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DOE OSTI2024

Anisotropic physics-regularized interpretable machine learning of microstructure evolution

Anisotropic Physics-Regularized Interpretable Machine Learning Microstructure Evolution (APRIMME) is a general-purpose machine learning solution for grain growth simulations. In prior work, PRIMME employed a deep neural network to predict site-specific migration as a function of its neighboring sites to model normal, isotropic, grain growth behavior. This work aims to extend this method by incorporating grain boundary misorientation-based grain growth behavior. APRIMME is trained on anisotropic simulations created using the Monte Carlo-Potts (MCP) model. Furthermore, the results of this work are compared statistically using grain radius, number of sides per grain, mean neighborhood misorientations, and the standard deviation of triple junction dihedral angles, and are found to match in most cases. The exceptions are small and seem to be related to two causes: (1) the deterministic model of APRIMME is learning from the stochastic simulations of MCP, which seems to accentuate triple junction behaviors; and, (2) a bias against very small grains is made evident in a quicker decrease in grains than expected at the beginning of an APRIMME simulation. APRIMME is also evaluated for its general ability to capture anisotropic grain growth behavior by first investigating different test case initial conditions, including a circle grain, three grain, and hexagonal grain microstructures.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Capturing the softening in T91 steel annealed with molten LBE through interfacial gradient plasticity

In order to study the effect of annealing with molten lead–bismuth eutectic alloy (mLBE) on the mechanical properties of T91 steel, micropillar compression tests were analyzed through the consideration of mechanical interface energy terms within gradient plasticity. The stress–strain curves of the micropillars showed significant stochastic effects, characterized by a different elastic and plastic behavior response for each pillar. Among the various pillars, some exhibited a similar trilinear behavior. Scanning electron microscopy (SEM) images of these specimens demonstrated localized slip deformation and slip planes after compression, while transmission electron microscopy (TEM) images showed the presence of a severe slip zone along the random grain boundaries (RGBs), indicating that the GBs played a dominant role in the deformation/slip. By employing interfacial gradient plasticity that can explicitly account for the presence of GBs, the trilinear response was captured, allowing for the determination of the mechanical interface parameter. As anticipated the pillars which underwent severe slip at the GBs had a lower value for the mechanical interface parameter. Finally, annealing with mLBE can, therefore, in some cases result in softening in the overall stress–strain, as it lowers the mechanical interface energy of GBs.

36 MATERIALS SCIENCE↗

NASA NTRS1976

A kinetic-theory approach to turbulent chemically reacting flows

The paper examines the mathematical and physical foundations for the kinetic theory of reactive turbulent flows, discussing the differences and relation between the kinetic and averaged equations, and comparing some solutions of the kinetic equations obtained by the Green's function method with those obtained by the approximate bimodal method. The kinetic method described consists essentially in constructing the probability density functions of the chemical species on the basis of solutions of the Langevin stochastic equation for the influence of eddies on the behavior of fluid elements. When the kinetic equations are solved for the structure of the diffusion flame established in a shear layer by the bimodal method, discontinuities in gradients of the mean concentrations at the two flame edges appear. This is a consequence of the bimodal approximation of all distribution functions by two dissimilar half-Maxwellian functions, which is a very crude approximation. These discontinuities do not appear when the solutions are constructed by the Green's function method described here.

Chung, P. M.↗

NASA NTRS1989

Evanescent radiation, quantum mechanics and the Casimir effect

An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.

Schatten, Kenneth H.↗

NASA NTRS2002

The Aeronautical Data Link: Taxonomy, Architectural Analysis, and Optimization

The future Communication, Navigation, and Surveillance/Air Traffic Management (CNS/ATM) System will rely on global satellite navigation, and ground-based and satellite based communications via Multi-Protocol Networks (e.g. combined Aeronautical Telecommunications Network (ATN)/Internet Protocol (IP)) to bring about needed improvements in efficiency and safety of operations to meet increasing levels of air traffic. This paper will discuss the development of an approach that completely describes optimal data link architecture configuration and behavior to meet the multiple conflicting objectives of concurrent and different operations functions. The practical application of the approach enables the design and assessment of configurations relative to airspace operations phases. The approach includes a formal taxonomic classification, an architectural analysis methodology, and optimization techniques. The formal taxonomic classification provides a multidimensional correlation of data link performance with data link service, information protocol, spectrum, and technology mode; and to flight operations phase and environment. The architectural analysis methodology assesses the impact of a specific architecture configuration and behavior on the local ATM system performance. Deterministic and stochastic optimization techniques maximize architectural design effectiveness while addressing operational, technology, and policy constraints.

