galaxies to peaks in the density field in order of density in descending order (‘top down’) so that galaxy groups ‘grow’ around the density peaks. Outliers in under-dense regions are prevented from joining groups by a specified hard threshold, while outliers at the group edges are clipped below a soft (blurred) interior density level. Results. The group assignments are largely insensitive to all free parameter variations apart from the hard density threshold and the kernel standard deviation, although this is a known feature of density-based group finder algorithms and it operates with a computing speed that increases linearly with the size of the input sample. In preparation for a companion paper, we also present a simple algorithm to select unique representative groups when duplicates occur. Conclusions. TD-ENCLOSER is tested on a mock galaxy catalogue using a smoothing scale of 0.3 Mpc and is found to be able to recover the input group distribution with sufficient accuracy to be applied to observed galaxy distributions.

79 ASTRONOMY AND ASTROPHYSICS↗

Kernel-based global sensitivity analysis obtained from a single data set

Results from global sensitivity analysis (GSA) often guide the understanding of complicated input–output systems. Kernel-based GSA methods have recently been proposed for their capability of treating a broad scope of complex systems. In this paper, we develop a new set of kernel GSA tools when only a single set of input–output data is available. Three key advances are made: (1) A new numerical estimator is proposed that demonstrates an empirical improvement over previous procedures. (2) A computational method for generating inner statistical functions from a single data set is presented. (3) A theoretical extension is made to define conditional sensitivity indices, which reveal the degree that the inputs carry shared information about the output when inherent input–input correlations are present. Utilizing these conditional sensitivity indices, a decomposition is derived for the output uncertainty based on what is called the optimal learning sequence of the input variables, which remains consistent when correlations exist between the input variables. Further, while these advances cover a range of GSA subjects, a common single data set numerical solution is provided by a technique known as the conditional mean embedding of distributions. The new methodology is implemented on benchmark systems to demonstrate the provided insights.

42 ENGINEERING↗

Fault Detection via Occupation Kernel Principal Component Analysis

Reliable operation of automatic systems is heavily dependent on the ability to detect faults in the underlying dynamics. While traditional model-based methods have been widely used for fault detection, data-driven approaches have garnered increasing attention due to their ease of deployment and minimal need for expert knowledge. In this letter, we present a novel principal component analysis (PCA) method that uses occupation kernels. Occupation kernels result in feature maps that are tailored to the measured data, have inherent noise-robustness due to the use of integration, and can utilize irregularly sampled system trajectories of variable lengths for PCA. The occupation kernel PCA method is used to develop a reconstruction error approach to fault detection and its efficacy is validated using numerical simulations.

42 ENGINEERING↗

Density Estimation with Mercer Kernels

We present a new method for density estimation based on Mercer kernels. The density estimate can be understood as the density induced on a data manifold by a mixture of Gaussians fit in a feature space. As is usual, the feature space and data manifold are defined with any suitable positive-definite kernel function. We modify the standard EM algorithm for mixtures of Gaussians to infer the parameters of the density. One benefit of the approach is it's conceptual simplicity, and uniform applicability over many different types of data. Preliminary results are presented for a number of simple problems.

Macready, William G.↗

A simple and fast method for computing the relativistic Compton Scattering Kernel for radiative transfer

The Klein-Nishina differential cross section averaged over a relativistic Maxwellian electron distribution is analytically reduced to a single integral, which can then be rapidly evaluated in a variety of ways. A particularly fast method for numerically computing this single integral is presented. This is, to the authors' knowledge, the first correct computation of the Compton scattering kernel.

Kershaw, David S.↗

A meshless stochastic method for Poisson–Nernst–Planck equations

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

Chemistry↗

Advanced stationary and nonstationary kernel designs for domain-aware Gaussian processes

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The mathematical methods we discuss in this paper are an extension of the Gaussian-process framework. We are proposing advanced kernel designs that only allow for functions with certain desirable characteristics to be elements of the reproducing kernel Hilbert space (RKHS) that underlies all kernel methods and serves as the sample space for Gaussian process regression. These desirable characteristics reflect the underlying physics; two obvious examples are symmetry and periodicity constraints. In addition, non-stationary kernel designs can be defined in the same framework to yield flexible multi-task Gaussian processes. We will show the impact of advanced kernel designs on Gaussian processes using several synthetic and two scientific data sets. The results of our research show that including domain knowledge, communicated through advanced kernel designs, has a significant impact on the accuracy and relevance of the function approximation.

97 MATHEMATICS AND COMPUTING↗