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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Stochastic Vector Techniques in Ground-State Electronic Structure

Herein we review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order many-body perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss effective techniques to reduce statistical errors. Finally, we review the use of stochastic vectors for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Mixed Stochastic-Deterministic Approach for Many-Body Perturbation Theory Calculations

Here, we present an approach for GW calculations of quasiparticle energies with quasi-quadratic scaling by approximating high-energy contributions to the Green's function in its Lehmann representation with effective stochastic vectors. The method is easy to implement without altering the GW code, converges rapidly with stochastic parameters, and treats systems of various dimensionality and screening response. Our calculations on a 5.75° twisted MoS 2 bilayer show how large-scale GW methods include geometry relaxations and electronic correlations on an equal basis in structurally nontrivial materials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Probabilistic-learning-based stochastic surrogate model from small incomplete datasets for nonlinear dynamical systems

We consider a high-dimensional nonlinear computational model of a dynamical system, parameterized by a vector-valued control parameter, in the presence of uncertainties represented by an uncontrolled parameter modeled by a vector-valued random variable, and possibly with stochastic excitation. The objective is to construct a statistical surrogate model where the input is any deterministic value of the control parameter, and the output is a vector-valued observation of the computational model, which is a random vector whose probability measure is updated using a target dataset. To construct this statistical surrogate model, the stochastic response of the computational model must be built, which is a vector-valued time-discretized stochastic process in high dimension, depending on the control parameter. It is assumed that the computational cost of a single evaluation of the deterministic model is high. For the probabilistic updating, we consider a subset of the components of the observation of the computational model, defined as the “identification observation” of the computational model, for which a small target dataset is available. Therefore, the target dataset is associated with partial observability, corresponding to an incomplete data case. Given a prior probability model of the random control and uncontrolled parameters, a training dataset is constructed, consisting of realizations of the random triplet composed of the stochastic response, the random identification observation, and the random control parameter. Since the computational cost of a single evaluation of the deterministic model is assumed to be large, the training dataset is also of small size. The main challenges in this problem are the high dimensionality, partial observability leading to incomplete data in the target dataset for the identification observation of the computational model (which is not sufficient to identify the computational stochastic responses), and the availability of a small training dataset. To address these challenges, we propose a methodology based on statistical methods for constructing necessary reduced representations, direct probabilistic learning under constraints using probabilistic learning on manifolds (PLoM) constrained by the target dataset, and the use of a weak formulation of the Fourier transform of probability measures. Statistical conditioning is also employed to explore the learned dataset. The constructed predictive statistical surrogate model can be implemented in the context of online computation. Here, we apply this approach to a problem of nonlinear stochastic dynamics in high dimensions within the framework of deformable solids mechanics.

Engineering↗
DOE OSTI2021

Flow-driven spectral chaos (FSC) method for long-time integration of second-order stochastic dynamical systems

For decades, uncertainty quantification techniques based on the spectral approach have been demonstrated to be computationally more efficient than the Monte Carlo method for a wide variety of problems, particularly when the dimensionality of the probability space is relatively low. The time-dependent generalized polynomial chaos (TD-gPC) is one such technique that uses an evolving orthogonal basis to better represent the stochastic part of the solution space in time. Here in this paper, we present a new numerical method that uses the concept of enriched stochastic flow maps to track the evolution of the stochastic part of the solution space in time. The computational cost of this proposed flow-driven stochastic chaos (FSC) method is an order of magnitude lower than TD-gPC for comparable solution accuracy. This gain in computational cost is realized because, unlike most existing methods, the number of basis vectors required to track the stochastic part of the solution space does not depend upon the dimensionality of the probability space. Four representative numerical examples are presented to demonstrate the performance of the FSC method for long-time integration of second-order stochastic dynamical systems in the context of stochastic dynamics of structures.

