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DOE OSTI2018

Efficient Generalizable Deep Learning

Stochastic optimization is a fundamental field of research for machine learning. Stochastic gradient descent (SGD) and related methods provide a feasible means to train complicated prediction models over large datasets. SGD, however, does not explicitly address the problem of overfitting, which can lead to predictions that perform poorly on new data. This difference between loss performance on unseen testing data verses that of training data defines the generalization gap of a model. We introduce a new computational kernel called Stochastic Hessian Projection (SHP) that uses a maximum likelihood framework to simultaneously estimate gradient noise covariance and local curvature of the loss function. Our analysis illustrates that these quantities affect the evolution of parameter uncertainty and therefore generalizability. We show how these computations allow us to predict the generalization gap without requiring holdout data. Explicitly assessing this metric for generalizability during training may improve machine learning predictions when data is scarce and understanding prediction variability is critical.

42 ENGINEERING↗

NASA NTRS2005

Development of Ionic Liquid Monopropellants for In-Space Propulsion

A family of new, low toxicity, high energy monopropellants is currently being evaluated at NASA Marshall Space Flight Center for in-space rocket engine applications such as reaction control engines. These ionic liquid monopropellants, developed in recent years by the Air Force Research Laboratory, could offer system simplification, less in-flight thermal management, and reduced handling precautions, while increasing propellant energy density as compared to traditional storable in-space propellants such as hydrazine and nitrogen tetroxide. However, challenges exist in identifying ignition schemes for these ionic liquid monopropellants, which are known to burn at much hotter combustion temperatures compared to traditional monopropellants such as hydrazine. The high temperature combustion of these new monopropellants make the use of typical ignition catalyst beds prohibitive since the catalyst cannot withstand the elevated temperatures. Current research efforts are focused on monopropellant ignition and burn rate characterization, parameters that are important in the fundamental understanding of the monopropellant behavior and the eventual design of a thruster. Laboratory studies will be conducted using alternative ignition techniques such as laser-induced spark ignition and hot wire ignition. Ignition delay, defined as the time between the introduction of the ignition source and the first sign of light emission from a developing flame kernel, will be measured using Schlieren visualization. An optically-accessible liquid monopropellant burner will be used to determine propellant burn rate as a function of pressure and initial propellant temperature. The burn rate will be measured via high speed imaging through the chamber s windows.

Blevins, John A.↗

DOE OSTI2024

Galaxy bispectrum in the spherical Fourier-Bessel basis

The bispectrum, the three-point correlation in Fourier space, is a crucial statistic for studying many effects targeted by the next-generation galaxy surveys, such as primordial non-Gaussianity (PNG) and general relativistic (GR) effects on large scales. In this work we develop a formalism for the bispectrum in the spherical Fourier-Bessel (SFB) basis—a natural basis for computing correlation functions on the curved sky, as it diagonalizes the Laplacian operator in spherical coordinates. Working in the SFB basis allows for line-of-sight effects such as redshift space distortions and GR to be accounted for exactly, i.e., without having to resort to perturbative expansions to go beyond the plane-parallel approximation. Only analytic results for the SFB bispectrum exist in the literature given the intensive computations needed. We numerically calculate the SFB bispectrum for the first time, enabled by a few techniques: We implement a template decomposition of the redshift-space kernel Z 2 into Legendre polynomials, and separately treat the PNG and velocity-divergence terms. We derive an identity to integrate a product of three spherical harmonics connected by a Dirac delta function as a simple sum and use it to investigate the limit of a homogeneous and isotropic Universe. Furthermore, we present a formalism for convolving the signal with separable window functions and use a toy spherically symmetric window to demonstrate the computation and give insights into the properties of the observed bispectrum signal. While our implementation remains computationally challenging, it is a step toward a feasible full extraction of information on large scales via a SFB bispectrum analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Black hole one-loop determinants in the large dimension limit