Morris, A. Terry↗

NASA NTRS2013

Time-Series Analysis of Supergranule Characterstics at Solar Minimum

Sixty days of Doppler images from the Solar and Heliospheric Observatory (SOHO) / Michelson Doppler Imager (MDI) investigation during the 1996 and 2008 solar minima have been analyzed to show that certain supergranule characteristics (size, size range, and horizontal velocity) exhibit fluctuations of three to five days. Cross-correlating parameters showed a good, positive correlation between supergranulation size and size range, and a moderate, negative correlation between size range and velocity. The size and velocity do exhibit a moderate, negative correlation, but with a small time lag (less than 12 hours). Supergranule sizes during five days of co-temporal data from MDI and the Solar Dynamics Observatory (SDO) / Helioseismic Magnetic Imager (HMI) exhibit similar fluctuations with a high level of correlation between them. This verifies the solar origin of the fluctuations, which cannot be caused by instrumental artifacts according to these observations. Similar fluctuations are also observed in data simulations that model the evolution of the MDI Doppler pattern over a 60-day period. Correlations between the supergranule size and size range time-series derived from the simulated data are similar to those seen in MDI data. A simple toy-model using cumulative, uncorrelated exponential growth and decay patterns at random emergence times produces a time-series similar to the data simulations. The qualitative similarities between the simulated and the observed time-series suggest that the fluctuations arise from stochastic processes occurring within the solar convection zone. This behavior, propagating to surface manifestations of supergranulation, may assist our understanding of magnetic-field-line advection, evolution, and interaction.

Dopplergrams↗

DOE OSTI2023

Fog Intermittency and Critical Behavior

The intermittency of fog occurrence (the switching between fog and no-fog) is a key stochastic feature that plays a role in its duration and the amount of moisture available. Here, fog intermittency is studied by using the visibility time series collected during the month of July 2022 on Sable Island, Canada. In addition to the visibility, time series of air relative humidity and turbulent kinetic energy, putative variables akin to the formation and breakup conditions of fog, respectively, are also analyzed in the same framework to establish links between fog intermittency and the underlying atmospheric variables. Intermittency in the time series is quantified with their binary telegraph approximations to isolate clustering behavior from amplitude variations. It is shown that relative humidity and turbulent kinetic energy bound many stochastic features of visibility, including its spectral exponent, clustering exponent, and the growth of its block entropy slope. Although not diagnostic, the visibility time series displays features consistent with Pomeau–Manneville Type-III intermittency in its quiescent phase duration PDF scaling (−3/2), power spectrum scaling (−1/2), and signal amplitude PDF scaling (−2). The binary fog time series exhibits properties of self-organized criticality in the relation between its power spectrum scaling and quiescent phase duration distribution.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Synergy of tensile strength and high cycle fatigue properties in a novel additively manufactured Al-Ni-Ti-Zr alloy with a heterogeneous microstructure

Alloy design strategies in additive manufacturing (AM) to achieve grain refinement and terminal eutectic solidification have been introduced to engineer Al alloys having microstructural hierarchy and heterogeneity. Such alloy design strategies enable crack-free builds with an expanded AM processing window and pushed the strength limit in Al alloys. However, fatigue performance of Al alloys made by AM is restricted by the presence of process induced defects and its stochasticity. In this work, tensile and high cycle fatigue (HCF) behavior of a novel Al-Ni-Ti-Zr alloy with a heterogeneous microstructure is studied in the as-built condition, supplemented by detailed microstructural and mechanical characterization. Excellent strength-ductility synergy of 342 MPa and 16% failure strain achieved in the alloy was associated with the microstructural attributes that pertain to the novel alloy. Additionally, the alloy showed excellent HCF performance with a fatigue endurance limit to ultimate tensile strength ratio of 0.29 in flexural fatigue mode. The study revealed the existence of multiple crack retardation mechanisms and favorable crack propagation pathways through the fine-grained regions which enabled good fatigue performance to the alloy. Further, a probabilistic model has been used to estimate the fatigue life of the alloy as a function of the stochastic microstructure by utilizing the statistical distribution of pores, solid-state inclusions, and grains in the AM Al alloy. Finally, the model parametric trends are consistent with the experimental observations.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Filament-Free Bulk Resistive Memory Enables Deterministic Analogue Switching