FSC↗
DOE OSTI2023

Protecting Customer Privacy Through Distributed Energy Resource Anonymization

Due to their stochastic nature, the increase of Renewable Energy Resources (RERs) as a primary source of energy for power grids creates challenges regarding the reliability and resilience of the system. In order to combat these obstacles, expansion of Distributed Energy Resources (DERs) and their participation in Demand Response (DR) programs is necessary. Widespread participation requires prioritizing customer privacy and addressing concerns that may arise regarding communication between DERs and the Grid Service Provider (GSP). This paper discusses the use of flow reservation resources to split the operating cycles of DER load profiles into unique phases. The splitting of phases increases anonymization of the DERs by making it more difficult to determine the individual characteristics of the device. We discuss an example of this using simulated DER load profile data and examine the resulting effectiveness by using a machine learning algorithm for classification, called Support Vector Machine (SVM).

Distributed Energy Resource, Anonymization, Renewa↗
DOE OSTI2025

First astrometric constraints on parity-violation in the gravitational wave background

Astrometry, the precise measurement of stellar positions and velocities, offers a promising approach to probing the low-frequency stochastic gravitational wave background (SGWB). Notably, astrometric vector sky maps are sensitive to parity-violating SGWB signals, which cannot be distinguished using pulsar timing array observations in an isotropic SGWB. We present the first astrometric constraints on parity-violating SGWB using quasar catalogs from Gaia DR3 and VLBA data. By analyzing the EB correlation in the two-point correlation function of the proper motions of the quasars, we find 2σ constraints on the parity-violating SGWB amplitude h 70 2 Ω V = -0.020 ± 0.025 from Gaia DR3 and h 70 2 Ω V = -0.004 ± 0.010 from VLBA. These constraints are valid in the frequency range 4.2 × 10 -18 Hz < f < 1.1 × 10 -8 Hz. Although not currently a tight constraint on theoretical models, this first attempt lays the groundwork for future investigations using more precise astrometric data.

Gravitational waves in GR and beyond: theory↗
DOE OSTI2022

Kink mechanism in Cu/Nb nanolaminates explored by $\mathcal{in}$ $\mathcal{situ}$ pillar compression

We report Nano metallic laminates (NMLs) exhibit different failure modes depending on the loading conditions due to their mechanical anisotropies. Kinking is a typical failure mode in many NMLs compressed along a layer-parallel direction. However, a detailed description of the microstructure evolution during kink band (KB) formation and an in-depth understanding of the formation mechanisms are lacking. In this work, the KB process is investigated in Cu/Nb NMLs by in situ micro pillar compression in the scanning electron microscope (SEM) along a layer-parallel direction. Post-mortem S/TEM and transmission Kikuchi diffraction (TKD) analyses show that kink banding leads to significant microstructure changes characterized by an accumulation of geometrically necessary dislocations (GNDs) and of tilt geometrically necessary boundaries (GNBs) near KB boundaries (KBBs). The distinct microstructure evolution implies that KB formation is facilitated by the inhomogeneous microstructures resulting in constrained deformation modes. Specifically, dislocations active on slip planes nearly parallel to the interfaces make a major contribution to kink evolution after the onset of kinking. Once layer-parallel slip systems are activated, preexisting lattice dislocations and dislocations nucleating from interfaces will accumulate as GNDs near KBBs via the stochastic storage of lattice dislocations that have certain Burgers vectors. GNDs can further transform into GNBs via cross-slip and climb driven processes near the KBB. Furthermore, GNBs near KBBs can grow by incorporating more GNDs or by coalescence to accommodate the KB evolution. We further hypothesize that microstructural perturbations and their ensuing stresses can initiate KB formation in Cu/Nb NMLs.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Hybrid feature-driven learning system for abnormality detection and localization

A cyber-physical system may have a plurality of monitoring nodes each generating a series of current monitoring node values over time representing current operation of the system. A data-driven features extraction computer platform may receive the series of current monitoring node values and generate current data-driven feature vectors based on the series of current monitoring node values. A residual features extraction computer platform may receive the series of current monitoring node values, execute a system model and utilize a stochastic filter to determine current residual values, and generate current residual-driven feature vectors based on the current residual values. An abnormal detection platform may then receive the current data-driven and residual-driven feature vectors and compare the current data-driven and residual-driven feature vectors with at least one decision boundary associated with an abnormal detection model. An abnormal alert signal may then be transmitted when appropriate based on a result of said comparison.