We calculate the contributions to the one-loop determinant for transverse traceless gravitons in an n + 3-dimensional Schwarzschild black hole background in the large dimension limit, due to the SO(n + 2)-type tensor and vector fluctuations, using the quasinormal mode method. Accordingly we find the quasinormal modes for these fluctuations as a function of a fiducial mass parameter Δ. We show that the behavior of the one-loop determinant at large Δ accords with a heat kernel curvature expansion in one lower dimension, lending further evidence towards a membrane picture for black holes in the large dimension limit.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Non-perturbative quarkonium dissociation rates in strongly coupled quark-gluon plasma

Heavy quarks and quarkonia are versatile probes of the transport properties of the hot QCD medium produced in ultra-relativistic heavy-ion collisions (URHICs). A robust description of heavy-flavor transport coefficients requires a microscopic approach that treats the open and hidden heavy-flavor sectors on the same footing. Here, we employ the quantum many-body T -matrix formalism to evaluate the dissociation rates of heavy quarkonia in the quark-gluon plasma (QGP). The basic ingredient is the heavy-light T -matrix, which utilizes a nonperturbative driving kernel constrained by lattice-QCD data. Its resummation in a ladder series provides a much enhanced interaction strength compared to a previously used perturbative coupling to the quasiparticle partons in the QGP. The in-medium quarkonium properties, particularly their temperature-dependent binding energies, are obtained from selfconsistent calculations with the same interaction kernel, including interference effects (also referred to as the imaginary part of the heavy-quark potential) as well as off-shell parton spectral functions. We systematically investigate the interplay of these effects and elaborate on the connections to the dipole approximation used in effective field theory.

effective field theories of QCD↗

DOE OSTI2025

From chiral effective field theory to perturbative QCD: A Bayesian model mixing approach to symmetric nuclear matter

Constraining the equation of state (EOS) of strongly interacting, dense matter is the focus of intense experimental, observational, and theoretical effort. Chiral effective field theory (𝜒⁢EFT ) can describe the EOS between the typical densities of nuclei and those in the outer cores of neutron stars, while perturbative QCD (pQCD) can be applied to properties of deconfined quark matter, both with quantified theoretical uncertainties. However, describing the full range of densities in between with a single EOS that has well-quantified uncertainties is a challenging problem. Bayesian multimodel inference from 𝜒⁢EFT and pQCD can help bridge the gap between the two theories. In this work, we introduce a correlated Bayesian model mixing framework that uses a Gaussian process (GP) to assimilate different information into a single QCD EOS for symmetric nuclear matter. The present implementation uses a stationary GP to infer this mixed EOS solely from the EOSs of 𝜒⁢EFT and pQCD while accounting for the truncation errors of each theory. The GP is trained on the pressure as a function of number density in the low- and high-density regions where 𝜒⁢EFT and pQCD are, respectively, valid. We impose priors on the GP kernel hyperparameters to suppress unphysical correlations between these regimes. This, together with the assumption of stationarity, results in smooth 𝜒⁢EFT-to-pQCD curves for both the pressure and the speed of sound. We show that using uncorrelated mixing requires uncontrolled extrapolation of at least one of 𝜒⁢EFT or pQCD into regions where the perturbative series breaks down and leads to an acausal EOS. Here, we also discuss extensions of this framework to nonstationary and less differentiable GP kernels, its future application to neutron-star matter, and the incorporation of additional constraints from nuclear theory, experiment, and multimessenger astronomy.