Digital computing is nearing its physical limits as computing needs and energy consumption rapidly increase. Analogue-memory-based neuromorphic computing can be orders of magnitude more energy efficient at data-intensive tasks like deep neural networks, but has been limited by the inaccurate and unpredictable switching of analogue resistive memory. Filamentary resistive random access memory (RRAM) suffers from stochastic switching due to the random kinetic motion of discrete defects in the nanometer-sized filament. Here, this stochasticity is overcome by incorporating a solid electrolyte interlayer, in this case, yttria-stabilized zirconia (YSZ), toward eliminating filaments. Filament-free, bulk-RRAM cells instead store analogue states using the bulk point defect concentration, yielding predictable switching because the statistical ensemble behavior of oxygen vacancy defects is deterministic even when individual defects are stochastic. Both experiments and modeling show bulk-RRAM devices using TiO2-X switching layers and YSZ electrolytes yield deterministic and linear analogue switching for efficient inference and training. Bulk-RRAM solves many outstanding issues with memristor unpredictability that have inhibited commercialization, and can, therefore, enable unprecedented new applications for energy-efficient neuromorphic computing. Beyond RRAM, this work shows how harnessing bulk point defects in ionic materials can be used to engineer deterministic nanoelectronic materials and devices.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Enabling site-specific well leakage risk estimation during geologic carbon sequestration using a modular deep-learning-based wellbore leakage model

Geologic carbon sequestration (GCS) is a promising technology for mitigating net carbon emissions and growing climate concern by storing CO 2 in reservoirs. Oil and gas brownfields are an attractive option for CO 2 storage, but these sites have many historical wellbores from petroleum production and can be a potential leakage pathway for CO 2 or formation brine. Therefore, risk management of GCS operations requires an assessment of potential well leakage. Due to the high uncertainty of the system, stochastic approaches are ideal for quantifying the range of risk behaviors, but they must be computationally efficient in the face of complex physics. Here, we develop a new physics-centric deep learning wellbore model to predict the leakage of CO 2 and brine through leaky wellbores. Multi-physics numerical simulations were used to generate data sets, and physics-informed features were introduced. Neural networks were optimized with an automated searching algorithm. Feature analysis quantifies the impact of each feature on model prediction and confirms the role of physics-inspired parameters. The model shows high predictive performance across a wide range of geologic and injection conditions and well attributes. In conclusion, a case study illustrates how the model is applied to assess well leakage in GCS operations.

58 GEOSCIENCES↗

NASA NTRS1975

Worst-error analysis of batch filter and sequential filter in navigation problems

This paper proposes a worst-error analysis for dealing with problems of estimation of spacecraft trajectories in deep space missions. Navigation filters in use assume either constant or stochastic (Markov) models for their estimated parameters. When the actual behavior of these parameters does not follow the pattern of the assumed model, the filters sometimes result in very poor performance. To prepare for such pathological cases, the worst errors of both batch and sequential filters are investigated based on the incremental sensitivity studies of these filters. By finding critical switching instances of non-gravitational accelerations, intensive tracking can be carried out around those instances. Also the worst errors in the target plane provide a measure in assignment of the propellant budget for trajectory corrections. Thus the worst-error study presents useful information as well as practical criteria in establishing the maneuver and tracking strategy of spacecraft's missions.

