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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Random field optimization

Herein we present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces (e.g., space and time) such as stochastic processes (e.g., time series, Gaussian processes, and Markov processes), random matrices, and random spatial fields. This paradigm involves sophisticated mathematical objects (e.g., stochastic differential equations and space-time kernel functions) and has been widely used in neuroscience, geoscience, physics, civil engineering, and computer graphics. Despite of this, however, random fields have seen limited use in optimization; specifically, existing optimization paradigms that involve uncertainty (e.g., stochastic programming and robust optimization) mostly focus on the use of finite random variables. This trend is rapidly changing with the advent of statistical optimization (e.g., Bayesian optimization) and multi-scale optimization (e.g., integration of molecular sciences and process engineering). Our work extends a recently-proposed abstraction for infinite-dimensional optimization problems by capturing more general uncertainty representations. Moreover, we discuss solution paradigms for this new class of problems based on finite transformations and sampling, and identify open questions and challenges.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fast estimation of the look-elsewhere effect using Gaussian random fields

Abstract We discuss the use of Gaussian random fields to estimate the look-elsewhere effect correction. We show that Gaussian random fields can be used to model the null-hypothesis significance maps from a large set of statistical problems commonly encountered in physics, such as template matching and likelihood ratio tests. Some specific examples are searches for dark matter using pixel arrays, searches for astronomical transients, and searches for fast-radio bursts. Gaussian random fields can be sampled efficiently in the frequency domain, and the excursion probability can be fitted with these samples to extend any estimation of the look-elsewhere effect to lower p values. In addition, in cases where the Gaussian random field is stationary and the parameter space is Euclidean, the look-elsewhere effect correction can be computed analytically. We demonstrate these methods using two example template matching problems. Finally, we apply these methods to estimate the trial factor of a $$4^3$$ 4 3 accelerometer array for the detection of dark matter tracks in the Windchime project. When a global significance of $$3\sigma $$ 3 σ is required, the estimated trial factor for such an accelerometer array is $$10^{14}$$ 10 14 for a one-second search, and $$10^{22}$$ 10 22 for a 1-year search.

Qin, Juehang (ORCID:0000000182288949)↗
DOE OSTI2025

COBRA:COMPUTED-TOMOGRAPHY BASED RANDOM-FIELD APPROXIMATION

SF-25-115 COBRA (COmputed-tomography Based Random-field Approximation) is a Python application for generating statistically equivalent random fields from CT-scan imagery. It leverages Karhunen–Loève expansions to model microstructural variability, enabling users to: Preprocess CT scans (filtering and Gaussian transformation); Fit covariance kernels fromempirical data; Solve eigenproblems to obtain KL modes; Sample random fields onsistent with fitted statistics; Postprocess samples back into the physical domain.

Hu, Tianchen↗
DOE OSTI2022

Augmented Gaussian random field: Theory and computation

We propose the novel augmented Gaussian random field (AGRF), which is a universal framework incorporating the data of observable and derivatives of any order. Rigorous theory is established. We prove that under certain conditions, the observable and its derivatives of any order are governed by a single Gaussian random field, which is the aforementioned AGRF. As a corollary, the statement "the derivative of a Gaussian process remains a Gaussian process" is validated, since the derivative is represented by a part of the AGRF. Moreover, a computational method corresponding to the universal AGRF framework is constructed. Both noiseless and noisy scenarios are considered. Formulas of the posterior distributions are deduced in a nice closed form. A significant advantage of our computational method is that the universal AGRF framework provides a natural way to incorporate arbitrary order derivatives and deal with missing data. We use four numerical examples to demonstrate the effectiveness of the computational method. The numerical examples are composite function, damped harmonic oscillator, Korteweg-De Vries equation, and Burgers' equation.

Mathematics↗
DOE OSTI2020

Experimental demonstration and analysis of random field effects in ferromagnet/antiferromagnet bilayers

More than 30 years ago, Malozemoff [Phys. Rev. B 35, 3679 (1987)] hypothesized that exchange interaction at the interface between a ferromagnet (F) and an antiferromagnet (AF) can act as an effective random field, which can profoundly affect the magnetic properties of the system. However, until now this hypothesis has not been directly experimentally tested. We utilize magnetoelectronic measurements to analyze the effective exchange fields at permalloy/CoO interface. Our results cannot be explained in terms of quasiuniform effective exchange fields but are in agreement with the random-field hypothesis of Malozemoff. Finally, the presented approach opens a new route for the quantitative analysis of effective exchange fields and anisotropies in magnetic heterostructures for memory, sensing and computing applications.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Using porous random fields to predict the elastic modulus of unoxidized and oxidized superfine graphite