Bayesian methods↗

DOE OSTI2021

A duality-based coupling of Cosserat crystal plasticity and phase field theories for modeling grain refinement

High-rate deformation processes of metals entail intense grain refinement and special attention needs to be paid to capture the evolution of microstructure. In this article, a new formulation for coupling Cosserat crystal plasticity and phase field is developed. A common approach is to penalize kinematic incompatibility between lattice orientation and displacement-based elastic rotation. However, this can lead to significant solution sensitivity to the penalty parameter, resulting in low accuracy and convergence rates. To address these issues, a duality-based formulation is developed which directly imposes the rotational kinematic compatibility. A weak inf-sup-based skew-symmetric stress projection is introduced to suppress instabilities present in the dual formulation. An additional least squares stabilization is introduced to suppress the spurious lattice rotation with a suitable parameter range derived analytically and validated numerically. The required high-order continuity is attained by the reproducing kernel approximation. It is observed that equal order displacement-rotation-phase field approximations are stable, which allows efficient employment of the same set of shape functions for all independent variables. The proposed formulation is shown to yield superior accuracy and convergence with marginal parameter sensitivity compared to the penalty-based approach and successfully captures the dominant rotational recrystallization mechanism including block dislocation structures and grain boundary migration.

42 ENGINEERING↗

NASA NTRS1989

Moment method with isoparametric elements for three-dimensional anisotropic scatterers

A novel method for computing the frequency-domain electromagnetic fields scattered from, and penetrating into, arbitrarily shaped, three-dimensional, lossy, inhomogeneous anisotropic scatters is presented. The method is based on a general volume integrodifferential formulation of the scattering problem and consists of the numerical solution of the coupled integral equations by the moment method and point matching. The numerical model of the scatterer is obtained by parametric volume elements, and the basis functions used to represent the field within each element are the same used in the finite-element method. Element integration problems due to the singular kernel of the integral equations are treated in some detail. Numerical results for both the isotropic and the anisotropic spherical scatterer are presented, including comparisons with results obtained by different numerical methods for the isotropic cases considered. The capability of the numerical code presented to deal with cases where the material parameters of the scatterer are given by singular matrices is discussed for two particular examples.

Graglia, Roberto D.↗

NASA NTRS2003

Presumed PDF Modeling of Early Flame Propagation in Moderate to Intense Turbulence Environments

The present paper describes the results obtained from a one-dimensional time dependent numerical technique that simulates early flame propagation in a moderate to intense turbulent environment. Attention is focused on the development of a spark-ignited, premixed, lean methane/air mixture with the unsteady spherical flame propagating in homogeneous and isotropic turbulence. A Monte-Carlo particle tracking method, based upon the method of fractional steps, is utilized to simulate the phenomena represented by a probability density function (PDF) transport equation. Gaussian distributions of fluctuating velocity and fuel concentration are prescribed. Attention is focused on three primary parameters that influence the initial flame kernel growth: the detailed ignition system characteristics, the mixture composition, and the nature of the flow field. The computational results of moderate and intense isotropic turbulence suggests that flames within the distributed reaction zone are not as vulnerable, as traditionally believed, to the adverse effects of increased turbulence intensity. It is also shown that the magnitude of the flame front thickness significantly impacts the turbulent consumption flame speed. Flame conditions studied have fuel equivalence ratio s in the range phi = 0.6 to 0.9 at standard temperature and pressure.

Carmen, Christina↗

DOE OSTI2023

Conditional Karhunen–Loève regression model with Basis Adaptation for high-dimensional problems: Uncertainty quantification and inverse modeling

Here, we propose a methodology for improving the accuracy of surrogate models of the observable response of physical systems as a function of the systems’ spatially heterogeneous parameter fields, with applications to uncertainty quantification and parameter estimation in high-dimensional problems. Practitioners often formulate finite-dimensional representations of spatially heterogeneous parameter fields using truncated unconditional Karhunen–Loève expansions (KLEs) for a certain choice of unconditional covariance kernel and construct surrogate models of the observable response with respect to the KLE coefficients. When direct measurements of the parameter fields are available, we propose improving the accuracy of these surrogate models by representing the parameter fields via conditional Karhunen-Loève expansions (CKLEs). CKLEs are constructed by conditioning the covariance kernel of the unconditional expansion on the direct measurements of the parameter field via Gaussian process regression, and then truncating the corresponding KLE. We apply the proposed methodology to constructing surrogate models via the Basis Adaptation (BA) method of the stationary hydraulic head response, measured at spatially discrete observation locations, of a groundwater flow model of the Hanford Site, as a function of the 1000-dimensional representation of the model’s log-transmissivity field. We find that BA surrogate models of the hydraulic head based on CKLEs are more accurate than BA surrogate models based on unconditional expansions for forward uncertainty quantification tasks. Furthermore, we find that inverse estimates of the hydraulic transmissivity field computed using CKLE-based BA surrogate models are more accurate than those computed using unconditional BA surrogate models.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Exploring Causal Physical Mechanisms via Non-Gaussian Linear Models and Deep Kernel Learning: Applications for Ferroelectric Domain Structures

