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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

MOOSE ProbML: Parallelizable Probabilistic Machine Learning and Uncertainty Quantification Capabilities

The Multiphysics Object Oriented Simulation Environment (MOOSE) is a widely used open- source finite element software for performing multiphysics multiscale simulations in a massively parallel fashion. Recently, the computational team at Idaho National Laboratory (INL) has implemented Probabilistic Machine Learning (ProbML) capabilities in MOOSE—in a parallelized fashion—and enable active learning with large-scale computational models for tasks such as surrogate model development, scale bridging, forward/inverse uncertainty quantification (UQ), Bayesian optimization, etc. This presentation summarizes these developments in MOOSE along with demonstrations on several real applications relevant to nuclear energy. At the fundamental level, samplers like Monte Carlo/Latin Hypercube, variance reduction, parallelized Markov Chain Monte Carlo (MCMC) support uncertainty propagation in both forward and inverse settings. These samplers can be integrated with the Gaussian processes (GP) suite in MOOSE, which offer several variants like scalar GPs, multi-output GPs, and deep GPs, to enable active learning. These GPs can be tuned using gradient-based optimization methods like Adam and its variants or gradient-free methods like the elliptical slice sampler (a variant of MCMC adept under Gaussian settings) for more complex covariance kernels or likelihoods whose gradient computations can be cumbersome. A variety of batch acquisition functions permit parallelized evaluation of the computational model and support different learning objectives with high efficiency like Bayesian inference, global surrogate development, optimization, etc. Furthermore, libtorch integration supports training, evaluation, and re-training of neural networks and other complex machine learning models in active learning settings. The impacts of these developments are shown on several real applications: (1) nuclear fuel inverse UQ and model inadequacy assessment using the Kennedy O’Hagan framework; (2) uncertainty aware surrogate modeling for additive manufacturing to predict field quantities; (3) nuclear reactor rare events analysis; and (4) complex fluid flow prediction using a global surrogate with quantified prediction uncertainty. Finally, the outlook of MOOSE ProbML is discussed for both outer-loop and inner-loop computations in the broad view to accelerate fuels and materials qualification, address gaps in knowledge and data, and assess new reactor/fuel systems.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Toward exascale whole-device modeling of fusion devices: Porting the GENE gyrokinetic microturbulence code to GPU

GENE solves the five-dimensional gyrokinetic equations to simulate the development and evolution of plasma microturbulence in magnetic fusion devices. The plasma model used is close to first principles and computationally very expensive to solve in the relevant physical regimes. In order to use the emerging computational capabilities to gain new physics insights, several new numerical and computational developments are required. Here, we focus on the fact that it is crucial to efficiently utilize GPUs (graphics processing units) that provide the vast majority of the computational power on such systems. In this paper, we describe the various porting approaches considered and given the constraints of the GENE code and its development model, justify the decisions made, and describe the path taken in porting GENE to GPUs. We introduce a novel library called gtensor that was developed along the way to support the process. Performance results are presented for the ported code, which in a single node of the Summit supercomputer achieves a speed-up of almost 15× compared to running on central processing unit (CPU) only. Typical GPU kernels are memory-bound, achieving about 90% of peak. Our analysis shows that there is still room for improvement if we can refactor/fuse kernels to achieve higher arithmetic intensity. We also performed a weak parallel scalability study, which shows that the code runs well on a massively parallel system, but communication costs start becoming a significant bottleneck.