Nuclear graphite is a candidate material for Generation IV nuclear power plants. Porous materials such as graphite can contain complex networks of pores that influence the material's mechanical and irradiation response. A methodology known as the random finite element method (RFEM) was adapted to create synthetic microstructures and predict the influence of porosity on the elastic properties of graphite during oxidation. RFEM combines random field theory and the finite element method in a Monte Carlo framework to estimate the mechanical response of a given grade of graphite. In this research, the random fields were verified through experimental characterization to predict the elastic response of three nuclear graphite grades, ETU-10, IG-110, and 2114. Finite element models (FEM) were generated using segmentations of x-ray computed tomography (XCT) data known as image-based models (IBMs) to validate and compare with the RFEM results and better understand the effects of uniform oxidation in these graphite grades. The RFEM predictions appear to correlate well with the experimental values of the measured Young’s modulus of the three graphite grades and display the same trends as IBMs.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Experimental Realization of the 1D Random Field Ising Model

Here we have measured magnetic-field-induced avalanches in a square artificial spin ice array of interacting nanomagnets. Starting from the ground state ordered configuration, we imaged the individual nanomagnet moments after each successive application of an incrementally increasing field. The statistics of the evolution of the moment configuration show good agreement with the canonical one-dimensional random field Ising model. We extract information about the microscopic structure of the arrays from our macroscopic measurements of their collective behavior, demonstrating a process that could be applied to other systems exhibiting avalanches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Hierarchical Gaussian Random Field Sampling for Multilevel Markov Chain Monte Carlo: Coupling Stochastic Partial Differential Equation and the Karhunen–Loève Decomposition

This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRFs) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods, such as those based on stochastic partial differential equations (SPDEs), often reduce the dimensionality of the sample space at the cost of accuracy of inference. Other approaches, such that those based on Karhunen-Loève (KL) expansions, offer sample space dimensionality reduction but sacrifice GRF representation accuracy and ergodicity of the Markov chain Monte Carlo (MCMC) sampler and are computationally expensive for high-dimensional problems. The proposed method integrates the dimensionality reduction capabilities of KL expansions with the scalability of SPDE-based sampling, thereby providing a robust, unified framework for high-dimensional uncertainty quantification (UQ) that is scalable and accurate, preserves ergodicity, and offers dimensionality reduction of the sample space. The hierarchy in our multilevel algorithm is derived from the geometric multigrid hierarchy. By constructing a hierarchical decomposition that maintains the covariance structure across the levels in the hierarchy, the approach enables efficient coarse-to-fine sampling while ensuring that all samples are drawn from the desired distribution. The effectiveness of the proposed method is demonstrated on a benchmark subsurface flow problem, demonstrating its effectiveness in improving computational efficiency and statistical accuracy. Furthermore, our proposed technique is more efficient and accurate and displays better convergence properties than existing methods for high-dimensional Bayesian inference problems.

Gaussian random fields↗
DOE OSTI2024

Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. Here we describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Random fields from quenched disorder in an archetype for correlated electrons: The parallel spin stripe phase of La 1.6 – x Nd 0.4 Sr x CuO 4 at the 1/8 anomaly

The parallel stripe phase is remarkable both in its own right, and in relation to the other phases with which it coexists. Its inhomogeneous nature makes such states susceptible to random fields from quenched magnetic vacancies. Here we argue this is the case by introducing low concentrations of nonmagnetic Zn impurities (0%–10%) into La 1.6–x ⁢Nd 0.4⁢ Sr x ⁢CuO 4 (Nd-LSCO) with x=0.125 in single-crystal form, well below the percolation threshold of ~41% for a two-dimensional square lattice. Elastic neutron scattering measurements on these crystals show clear magnetic quasi-Bragg peaks at all Zn dopings. While all the Zn-doped crystals display order parameters that merge into each other and the background at ~68 K, the temperature dependence of the order parameter as a function of Zn concentration is drastically different. This result is consistent with meandering charge stripes within the parallel stripe phase, which are pinned in the presence of quenched magnetic vacancies. In turn it implies vacancies that preferentially occupy sites within the charge stripes, and hence that can be very effective at disrupting superconductivity in Nd-LSCO (x=0.125), and, by extension, in all systems exhibiting parallel stripes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, which are evaluated via kernel density estimation of the associated conditional cumulative distributions. Furthermore, we extend the construction to random field data via the Karhunen–Loève expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model and a synthetic example controlled by a parameter that enables a switch from unimodal to bimodal response distributions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Discrete-Direct Model Calibration and Uncertainty Propagation Method Confirmed on Multi-Parameter Plasticity Model Calibrated to Sparse Random Field Data

A discrete direct (DD) model calibration and uncertainty propagation approach is explained and demonstrated on a 4-parameter Johnson-Cook (J-C) strain-rate dependent material strength model for an aluminum alloy. The methodology's performance is characterized in many trials involving four random realizations of strain-rate dependent material-test data curves per trial, drawn from a large synthetic population. The J-C model is calibrated to particular combinations of the data curves to obtain calibration parameter sets which are then propagated to “Can Crush” structural model predictions to produce samples of predicted response variability. These are processed with appropriate sparse-sample uncertainty quantification (UQ) methods to estimate various statistics of response with an appropriate level of conservatism. This is tested on 16 output quantities (von Mises stresses and equivalent plastic strains) and it is shown that important statistics of the true variabilities of the 16 quantities are bounded with a high success rate that is reasonably predictable and controllable. The DD approach has several advantages over other calibration-UQ approaches like Bayesian inference for capturing and utilizing the information obtained from typically small numbers of replicate experiments in model calibration situations—especially when sparse replicate functional data are involved like force–displacement curves from material tests. The DD methodology is straightforward and efficient for calibration and propagation problems involving aleatory and epistemic uncertainties in calibration experiments, models, and procedures.