Rapid emergence of multimodal imaging in scanning probe, electron, and optical microscopies has brought forth the challenge of understanding the information contained in these complex data sets, targeting the intrinsic correlations between different channels, and further exploring the underpinning causal physical mechanisms. Here, we develop such an analysis framework for Piezoresponse Force Microscopy. We argue that under certain conditions, we can bootstrap experimental observations with the prior knowledge of materials structure to get information on certain nonobserved properties, and demonstrate linear causal analysis for PFM observables. We further demonstrate that the strength of individual causal links between complex descriptors can be ascertained using the deep kernel learning (DKL) model. In this DKL analysis, we use the prior information on domain structure within the image to predict the physical properties. This analysis demonstrates the correlative relationships between morphology, piezoresponse, elastic property, etc., at nanoscale. The prediction of morphology and other physical parameters illustrates a mutual interaction between surface condition and physical properties in ferroelectric materials. Overall, this analysis is universal and can be extended to explore the correlative relationships of other multichannel data sets, and allow for high-fidelity reconstruction of underpinning functionalities and physical mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Model selection and signal extraction using Gaussian Process regression

We present a novel computational approach for extracting localized signals from smooth background distributions. We focus on datasets that can be naturally presented as binned integer counts, demonstrating our procedure on the CERN open dataset with the Higgs boson signature, from the ATLAS collaboration at the Large Hadron Collider. Our approach is based on Gaussian Process (GP) regression — a powerful and flexible machine learning technique which has allowed us to model the background without specifying its functional form explicitly and separately measure the background and signal contributions in a robust and reproducible manner. Unlike functional fits, our GP-regression-based approach does not need to be constantly updated as more data becomes available. We discuss how to select the GP kernel type, considering trade-offs between kernel complexity and its ability to capture the features of the background distribution. We show that our GP framework can be used to detect the Higgs boson resonance in the data with more statistical significance than a polynomial fit specifically tailored to the dataset. Finally, we use Markov Chain Monte Carlo (MCMC) sampling to confirm the statistical significance of the extracted Higgs signature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Online MCMC Thinning with Kernelized Stein Discrepancy

A fundamental challenge in Bayesian inference is efficient representation of a target distribution. Many nonparametric approaches do so by sampling a large number of points using variants of Markov chain Monte Carlo (MCMC). Here, we propose an MCMC variant that retains only those posterior samples which exceed a kernelized Stein discrepancy (KSD) threshold, which we call KSD thinning. We establish the convergence and complexity trade-offs for several settings of KSD thinning as a function of the KSD threshold parameter, sample size, and other problem parameters. We provide experimental comparisons against other online nonparametric Bayesian methods that generate low-complexity posterior representations. We observe superior consistency/complexity trade-offs across a range of settings including MCMC sampling on two Bayesian inference problems from the biological sciences, and 10 × inference speedup and storage reduction for Bayesian neural networks with no loss of accuracy and no increase in training time. Our code is available at https://github.com/colehawkins/KSD-Thinning.

