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DOE OSTI2022

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↗

DOE OSTI2023

Real-space Green's function approach for intrinsic losses in x-ray spectra

Intrinsic inelastic losses in x-ray spectra originate from excitations in an interacting electron system due to a suddenly created core-hole. These losses characterize the features observed in x-ray photoemission spectra (XPS), as well as many-body effects such as satellites and edge-singularities in x-ray absorption spectra (XAS). However, they are usually neglected in practical calculations. As shown by Langreth these losses can be treated within linear response in terms of a cumulant Green's function in momentum space. Here we present a complementary ab initio real-space Green's function generalization of the Langreth cumulant in terms of the dynamically screened core-hole interaction W c (ω) and the independent particle response function. Here we find that the cumulant kernel β⁡(ω) is analogous to XAS, but with the transition operator replaced by the core-hole potential with monopole selection rules. The behavior reflects the analytic structure of the loss function, with peaks near the zeros of the dielectric function, consistent with delocalized quasiboson excitations. The approach simplifies when W c (ω) is localized and spherically symmetric. In conclusion, illustrative results and comparisons are presented for the electron gas, sodium, and some early transition metal compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1990

ART/Ada and CLIPS/Ada

Although they have reached a point of commercial viability, expert systems were originally developed in artificial intelligence (AI) research environments. Many of the available tools still work best in such environments. These environments typically utilize special hardware such as LISP machines and relatively unfamiliar languages such as LISP or Prolog. Space Station applications will require deep integration of expert system technology with applications developed in conventional languages, specifically Ada. The ability to apply automation to Space Station functions could be greatly enhanced by widespread availability of state-of-the-art expert system tools based on Ada. Although there have been some efforts to examine the use of Ada for AI applications, there are few, if any, existing products which provide state-of-the-art AI capabilities in an Ada tool. The goal of the ART/Ada Design Project is to conduct research into the implementation in Ada of state-of-the-art hybrid expert systems building tools (ESBT's). This project takes the following approach: using the existing design of the ART-IM ESBT as a starting point, analyze the impact of the Ada language and Ada development methodologies on that design; redesign the system in Ada; and analyze its performance. The research project will attempt to achieve a comprehensive understanding of the potential for embedding expert systems in Ada systems for eventual application in future Space Station Freedom projects. During Phase 1 of the project, initial requirements analysis, design, and implementation of the kernel subset of ART-IM functionality was completed. During Phase 2, the effort has been focused on the implementation and performance analysis of several versions with increasing functionality. Since production quality ART/Ada tools will not be available for a considerable time, and additional subtask of this project will be the completion of an Ada version of the CLIPS expert system shell developed by NASA. This tool will provide full syntactic compatibility with any eventual products of the ART/Ada design while allowing SSFP developers early access to this technology.

Culbert, Chris↗

DOE OSTI2019

An adaptive fast multipole method in Cartesian basis, enabled by algorithmic differentiation

A novel form of the fast multipole method is realized by the combination of adaptive data structures with implementation of the multipole expansions and their translations in Cartesian basis, and enabled by algorithmic differentiation. It may be possible to generalize it to any kernel that allows its formulation as a function of small quantities with respect to which they can be expanded. There is no hard and fast rule recipe that works for all cases. However, it is shown how to do it for the softened Coulomb kernel, which is different from the Coulomb kernel. The characteristics and performance of the method are mapped and shown to provide an attractive option for a generic fast multipole algorithm in a wide region of the parameter space. The algorithm is illustrated with a beam dynamics application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Post-irradiation Heating Tests of As-Irradiated AGR-3/4 TRISO Fuel Compacts

Four post-irradiation heating tests of fuel compacts from the U.S. Advanced Gas Reactor (AGR)-3/4 irradiation experiment were completed. In addition to tristructural isotropic (TRISO)-coated driver fuel, each compact contained designed-to-fail (DTF) particles with fuel kernels coated only in pyrocarbon so as to simulate exposed kernels. Tests at 1600/1700°C, 1400°C, and 1200°C were performed to measure fission product release as a function of time and temperature. Silver release was highest in the 1200°C test, supporting the observation that silver release rates are highest in the 1100–1300°C range. Compared to tests of AGR-1 compacts with no exposed kernels, the Cs-134 and Kr-85 releases were noticeably higher in AGR-3/4. The exposed kernels’ contributions to Eu and Sr release are inconclusive, due to the difficulty in distinguishing among the combined effects of higher irradiation temperatures in these particular AGR-3/4 compacts, the presence of the DTF particles, and the Fuel Accident Condition Simulator (FACS) test temperatures. These data can be used to make inferences about fission product retention in exposed kernels as a function of time and temperature.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2016