Nishimura, T.↗

NASA NTRS1984

A performability solution method for degradable nonrepairable systems

The present performability model-solving algorithm identifies performance with 'reward', representing the state behavior of a system S by a finite-state stochastic process and determining reward by means of reward rates that are associated with the states of the base model. A general method is obtained for determining the probability distribution function of the performance (reward) variable, and therefore the performability, of the corresponding system. This is done for bounded utilization periods, and the result is an integral expression which is either analytically or numerically solvable.

Furchtgott, D. G.↗

DOE OSTI2022

Stochastic agent-based model for predicting turbine-scale raptor movements during updraft-subsidized directional flights

Rapid expansion of wind energy development across the world has highlighted the need to better understand turbine-caused avian mortality. The risk to golden eagles (Aquila chrysaetos) is of particular concern due to their small population size and conservation status. Golden eagles subsidize their flight in part by soaring in orographic updrafts, which can place them in conflict with wind turbines utilizing the same low-altitude wind resource. Understanding the behavior of soaring raptors in varying atmospheric conditions can therefore be relevant to predicting and mitigating their risk of collision. We present a predictive movement model that simulates individual paths of golden eagles during directional flight (such as migration) that is subsidized by orographic updraft. We modeled eagles in a 50 km by 50 km study area in Wyoming containing three wind power plants with documented golden eagle collisions with turbines. The movement model is applicable to any region where ground elevation is known at turbine scale (50 m) and wind conditions are known at facility scale (3 km). For a given set of atmospheric conditions, the model simulates movements of thousands of orographic soaring eagles to produce a density map quantifying the relative probability of eagle presence. We validated the simulated tracks with GPS telemetry data showing four directional tracks made by golden eagles transiting through the area in 2019 and 2020. For each eagle track, validation was performed using the ratio of the model-simulated eagle presence likelihood with uniform eagle presence and the presence computed using directed random-walk movements. We found that the predictive performance of the model was significantly better (likelihood ratio 1) for low-altitude movements than high-altitude movements that can involve thermal-soaring. We employed the model to produce seasonal presence maps for migrating golden eagles. We found significant turbine-level variations in eagle presence between northerly and southerly migration routes through the study area. Overall, the proposed model offers a generalizable, probabilistic, and predictive tool to assist wind energy developers, ecologists, wildlife managers, and industry consultants in estimating the potential for conflict between soaring birds and wind turbines, thereby reducing the need for site-specific data on golden eagle movements.

17 WIND ENERGY↗

NASA NTRS1992

Path integrals, differential renormalization-group, and stochastic systems near criticality

It is demonstrated, using the techniques of path integrals and renormalization-group, that nonlinear stochastic systems near criticality (including self-organized criticality) generally exhibit low-dimensional behavior. The symmetry which characterizes a particular criticality can be broken by the appearance of relevant scaling fields. A connection is made between the fractal dimensions of finite-dimensional chaotic systems and the anomalous dimensions in stochastic systems near criticality. The effect of additional random noise on stochastic systems is also delineated.

Chang, Tom↗

DOE OSTI2021

On the Stochastic Stability of Deep Markov Models

Deep Markov models (DMM) are generative models which are scalable and expressive generalization of Markov models for representation, learning, and inference problems. DMMs using deep neural networks to parametrize the transition of Markov probability distributions have recently been shown to provide more expressiveness in modeling sequential data and dynamical system responses. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we present a rigorous analytical method to prove the necessary and sufficient conditions of DMM's stochastic stability. This task is achieved by spectral analysis of the efficiently computed Jacobians of probabilistic maps modeled by deep neural networks. We make theoretical connections between the eigenvalues of neural network's weights and the different activation function types used on the stability and overall dynamic behavior of DMMs with Gaussian distributions. We empirically substantiate our theoretical results on stochastic stability and eigenvalue spectra via several numerical experiments. Formal stability guarantees of DMMs can substantially improve their robustness and trustworthiness, necessary for reliable use in safety-critical real-world applications.