Germaschewski, K. (ORCID:0000000284956354)↗
DOE OSTI2014

Demonstration of Full Core Reactor Depletion with MPACT

MPACT is a three-dimensional (3-D) whole core transport code capable of generating sub-pin level power distributions. This feature is accomplished by obtaining the integral transport solutions to the heterogeneous reactor problem in which the actual detailed geometrical configuration of fuel components such as the pellet and cladding is modelled explicitly.. The cross section data needed for the neutron transport calculation are obtained directly from a multigroup microscopic cross section library similar to those used in lattice physics codes. Hence MPACT involves neither a priori homogenization nor group condensation for the core spatial solution. The integral transport solution is obtained by means of the method of characteristics (MOC) that employs discrete ray tracing. Since the direct application of the 3-D MOC capability in MPACT to 3-D core configuration requires considerable amounts of memory and computing time for practical reactor applications, an alternative approximate 3-D solution method was implemented in MPACT based on a 2D-1D approach which employs planar MOC solutions in the framework of the 3-D coarse mesh finite difference (CMFD) formulation. The axial coupling is resolved by one-dimensional (1-D) diffusion solutions and the planar and axial problems are coupled through the transverse leakage. The use of a lower order 1-D solution in the axial direction is justified by the fact that most heterogeneity in the core occurs in the radial direction rather than the axial. However, it is possible to use one of the higher order methods in MPACT such as the 1-D SN kernel if improved solution accuracy is desired. The CMFD formulation which originally served as an efficient nodal formulation is used in MPACT to accelerate the whole core transport calculation. The basic mesh in the CMFD formulation is a pin cell which is much coarser than the flat source regions defined for MOC calculations. The concept of dynamic homogenization of group constants for the pin cells provides the basis of the CMFD formulation in whole core transport calculation. The intra-cell flux distribution determined from the MOC calculation is used to generate the homogenized cell constants while the MOC cell surface averaged currents are used to determine the radial nodal coupling coefficients. This dynamic implementation of the equivalence theory formulation ensures the same transport solution is obtained with CMFD as the one obtained using unaccelerated MOC calculations alone. The ability of MPACT to predict the Hot, Zero Power (HZP) condition of a reactor was reported in CASL-U-2014-0045-000. The purpose of this report is to demonstrate the capability of MPACT to simulate the operation of a reactor at Hot, Full Power (HFP) conditions during normal operation throughout a full operating cycle. The time scale for a reactor burnup cycle is typically one to two years and therefore short time phenomena such as the effect of delayed neutrons can be neglected. Instead the time dependence can be treated quasi-statically using the depletion algorithm presented in CASL-U-2013-0276-001. The full power operation requires thermal hydraulic feedback to be present during the entire simulation which will utilize the work in CASL-U-2014-0051-000. However, due to the significant computational burden of the coupled physics simulation, a simplified thermal hydraulic model is used for the analysis reported here which is principally intended to demonstrate the full core neutronics depletion. In addition to the thermal hydraulic feedback, the effect of Boron 10 depletion should be modeled in cases where major boron additions are not performed for extended periods of time. Each of these capabilities will be described in the following sections.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Free Fermions and the Classical Compact Groups

There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Redshift space power spectrum beyond Einstein-de Sitter kernels

Abstract We develop a framework to compute the redshift space power spectrum (PS), with kernels beyond Einstein-de Sitter (EdS), that can be applied to a wide variety of generalized cosmologies. We build upon a formalism that was recently employed for standard cosmology in Chen, Vlah & White (2020), and utilize an expansion of the density-weighted velocity moment generating function that explicitly separates the magnitude of the k-modes and their angle to the line-of-sight direction dependencies. We compute the PS for matter and biased tracers to 1-loop Perturbation Theory (PT) and show that the expansion has a correct infrared and ultraviolet behavior, free of unwanted divergences. We also add Effective Field Theory (EFT) counterterms, necessary to account for small-scale contributions to PT, and employ an IR-resummation prescription to properly model the smearing of the BAO due to large scale bulk flows within Standard-PT. To demonstrate the applicability of our formalism, we apply it on the ΛCDM and the Hu-Sawicki f(R) models, and compare our numerical results against the elephant suite of N-body simulations, finding very good agreement up to k = 0.27 Mpc -1 h at z = 0.5 for the first three non-vanishing Legendre multipoles of the PS. To our knowledge, the model presented in this work is the most accurate theoretical EFT-PT for modified gravity to date, being the only one that accounts for beyond linear local biasing in redshift-space. Hence, we argue our RSD modeling is a promising tool to construct theoretical templates in order to test deviations from ΛCDM using real data obtained from the next stage of cosmological surveys such as DESI and LSST.

Astronomy & Astrophysics↗
DOE OSTI2016

Preliminary Compendium of the Initial Conditions and Evolution of the Fundamental Interactions of SiC with Ag and Pd