SU-F-T-548: An Extraction Method for Correction of Detector Volume Effect in Small Field Profile Measurement

Purpose: To investigate the appropriateness of Gaussian detector response function in SRS profile measurement. Methods: In-air profile data for a 6MV beam were collected by using ionization chambers and radiochromic film. Two ionization chambers (FC65-G(IBA) and PinPoint(PTWTW31009)) were used to scan the beam profile. Film was used to measure the beam penumbra. A half-blocked beam was acquired with stepping size of 0.2mm and gradient of the measured profile represents the detector response function. The field widths of 2cm and 3cm were measured at SAD. Two detector response functions were evaluated, i.e. a traditional single Gaussian and a three-Gaussian symmetric function. Two corresponding models were used to fit measured data. One was error functions with one shaping parameter. The other model was a symmetrical superposition of three sets of error functions with fixed separation and two different shaping parameters. In both fitting, resultant Gaussian kernels and corresponding σs could be calculated analytically. SNR of the fitted curves were obtained and compared. Results: Our measured data indicated that the ionization chambers had a three-peak response function. From the first modeling, SNR for FC65-G were 36.0dB and 38.3dB for 2cm and 3cm field respectively. The corresponding SNR for the PinPoint were 43.6dB and 42.5dB. From the second modeling, SNR for FC65-G were 42.5dB and 47.4dB for 2cm and 3cm field respectively. The corresponding SNR for the PinPoint were 44.0dB and 44.5 dB. Three-gaussian model had an observable improvement for FC65-G chamber. Film measured penumbra was 3–5 times smaller than that of ionization-chambers. Conclusion: Superposition of three Gaussian kernels resembles the detector response due to central electrode and chamber wall and results in a better fitting to the measurement data than a single Gaussian kernel. Our study indicated that the Three-Gaussian model was more suitable for the detector with sigma comparable to penumbra width.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Non-uniform active learning for Gaussian process models with applications to trajectory informed aerodynamic databases

The ability to non-uniformly weight the input space is desirable for many applications, and has been explored for space-filling approaches. Increased interests in linking models, such as in a digital twinning framework, increases the need for sampling emulators where they are most likely to be evaluated. In particular, here we apply non-uniform sampling methods for the construction of aerodynamic databases. This paper combines non-uniform weighting with active learning for Gaussian Processes (GPs) to develop a closed-form solution to a non-uniform active learning criterion. We accomplish this by utilizing a kernel density estimator as the weight function. We demonstrate the need and efficacy of this approach with an atmospheric entry example that accounts for both model uncertainty as well as the practical state space of the vehicle, as determined by forward modeling within the active learning loop.

42 ENGINEERING↗

DOE OSTI2018

Neutronics Calculation of Fast Reactor Using Modern Computing Systems

The possibility of using the LUCKY-A three-dimensional multiprocessor transport code as a neutronics module for the COREMELT integrated non-stationary code for performing safety analysis, which is used for fast sodium reactor safety validation, is discussed. In this application, more stringent requirements are imposed on the computing speed of the LUCKY-A code. To test LUCKY-A possibilities, a typical computational problem is examined in a formulation characteristic for the proposed use of the code. The possibilities of the code for parallelized calculations are shown, and a comparison is made with calculations performed with the MMKKENO and TRIGEX codes. The efficacy of a parallel computational process is investigated as a function of the number of computing kernels used.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

A comprehensive techno-eco-assessment of CO 2 enhanced oil recovery projects using a machine-learning assisted workflow

Carbon dioxide enhanced oil recovery (CO 2 -EOR) projects not only extract residual oil but also sequestrate CO 2 in the depleted reservoirs. Here, this study develops a machine-learning-based workflow to co-optimize the hydrocarbon recovery, CO 2 sequestration volume and project net present value (NPV) simultaneously. Considering the trade-off relationships among the objective functions, support vector regression with Gaussian kernel (Gaussian- SVR) proxies are coupled with multi-objective particle swarm optimization (PSO) protocol and generate Pareto optimal solutions. Taking advantage of the high computational efficacy of the proxy model, economic uncertainties introduced by tax credits, capital costs and oil price are investigated by this study. The results indicate that the tax incentive policy (Section 45Q) plays a vital role in enhancing the economic returns of CO 2 -EOR projects, especially under the depression of crude oil market. The proposed workflow has been successfully implemented to optimize a water alternative CO 2 (CO 2 -WAG) injection project in a depleted oil sand in the US. The optimization results yield an incremental oil production of 15.8 MM STB and 1.37 MM metric tons of CO 2 storage in a 20-year development strategy, with the highest project NPV to be 205.6 MM US dollars.