Drgona, Jan↗

DOE OSTI2021

Developing and Testing a Novel Stochastic Ice Microphysics Parameterization for Cloud and Climate Models Using ARM Field Campaign Data (Final Progress Report)

The major goals of this project were: 1) to use field campaign measurements from DOE’s Atmospheric Radiation Measurement (ARM) program to characterize variability of important parameters describing properties of ice particles in the atmosphere; 2) based on this observational analysis, to develop a parameterization scheme for weather and climate models that stochastically varies these parameters, and implement the new scheme into a weather model called the Weather Research and Forecasting model (WRF); 3) to use WRF coupled with the new stochastic scheme to simulate ARM field campaign thunderstorm cases and analyze how accounting for this parameter variability affects the model simulations. This work was performed jointly between the National Center for Atmospheric Research, University of Oklahoma, and University of Utah. To accomplish these goals, we extended an approach previously developed to characterize the variability in the size distribution of ice particles to parameters that are explicitly represented in models (i.e., relationships between ice particle mass and size, and between particle fall velocity and size). Our project was, to our knowledge, the first to apply observationally-constrained estimates of this parameter variability describing mass-size and fall velocity-size in a modeling framework. Our results showed efficacy of the approach, evaluated using ARM observations. Similarly, to our knowledge, work in this project was the first to propose and evaluate in detail a stochastic approach for unresolved turbulent mixing in high-resolution model simulations against detailed, benchmark large eddy simulations and ARM observations. Results showed some promising behavior, particularly with increased mixing and dilution of air in thunderstorm cores with surrounding environmental air, bringing the stochastic simulations closer to the benchmark large eddy simulations; however, results were somewhat degraded using stochastic mixing compared to observations from the AMIE/DYNAMO field campaign. This project also further refined and applied a modeling methodology called “piggybacking” that can robustly separate dynamical and thermodynamic impacts of model changes, and comparison studies of different models based on cases developed from ARM observations. Finally, this project directly supported three graduate students who completed their PhDs as well as a postdoctoral research fellow.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A Binomial Stochastic Framework for Efficiently Modeling Discrete Statistics of Convective Populations

Abstract Understanding the coupling between convective clouds and the general circulation, as well as addressing the gray zone problem in convective parameterization, requires insight into the genesis and maintenance of spatial patterns in cumulus cloud populations. In this study, a simple toy model for recreating populations of interacting convective objects as distributed over a two‐dimensional Eulerian grid is formulated to this purpose. Key elements at the foundation of the model include i) a fully discrete formulation for capturing discrete behavior in convective properties at small population sample sizes, ii) object age‐dependence for representing life‐cycle effects, and iii) a prognostic number budget allowing for object interactions and co‐existence of multiple species. A primary goal is to optimize the computational efficiency of this system. To this purpose the object birth rate is represented stochastically through a spatially aware Bernoulli process. The same binomial stochastic operator is applied to horizontal advection of objects, conserving discreteness in object number. The applicability to atmospheric convection as well as behavior implied by the formulation is assessed. Various simple applications of the BiOMi model (Binomial Objects on Microgrids) are explored, suggesting that important convective behavior can be captured at low computational cost. This includes i) subsampling effects and associated powerlaw scaling in the convective gray zone, ii) stochastic predator‐prey behavior, iii) the downscale turbulent energy cascade, and iv) simple forms of spatial organization and convective memory. Consequences and opportunities for convective parameterization in next‐generation weather and climate models are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Profiles of upcoming HPC Applications and their Impact on Reservation Strategies

With the expected convergence between HPC, BigData and AI, new applications with different profiles are coming to HPC infrastructures. Here, we aim at better understanding the features and needs of these applications in order to be able to run them efficiently on HPC platforms. The approach followed is bottom-up: we study thoroughly an emerging application from the neuroscience community (SLANT) to understand its behavior. Based on these observations, we derive a generic, yet simple, application model (namely, a linear sequence of stochastic jobs). We expect this model to be representative for a large set of upcoming applications that require the computational power of HPC clusters without fitting the typical behavior of large-scale traditional applications. In a second step, we show how one can manipulate this generic model in a scheduling framework. Specifically we consider the problem of making reservations (both time and memory) for an execution on an HPC platform. We derive solutions using the model of the first step of this work. We experimentally show the robustness of the model, even with very few data or with another application, to generate the model, and provide performance gains with regards to standard and more recent approaches used in the neuroscience community.

97 MATHEMATICS AND COMPUTING↗