Tri-structural isotropic (TRISO) particles are the fuel of choice for very-high temperature reactors. At the core, these spherical particles consist of an inner fuel kernel of UO{sub 2}, UC{sub 2} or a combination of both, which is coated radially outward by successive layers of low density pyrolytic graphite, an inner high density pyrolytic graphite layer, silicon carbide (SiC) and an outer high density pyrolytic graphite layer. SiC is the main diffusion barrier against the release of fission products due to its hardness and high melting point. Irradiation testing of TRISO particles indicates that trace amounts of metallic fission products can damage or potentially escape through the barrier layer. Surrogate experimental studies have previously been performed by various methods seeking to shed light on and explain the diffusion behavior of Ag and Pd. Although some of these experiments have yielded realistic diffusion coefficients the discrepancy of results between different groups is such that the essential details of the diffusive behavior are still to be fully understood. This work aims to understand the fundamental physical and chemical interactions that take place at the interface of SiC and Ag/Pd, and which give rise to the observed diffusion behavior of these metallic species in TRISO particles. Theoretical simulations of the diffusion of Ag through SiC have been exhaustive but typically yield bulk diffusion coefficients that due to the nature of bulk diffusion phenomena (i.e. slow diffusion) the diffusion coefficients are calculated to be orders of magnitude lower than what experimental observations suggest. This in part is due to the difficulty in simulating realistic models that include various polymorphs of SiC, and the dynamical structural transformations that SiC undergoes in the TRISO environment (which are also to be explained). The result is a particularly challenging problem to solve given that the initial conditions of the interactions of Ag and Pd with SiC are difficult to address, both in theoretical models and surrogate experiments. In order to improve these models the approach taken here is to consider fundamental interactions between Ag and SiC that take place in short time scales by varying the initial environmental conditions, i.e. annealing temperature and time, initial amounts of the metallic species (M) Ag, Pd in SiC/M/SiC multilayers. This work aims to understand the fundamental physical and chemical interactions that take place at the interface of SiC and Ag/Pd, and which give rise to the observed diffusion behavior of these metallic species in TRISO particles. In order to do so we have synthesized SiC/Ag/SiC and SiC/Pd/SiC multilayers of various thicknesses by PLD and characterized them using SEM/EDS. Initial results show that upon annealing Ag agglomerates and ruptures the SiC layer to be released. In the case of Pd a strong chemical interaction is deduced from the slow interlayer diffusion and limited release. Further studies using photoelectron spectroscopy and RHEED will be carried out in order obtain detailed information on the chemical and physical transitions that undergo upon annealing of these systems. (authors)

36 MATERIALS SCIENCE↗
DOE OSTI2021

Fluctuation–dissipation relation for a quantum Brownian oscillator in a parametrically squeezed thermal field

In this paper we study the nonequilibrium evolution of a quantum Brownian oscillator, modeling the internal degree of freedom of a harmonic atom or an Unruh–DeWitt detector, coupled to a nonequilibrium and nonstationary quantum field bath and inquire whether a fluctuation–dissipation relation (FDR) can exist after/if it approaches equilibration. This is a nontrivial issue because a squeezed field bath cannot reach equilibration and yet, as this work shows, the system oscillator indeed can, which is a necessary condition for FDRs. We discuss three different settings: (A) The bath field essentially remains in a squeezed thermal state throughout, whose squeeze parameter is a mode- and time-independent constant. This situation is often encountered in quantum optics and quantum thermodynamics. (B) The bath field is initially in a thermal state, but is subjected to a parametric process leading to mode- and time-dependent squeezing. This scenario is encountered in cosmology and dynamical Casimir effects. The squeezing in the bath in both types of processes will affect the oscillator’s nonequilibrium evolution. We show that at late times it approaches equilibration and this stationarity condition warrants the existence of a FDR. The trait of squeezing is marked by the oscillator’s effective equilibrium temperature, and the proportionality factor in the FDR is only related to the stationary component of the noise kernel of the bath field. Setting (C) is more subtle: A finite system–bath coupling strength can set the oscillator in a squeezed state even though the bath field is stationary and does not engage in any parametric process. The squeezing of the system in this case is in general time-dependent but becomes constant when the internal dynamics is fully relaxed. We begin with comments on the broad range of physical processes involving squeezed thermal baths and end with some remarks on the significance of FDRs in capturing the essence of quantum backreaction in nonequilibrium and stochastic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties

Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Here, an approach to estimate them by using data from physical experiments and computer simulations. A theoretical framework is given which allows us to study the issues of parameter identifiability and estimation. We define the L 2 -consistency for calibration as a justification for calibration methods. It is shown that a simplified version of the original KO method leads to asymptotically L 2 -inconsistent calibration. This L 2 -inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the L 2 calibration, is proposed and proven to be L 2 -consistent and enjoys optimal convergence rate. Furthermore a numerical example and some mathematical analysis are used to illustrate the source of the L 2 -inconsistency problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Review of Enabling Technologies to Facilitate Secure Compute Customization