03 NATURAL GAS↗

DOE OSTI2015

Machine Learning for Quantum Mechanical Properties of Atoms in Molecules

Here we introduce machine learning models of quantum mechanical observables of atoms in molecules. Instant out-of-sample predictions for proton and carbon nuclear chemical shifts, atomic core level excitations, and forces on atoms reach accuracies on par with density functional theory reference. Locality is exploited within nonlinear regression via local atom-centered coordinate systems. The approach is validated on a diverse set of 9 k small organic molecules. Linear scaling of computational cost in system size is demonstrated for saturated polymers with up to submesoscale lengths.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Interparameter tradeoff quantification for isotropic-elastic full-waveform inversion with various model parameterizations

Simultaneous determination of multiple physical parameters using full-waveform inversion (FWI) suffers from interparameter tradeoff diffculty. Analyzing the interparameter tradeoffs in different model parameterizations of isotropic-elastic FWI, and thus determining the appropriate model parameterization, are critical for efficient inversion and obtaining reliable inverted models. Five different model parameterizations are considered and compared including velocity-density, modulus-density, impedance-density and two velocity-impedance parameterizations. The scattering radiation patterns are first used for interparameter tradeoff analysis. Furthermore, a new framework is developed to evaluate the interparameter tradeoff based upon multiparameter Hessian-vector products: multiparameter point spread functions (MPSFs) and interparameter contamination sensitivity kernels (ICSKs), which provide quantitative, second-order measurements of the interparameter contaminations. In the numerical experiments, the interparameter tradeoffs in various model parameterizations are evaluated using the MPSFs and ICSKs. Inversion experiments are then carried out with simple Gaussian-anomaly models and complex Marmousi model. Overall, the parameterization of P-wave velocity, S-wave velocity and density and the parameterization of P-wave velocity, S-wave velocity and S-wave impedance perform best for reconstructing all of the physical parameters. Isotropic-elastic FWI of the Hussar low frequency dataset with various model parameterizations verifies the conclusions.

58 GEOSCIENCES↗

DOE OSTI2023

Simulating Hydrodynamics in Cosmology with CRK-HACC

Abstract We introduce CRK-HACC, an extension of the Hardware/Hybrid Accelerated Cosmology Code (HACC), to resolve gas hydrodynamics in large-scale structure formation simulations of the universe. The new framework couples the HACC gravitational N -body solver with a modern smoothed-particle hydrodynamics (SPH) approach called conservative reproducing kernel SPH (CRKSPH). CRKSPH utilizes smoothing functions that exactly interpolate linear fields while manifestly preserving conservation laws (momentum, mass, and energy). The CRKSPH method has been incorporated to accurately model baryonic effects in cosmology simulations—an important addition targeting the generation of precise synthetic sky predictions for upcoming observational surveys. CRK-HACC inherits the codesign strategies of the HACC solver and is built to run on modern GPU-accelerated supercomputers. In this work, we summarize the primary solver components and present a number of standard validation tests to demonstrate code accuracy, including idealized hydrodynamic and cosmological setups, as well as self-similarity measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1982