Abbaszadeh, Masoud↗
DOE OSTI2024

Optical spin hall effect in exciton–polariton condensates in lead halide perovskite microcavities

An exciton–polariton condensate is a hybrid light–matter state in the quantum fluid phase. The photonic component endows it with characters of spin, as represented by circular polarization. Spin-polarization can form stochastically for quasi-equilibrium exciton–polariton condensates at parallel momentum vector k|| ∼ 0 from bifurcation or deterministically for propagating condensates at k|| > 0 from the optical spin-Hall effect (OSHE). Here, we report deterministic spin-polarization in exciton–polariton condensates at k|| ∼ 0 in microcavities containing methylammonium lead bromide perovskite (CH3NH3PbBr3) single crystals under non-resonant and linearly polarized excitation. We observe two energetically split condensates with opposite circular polarizations and attribute this observation to the presence of strong birefringence, which introduces a large OSHE at k|| ∼ 0 and pins the condensates in a particular spin state. Such spin-polarized exciton–polariton condensates may serve not only as circularly polarized laser sources but also as effective alternatives to ultracold atom Bose–Einstein condensates in quantum simulators of many-body spin–orbit coupling processes.

Chemistry↗
DOE OSTI2024

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗
DOE OSTI2024

A three-point velocity estimation method for two-dimensional coarse-grained imaging data

Time delay and velocity estimation methods have been widely studied subjects in the context of signal processing, with applications in many different fields of physics. The velocity of waves or coherent fluctuation structures is commonly estimated as the distance between two measurement points divided by the time lag that maximizes the cross correlation function between the measured signals, but this is demonstrated to result in erroneous estimates for two spatial dimensions. We present an improved method to accurately estimate both components of the velocity vector, relying on three non-aligned measurement points. We introduce a stochastic process describing the fluctuations as a superposition of uncorrelated pulses moving in two dimensions. Using this model, we show that the three-point velocity estimation method, using time delays calculated through cross correlations, yields the exact velocity components when all pulses have the same velocity. The two- and three-point methods are tested on synthetic data generated from realizations of such processes for which the underlying velocity components are known. The results reveal the superiority of the three-point technique. Finally, we demonstrate the applicability of the velocity estimation on gas puff imaging data of strongly intermittent plasma fluctuations due to the radial motion of coherent, blob-like structures at the boundary of the Alcator C-Mod tokamak.

Materials Science↗
DOE OSTI2021

A stochastic solver based on the residence time algorithm for crystal plasticity models

Abstract The deformation of crystalline materials by dislocation motion takes place in discrete amounts determined by the Burgers vector. Dislocations may move individually or in bundles, potentially giving rise to intermittent slip. This confers plastic deformation with a certain degree of variability that can be interpreted as being caused by stochastic fluctuations in dislocation behavior. However, crystal plasticity (CP) models are almost always formulated in a continuum sense, assuming that fluctuations average out over large material volumes and/or cancel out due to multi-slip contributions. Nevertheless, plastic fluctuations are known to be important in confined volumes at or below the micron scale, at high temperatures, and under low strain rate/stress deformation conditions. Here, we develop a stochastic solver for CP models based on the residence-time algorithm that naturally captures plastic fluctuations by sampling among the set of active slip systems in the crystal. The method solves the evolution equations of explicit CP formulations, which are recast as stochastic ordinary differential equations and integrated discretely in time. The stochastic CP model is numerically stable by design and naturally breaks the symmetry of plastic slip by sampling among the active plastic shear rates with the correct probability. This can lead to phenomena such as intermittent slip or plastic localization without adding external symmetry-breaking operations to the model. The method is applied to body-centered cubic tungsten single crystals under a variety of temperatures, loading orientations, and imposed strain rates.