High performance computing environments are often used for a wide variety of workloads ranging from simulation, data transformation and analysis, and complex workflows to name just a few. These systems may process data for a variety of users, often requiring strong separation between job allocations. There are many challenges to establishing these secure enclaves within the shared infrastructure of high-performance computing (HPC) environments. The isolation mechanisms in the system software are the basic building blocks for enabling secure compute enclaves. There are a variety of approaches and the focus of this report is to review the different virtualization technologies that facilitate the creation of secure compute enclaves. The report reviews current operating system (OS) protection mechanisms and modern virtualization technologies to better understand the performance/isolation properties. We also examine the feasibility of running ``virtualized'' computing resources as non-privileged users, and providing controlled administrative permissions for standard users running within a virtualized context. Our examination includes technologies such as Linux containers (LXC [32], Docker [15]) and full virtualization (KVM [26], Xen [5]). We categorize these different approaches to virtualization into two broad groups: OS-level virtualization and system-level virtualization. The OS-level virtualization uses containers to allow a single OS kernel to be partitioned to create Virtual Environments (VE), e.g., LXC. The resources within the host's kernel are only virtualized in the sense of separate namespaces. In contrast, system-level virtualization uses hypervisors to manage multiple OS kernels and virtualize the physical resources (hardware) to create Virtual Machines (VM), e.g., Xen, KVM. This terminology of VE and VM, detailed in Section 2, is used throughout the report to distinguish between the two different approaches to providing virtualized execution environments. As part of our technology review we analyzed several current virtualization solutions to assess their vulnerabilities. This included a review of common vulnerabilities and exposures (CVEs) for Xen, KVM, LXC and Docker to gauge their susceptibility to different attacks. The complete details are provided in Section 5 on page 33. Based on this review we concluded that system-level virtualization solutions have many more vulnerabilities than OS level virtualization solutions. As such, security mechanisms like sVirt (Section 3.3) should be considered when using system-level virtualization solutions in order to protect the host against exploits. The majority of vulnerabilities related to KVM, LXC, and Docker are in specific regions of the system. Therefore, future "zero day attacks" are likely to be in the same regions, which suggests that protecting these areas can simplify the protection of the host and maintain the isolation between users. The evaluations of virtualization technologies done thus far are discussed in Section 4. This includes experiments with 'user' namespaces in VEs, which provides the ability to isolate user privileges and allow a user to run with different UIDs within the container while mapping them to non-privileged UIDs in the host. We have identified Linux namespaces as a promising mechanism to isolate shared resources, while maintaining good performance. In Section 4.1 we describe our tests with LXC as a non-root user and leveraging namespaces to control UID/GID mappings and support controlled sharing of parallel file-systems. We highlight several of these namespace capabilities in Section 6.2.3. The other evaluations that were performed during this initial phase of work provide baseline performance data for comparing VEs and VMs to purely native execution. In Section 4.2 we performed tests using the High-Performance Computing Conjugate Gradient (HPCCG) benchmark to establish baseline performance for a scientific application when run on the Native (host) machine in contrast with execution under Docker and KVM. Our tests verified prior studies showing roughly 2-4% overheads in application execution time & MFlops when running in hypervisor-base environments (VMs) as compared to near native performance with VEs. For more details, see Figures 4.5 (page 28), 4.6 (page 28), and 4.7 (page 29). Additionally, in Section 4.3 we include network measurements for TCP bandwidth performance over the 10GigE interface in our testbed. The Native and Docker based tests achieved >= ~9Gbits/sec, while the KVM configuration only achieved 2.5Gbits/sec (Table 4.6 on page 32). This may be a configuration issue with our KVM installation, and is a point for further testing as we refine the network settings in the testbed. The initial network tests were done using a bridged networking configuration. The report outline is as follows: - Section 1 introduces the report and clarifies the scope of the proj...

Aderholdt, Ferrol↗
DOE OSTI2016

Comparison of silver release predictions using PARFUME with results from the AGR-2 irradiation experiment - 18579