The crack problem for a nonhomogeneous plane

The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

Delale, F.↗

NASA NTRS1983

The crack problem for a nonhomogeneous plane

Delale, F.↗

NASA NTRS1988

Magnetic reversal spurts: Rain gauges for comet showers

Abrupt increases in the rate of magnetic reversals (magnetic reversal spurts) were first studied by many others. They hypothesized that spurts result from increased turbulence in the earth's core dynamo during episodes of intense bolide bombardment of the earth. Mechanisms for creating episodes of intense bombardment of the earth involve gravitational perturbation of the Oort cloud of comets, either by a hidden planet, a solar companion, or massive matter in the galactic plane. Herein, the time variation in reversal rate is analyzed using methods of statistical density estimation. A smooth, continuous estimate of reversal rate is obtained using an adaptive kernel method, in which the kernel width is adjusted as a function of reversal rate. The estimates near the ends of the data series (at 165 my ago and the present) are obtained by extending the data by reflection. The results show that the reversal spurts are not associated demonstrably with extinctions or well-dated impacts. If the spurts do record episodes of intense bombardment of the earth, then the mass extinctions do not, in general, occur at times of impacts. Furthermore, the large impact craters seen are not obviously related to the spurts, suggesting that the craters may have been caused by bolides of a different nature and with a different temporal pattern. However, the most simple explanation seems to be that the spurts do not record comet showers, either because the recording mechanism suggested by Muller and Morris is not effective or because comet showers are not triggered in the ways considered by Hut et al.

Lutz, T. M.↗

DOE OSTI2019

Extensions of BLUP Models for Genomic Prediction in Heterogeneous Populations: Application in a Diverse Switchgrass Sample

Genomic prediction is a useful tool to accelerate genetic gain in selection using DNA marker information. However, this technology typically relies on standard prediction procedures, such as genomic BLUP, that are not designed to accommodate population heterogeneity resulting from differences in marker effects across populations. In this study, we assayed different prediction procedures to capture marker-by-population interactions in genomic prediction models. Prediction procedures included genomic BLUP and two kernel-based extensions of genomic BLUP which explicitly accounted for population heterogeneity. To model population heterogeneity, dissemblance between populations was either depicted by a unique coefficient (as previously reported), or a more flexible function of genetic distance between populations (proposed herein). Models under investigation were applied in a diverse switchgrass sample under two validation schemes: whole-sample calibration, where all individuals except selection candidates are included in the calibration set, and cross-population calibration, where the target population is entirely excluded from the calibration set. First, we showed that using fixed effects, from principal components or putative population groups, appeared detrimental to prediction accuracy, especially in cross-population calibration. Then we showed that modelling population heterogeneity by our proposed procedure resulted in highly significant improvements in model fit. In such cases, gains in accuracy were often positive. These results suggest that population heterogeneity may be parsimoniously captured by kernel methods. However, in cases where improvement in model fit by our proposed procedure is null-to-moderate, ignoring heterogeneity should probably be preferred due to the robustness and simplicity of the standard genomic BLUP model.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Bayesian force fields from active learning for simulation of inter-dimensional transformation of stanene

Abstract We present a way to dramatically accelerate Gaussian process models for interatomic force fields based on many-body kernels by mapping both forces and uncertainties onto functions of low-dimensional features. This allows for automated active learning of models combining near-quantum accuracy, built-in uncertainty, and constant cost of evaluation that is comparable to classical analytical models, capable of simulating millions of atoms. Using this approach, we perform large-scale molecular dynamics simulations of the stability of the stanene monolayer. We discover an unusual phase transformation mechanism of 2D stanene, where ripples lead to nucleation of bilayer defects, densification into a disordered multilayer structure, followed by formation of bulk liquid at high temperature or nucleation and growth of the 3D bcc crystal at low temperature. The presented method opens possibilities for rapid development of fast accurate uncertainty-aware models for simulating long-time large-scale dynamics of complex materials.

Chemistry↗

DOE OSTI2015

Three-dimensional Fréchet sensitivity kernels for electromagnetic wave propagation

Electromagnetic imaging methods are useful tools for monitoring subsurface changes in pore-fluid content and the associated changes in electrical permittivity and conductivity. The most common method for georadar tomography uses a high frequency ray-theoretic approximation that is valid when material variations are sufficiently small relative to the wavelength of the propagating wave. Georadar methods, however, often utilize electromagnetic waves that propagate within heterogeneous media at frequencies where ray theory may not be applicable. In this paper we describe the 3-D Fréchet sensitivity kernels for EM wave propagation. Various data functional types are formulated that consider all three components of the electric wavefield and incorporate near-, intermediate-, and far-field contributions. We show that EM waves exhibit substantial variations for different relative source-receiver component orientations. The 3-D sensitivities also illustrate out-of-plane effects that are not captured in 2-D sensitivity kernels and can influence results obtained using 2-D inversion methods to image structures that are in reality 3-D.

58 GEOSCIENCES↗