42 ENGINEERING↗
DOE OSTI2023

Data-Driven Transition Path Analysis Yields a Statistical Understanding of Sudden Stratospheric Warming Events in an Idealized Model

Abstract Atmospheric regime transitions are highly impactful as drivers of extreme weather events, but pose two formidable modeling challenges: predicting the next event (weather forecasting) and characterizing the statistics of events of a given severity (the risk climatology). Each event has a different duration and spatial structure, making it hard to define an objective “average event.” We argue here that transition path theory (TPT), a stochastic process framework, is an appropriate tool for the task. We demonstrate TPT’s capacities on a wave–mean flow model of sudden stratospheric warmings (SSWs) developed by Holton and Mass, which is idealized enough for transparent TPT analysis but complex enough to demonstrate computational scalability. Whereas a recent article (Finkel et al. 2021) studied near-term SSW predictability, the present article uses TPT to link predictability to long-term SSW frequency. This requires not only forecasting forward in time from an initial condition, but also backward in time to assess the probability of the initial conditions themselves. TPT enables one to condition the dynamics on the regime transition occurring, and thus visualize its physical drivers with a vector field called the reactive current . The reactive current shows that before an SSW, dissipation and stochastic forcing drive a slow decay of vortex strength at lower altitudes. The response of upper-level winds is late and sudden, occurring only after the transition is almost complete from a probabilistic point of view. This case study demonstrates that TPT quantities, visualized in a space of physically meaningful variables, can help one understand the dynamics of regime transitions.

Meteorology & Atmospheric Sciences↗
DOE OSTI2025

Optimizing stochastic algorithms for hadron correlation function computations in lattice QCD using a localized distillation basis

Distillation is a quark-smearing method for the construction of a broad class of hadron operators useful in lattice QCD computations and defined via a projection operator into a vector space of smooth gauge-covariant fields. A new orthonormal basis for this space is constructed which builds in locality. This basis is useful for the construction of stochastic methods to estimate the correlation functions computed in Monte Carlo calculations relevant for hadronic physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗
DOE OSTI2024

Explicit simulation of the Brownian rotation of arbitrary shaped aerosol particles using quaternions

The shape of an aerosol particle strongly influences its mass and momentum transfer cross-sections, charging properties, and other physical properties. Here, we present an explicit time-stepping procedure to simulate the rotational Brownian motion of arbitrary shaped aerosol particles by solving Euler’s equation of rotation. A Langevin formulation of the rotation equations is used, wherein Brownian motion due to thermal collisions between a particle and background gas molecules is represented using a stochastic fluctuating torque and fluid resistance is included as a drag torque. To avoid singularities associated with describing the orientation of a shape with Euler angles, we employ a quaternion formulation that leads to first-order stochastic differential equations to describe the evolution of the angular position and angular velocity of a rigid body. We perform all the rotational dynamics calculations in the body-fixed frame of reference attached to the rotating shape whose basis vectors are the normalized eigenvectors of the inertia tensor of the particle. Numerical solutions to rotation under torque-free conditions, damped rotation without Brownian motion, and stochastic rotation for arbitrary shapes are presented and discussed. The presented method enables time-resolved simulation of Brownian rotation for direct comparison with experimentally measured trajectories or statistical measures. The second order accuracy of the used time-stepping procedure places a severe restriction on the timestep that can be used for obtaining accurate results. Animations of presented simulations are included for visualizing rotational motion at various gas pressures. To aid implementation, MATLAB ® codes are also provided. Extension to include translation Brownian motion is straightforward.

Roy, Mrittika↗