The PARFUME (Particle Fuel Model) code was used to predict silver release from tri-structural isotropic (TRISO) coated fuel particles and compacts during the second irradiation experiment (AGR-2) of the Advanced Gas Reactor Fuel Development and Qualification program. The PARFUME model for the AGR-2 experiment used the fuel compact volume average temperature for each of the 559 days of irradiation to calculate the release of fission product silver from a representative particle for a select number of AGR-2 compacts and individual fuel particles containing either mixed uranium carbide/oxide (UCO) or 100% uranium dioxide (UO{sub 2}) kernels. Post-irradiation examination (PIE) measurements were performed to provide data on release of silver from these compacts and individual fuel particles. The available experimental fractional releases of silver were compared to their corresponding PARFUME predictions. Preliminary comparisons show that PARFUME under-predicts the PIE results in UCO compacts and is in reasonable agreement with experimental data for UO{sub 2} compacts. The accuracy of PARFUME predictions is impacted by the code limitations in the modeling of the temporal and spatial distributions of the temperature across the compacts. Nevertheless, the comparisons on silver release lie within the same order of magnitude. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration

This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

determining the mass of kepler-78b with nonparametric Gaussian process estimation

Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hr. The mass of Kepler-78b has been independently reported by two teams based on radial velocity (RV) measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in RV data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the RV data sets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV data sets, giving a Doppler amplitude of 1.86 ± 0.25 m s{sup −1} and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87{sub −0.26}{sup +0.27} M{sub ⊕} is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0{sub −1.4}{sup +1.9} g cm{sup −3}. We estimate that Kepler-78b is 32% ± 26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Coarse-Grained Density Functional Theory Predictions via Deep Kernel Learning

Scalable electronic predictions are critical for soft materials design. Recently, the Electronic Coarse-Graining (ECG) method was introduced to renormalize all-atom quantum chemical (QC) predictions to coarse-grained (CG) resolutions using deep neural networks (DNNs). While DNNs can learn complex representations that prove challenging for kernel-based methods, they are susceptible to overfitting and the overconfidence of uncertainty estimations. Here, we develop ECG within a GPU-accelerated Deep Kernel Learning (DKL) framework to enable CG QC predictions using range-separated hybrid density functional theory (DFT), obtaining a 107 speedup relative to naive all-atom QC. By treating the predicted electronic properties as random Gaussian Processes, DKL incorporates CG mapping degeneracy by learning the distribution of electronic energies as a function of CG configuration. DKL-ECG accurately reproduces molecular orbital energies from range-separated DFT while facilitating efficient training via active learning using the uncertainties provided by DKL. Further, we show that while active learning algorithms enable efficient sampling of a more diverse configurational space relative to random sampling, all explored query methods exhibit comparable performance for the examined system. We attribute this result to the significant overlap of the feature space and output property distributions across multiple temperatures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗
DOE OSTI2014

Ultra-nonlocality in density functional theory for photo-emission spectroscopy

We derive an exact expression for the photocurrent of photo-emission spectroscopy using time-dependent current density functional theory (TDCDFT). This expression is given as an integral over the Kohn-Sham spectral function renormalized by effective potentials that depend on the exchange-correlation kernel of current density functional theory. We analyze in detail the physical content of this expression by making a connection between the density-functional expression and the diagrammatic expansion of the photocurrent within many-body perturbation theory. We further demonstrate that the density functional expression does not provide us with information on the kinetic energy distribution of the photo-electrons. Such information can, in principle, be obtained from TDCDFT by exactly modeling the experiment in which the photocurrent is split into energy contributions by means of an external electromagnetic field outside the sample, as is done in standard detectors. We find, however, that this procedure produces very nonlocal correlations between the exchange-correlation fields in the sample and the detector.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Learning the structure of wind: A data-driven nonlocal turbulence model for the atmospheric boundary layer

In this work, we develop a novel data-driven approach to modeling the atmospheric boundary layer. This approach leads to a nonlocal, anisotropic synthetic turbulence model which we refer to as the deep rapid distortion (DRD) model. Our approach relies on an operator regression problem that characterizes the best fitting candidate in a general family of nonlocal covariance kernels parameterized in part by a neural network. This family of covariance kernels is expressed in Fourier space and is obtained from approximate solutions to the Navier–Stokes equations at very high Reynolds numbers. Each member of the family incorporates important physical properties such as mass conservation and a realistic energy cascade. The DRD model can be calibrated with noisy data from field experiments. After calibration, the model can be used to generate synthetic turbulent velocity fields. To this end, we provide a new numerical method based on domain decomposition which delivers scalable, memory-efficient turbulence generation with the DRD model as well as others. We demonstrate the robustness of our approach with both filtered and noisy data coming from the 1968 Air Force Cambridge Research Laboratory Kansas experiments. Using these data, we witness exceptional accuracy with the DRD model, especially when compared to the International Electrotechnical Commission standard.

17 WIND ENERGY↗
DOE OSTI2016

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↗