Bayesian inference↗

DOE OSTI2023

Solving 3d gravity with Virasoro TQFT

We propose a precise reformulation of 3d quantum gravity with negative cosmological constant in terms of a topological quantum field theory based on the quantization of the Teichmüller space of Riemann surfaces that we refer to as “Virasoro TQFT”. This TQFT is similar, but importantly not equivalent, to SL(2, \mathbb{R} ℝ ) Chern-Simons theory. This sharpens the folklore that 3d gravity is related to SL(2, \mathbb{R} ℝ ) Chern-Simons theory into a precise correspondence, and resolves some well-known issues with this lore at the quantum level. Our proposal is computationally very useful and provides a powerful tool for the further study of 3d gravity. In particular, we explain how together with standard TQFT surgery techniques this leads to a fully algorithmic procedure for the computation of the gravity partition function on a fixed topology exactly in the central charge. Mathematically, the relation leads to many nontrivial conjectures for hyperbolic 3-manifolds, Virasoro conformal blocks and crossing kernels.

Collier, Scott↗

DOE OSTI2022

Automated Experiment in 4D-STEM: Exploring Emergent Physics and Structural Behaviors

Automated experiments in 4D scanning transmission electron microscopy (STEM) are implemented for rapid discovery of local structures, symmetry-breaking distortions, and internal electric and magnetic fields in complex materials. Deep kernel learning enables active learning of the relationship between local structure and 4D-STEM-based descriptors. With this, efficient and “intelligent” probing of dissimilar structural elements to discover desired physical functionality is made possible. This approach allows effective navigation of the sample in an automated fashion guided by either a predetermined physical phenomenon, such as strongest electric field magnitude, or in an exploratory fashion. Therefore, we verify the approach first on preacquired 4D-STEM data and further implement it experimentally on an operational STEM. The experimental discovery workflow is demonstrated using graphene and subsequently extended toward a lesser-known layered 2D van der Waals material, MnPS 3 . This approach establishes a pathway for physics-driven automated 4D-STEM experiments that enable probing the physics of strongly correlated systems and quantum materials and devices, as well as exploration of beam-sensitive materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Cross Inference of Throughput Profiles Using Micro Kernel Network Method

Dedicated network connections are being increasingly deployed in cloud, centralized and edge computing and data infrastructures, whose throughput profiles are critical indicators of the underlying data transfer performance. Due to the cost and disruptions to physical infrastructures, network emulators, such as Mininet, are often used to generate measurements needed to estimate throughput profiles, typically expressed as a function of the connection round trip time. The profiles estimated using measurements from such emulated networks are usually inaccurate for high bandwidth and high latency connections, since they do not accurately reflect the critical network transport dynamics mainly due to computing and memory constraints of the host. We present a machine learning (ML) method to estimate the throughput profiles using emulation measurements to closely match the testbed and production network profiles. In particular, we propose a micro Kernel Network (mKN) that provides baseline throughput measurements on the host running Mininet emulations, which are used to learn a regression map that converts them to the corresponding testbed measurement estimates. Once initially learned, this map is applied to measurements from subsequent network emulations on the same host. We present experimental measurements to illustrate this approach, and derive generalization equations for the proposed mKN-ML method. Using a four-site scenario emulation, we show the effectiveness of this method in providing accurate concave throughput profiles from inaccurate convex or non-smooth ones indicated by Mininet emulation.

Rao, Nageswara↗

DOE OSTI2021

Next-Cycle Optimal Fuel Control for Cycle-to-Cycle Variability Reduction in EGR-Diluted Combustion

In this simulation study, cycle-to-cycle fuel control was used to reduce CCV by injecting additional fuel in operating conditions with sporadic misfires and partial burns. An optimal control policy was proposed that utilizes 1) a physics-based model that tracks in-cylinder gas composition and 2) a one-step-ahead prediction of the combustion efficiency based on a kernel density estimator. The optimal solution, however, presents a tradeoff between the reduction in combustion CCV and the increase in fuel injection quantity required to stabilize the charge. Such a tradeoff can be ad- just by a single parameter embedded in the cost function.

Maldonado, BryanP. [Oak Ridge National Lab. (ORNL)↗