42 ENGINEERING↗
DOE OSTI2021

Beyond magnons in Nd 2 ScNbO 7 : An Ising pyrochlore antiferromagnet with all-in–all-out order and random fields

We report the low-temperature magnetic properties of Nd 3+ pyrochlore Nd 2 ScNbO 7 . Susceptibility and magnetization show an easy-axis moment, and heat capacity reveals a phase transition to long-range order at T N =371(2) mK with a fully recovered ΔS=Rln(2), 53% of it recovered for T>T N . Elastic neutron scattering shows a long-range all-in all-out magnetic order with low-Q diffuse elastic scattering. Inelastic neutron scattering shows a low-energy flat band, indicating a magnetic Hamiltonian similar to Nd 2 Zr 2 O 7 . Nuclear hyperfine excitations measured by ultra-high-resolution neutron backscattering indicate a distribution of static electronic moments below T N , which may be due to B-site disorder influencing Nd crystal electric fields. Analysis of heat-capacity data shows an unexpected T-linear or T 3/2 term which is inconsistent with conventional magnon quasiparticles, but is consistent with fractionalized spinons or gapless local spin excitations. We use legacy data to show similar behavior in Nd 2 Zr 2 O 7 . Comparing local static moments also reveals a suppression of the nuclear Schottky anomaly in temperature, evidencing a fraction of Nd sites with nearly zero static moment, consistent with exchange-disorder-induced random singlet formation. Finally, taken together, these measurements suggest an unusual fluctuating magnetic ground state which mimics a spin liquid, but may not actually be one.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Dynamic Mode Decomposition of Random Pressure Fields over Bluff Bodies

Fluctuating surface pressures on a bluff body exposed to a boundary layer flow generally are characterized as a spatiotemporally varying random field. In this paper, a dynamic mode decomposition (DMD) was applied to extract dominant features embedded in these random pressure fields. Utilizing an unsupervised machine learning algorithm, spatial modes and their temporal variations were grouped into different clusters at scales, e.g., macro, meso, and micro. A proper orthogonal decomposition (POD) of the experimental data was carried out to observe commonalities and distinctive perspectives each decomposition offers. Here, a comprehensive examination of the DMD/POD for their convergence criteria, data sufficiency, and modal components analysis was conducted. The physical interpretation of the spatiotemporal pressure field based on these decomposition schemes was discussed. At different scales, the DMD modes can capture the evolution of aerodynamic features, e.g., convection of vortices (or vortex tubes) and other structures. The distribution of energy among these three broad scales also reflects an energy cascade in pressure fluctuations akin to turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo

In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well suited to incorporating into multilevel Markov chain Monte Carlo (MCMC) algorithms. This approach builds off of other partial differential equation (PDE) approaches for generating Gaussian random field realizations; in particular, a single field realization may be formed by solving a reaction-diffusion PDE with a spatial white noise source function as the right-hand side. While these approaches have been explored to accelerate forward uncertainty quantification tasks, e.g., multilevel Monte Carlo, the previous constructions are not directly applicable to multilevel MCMC frameworks which build fine-scale random fields in a hierarchical fashion from coarse-scale random fields. Our new hierarchical multilevel method relies on a hierarchical decomposition of the white noise source function in $L^2$ which allows us to form Gaussian random field realizations across multiple levels of discretization in a way that fits into multilevel MCMC algorithmic frameworks. After presenting our main theoretical results and numerical scaling results to showcase the utility of this new hierarchical PDE method for generating Gaussian random field realizations, this method is tested on a four-level MCMC algorithm to explore its feasibility.

algebraic multigrid↗
DOE OSTI2023

Random magnetic field and the Dirac Fermi surface

In this paper, we study a single two-dimensional Dirac fermion at finite density, subject to a quenched random magnetic field. At low energies and sufficiently weak disorder, the theory maps onto an infinite collection of 1D chiral fermions (associated to each point on the Fermi surface) coupled by a random vector potential. This low-energy theory exhibits an exactly solvable random fixed line, along which we directly compute various disorder-averaged observables without the need for the usual replica, supersymmetry, or Keldysh techniques. We find the longitudinal dc conductivity in the collisionless $\hbar$ω/k B T→∞ limit to be nonuniversal and to vary continuously along the fixed line.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