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DOE OSTI2026

Zentropy Theory for Transformative Functionalities of Magnetic and Superconducting Materials

The proposed research developed the zentropy theory through applications to complex magnetic materials and superconductors under the hypothesis that the emergent properties of complex magnetic materials and superconductors can be predicted by statistical mechanics of ergodic microstates with their partition functions computed from DFT-predicted free energies. The key objective is to develop approaches to systematically determine the types and number of microstates and the supercell size in DFT-based calculations through convergency of macroscopic functionalities, with the incorporation of our mixed-space approach accounting for the interactions between periodic supercells. In addition to use scientific intuitions to guide the design of important microstates, the key innovation of the proposed research is to integrate the domain knowledge and the material-property-descriptor database (MPDD) with 4 million microstates, which is supported by our deep neural network machine learning models (SIPFENN: structure-informed prediction of formation energy using neural networks) and integrated with our high throughput DFT Tool Kit (DFTTK). For complex magnetic materials, one of the objectives is to develop approaches to calculate short-range ordering from the statistical distribution of each microstate. For superconductors, the divergency of quasiparticle effective mass at a quantum critical point will be investigated, and the superconducting and non-superconducting microstates will be delineated through analysis of electronic band structure, density of states, charge density, and Fermi surface.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Recovering the effects of subgrid heterogeneity in simulations of radionuclide transport through fractured media

Groundwater flow and contaminant transport through fractured media can be simulated using Discrete Fracture Network (DFN) models which provide a natural description of structural heterogeneity. However, this approach is computationally expensive, with the large number of intersecting fractures necessitated by many real-world applications requiring modeling simplifications to be made for calculations to be tractable. Upscaling methods commonly used for this purpose can result in some loss of local-scale variability in the groundwater flow velocity field, resulting in underestimation of particle travel times, transport resistance and retention in transport calculations. In this paper, a transport downscaling algorithm to recover the transport effects of heterogeneity is tested on a synthetic Brittle Fault Zone model, motivated by the problem of large safety assessment calculations for geological repositories of spent nuclear fuel. We show that the variability in the local-scale velocity field which is lost by upscaling can be recovered by sampling from a library of DFN transport paths, accurately reproducing DFN transport statistic distributions and radionuclide breakthrough curves in an upscaled model.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Damage and Failure in a Statistical Crack Model

In this paper I will take a close look at a statistical crack model (SCM) as is used in engineering computer codes to simulate fracture at high strain rates. My general goal is to understand the macroscopic behavior effected by the microphysical processes incorporated into an SCM. More specifically, I will assess the importance of including local interactions between cracks into the growth laws of an SCM. My strategy will be to construct a numerical laboratory that represents a single computational cell containing a realization of a statistical distribution of cracks. The cracks will evolve by the microphysical models of the SCM, leading to quantifiable damage and failure of the computational cell. I will use the numerical data generated by randomly generated ensembles of the fracture process to establish scaling laws that will modify and simplify the implementation of the SCM into large scale engineering codes.

42 ENGINEERING↗

DOE OSTI2021

Detection of Outliers in LiDAR Data Acquired by Multiple Platforms over Sorghum and Maize

High-resolution point cloud data acquired with a laser scanner from any platform contain random noise and outliers. Therefore, outlier detection in LiDAR data is often necessary prior to analysis. Applications in agriculture are particularly challenging, as there is typically no prior knowledge of the statistical distribution of points, plant complexity, and local point densities, which are crop-dependent. The goals of this study were first to investigate approaches to minimize the impact of outliers on LiDAR acquired over agricultural row crops, and specifically for sorghum and maize breeding experiments, by an unmanned aerial vehicle (UAV) and a wheel-based ground platform; second, to evaluate the impact of existing outliers in the datasets on leaf area index (LAI) prediction using LiDAR data. Two methods were investigated to detect and remove the outliers from the plant datasets. The first was based on surface fitting to noisy point cloud data via normal and curvature estimation in a local neighborhood. The second utilized the PointCleanNet deep learning framework. Both methods were applied to individual plants and field-based datasets. To evaluate the method, an F-score was calculated for synthetic data in the controlled conditions, and LAI, the variable being predicted, was computed both before and after outlier removal for both scenarios. Results indicate that the deep learning method for outlier detection is more robust than the geometric approach to changes in point densities, level of noise, and shapes. The prediction of LAI was also improved for the wheel-based vehicle data based on the coefficient of determination (R2) and the root mean squared error (RMSE) of the residuals before and after the removal of outliers.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Multi-frequency General Relativistic Radiation-hydrodynamics with M 1 Closure

We report on recent upgrades to our general relativistic radiation-magnetohydrodynamics code, Cosmos++ , which expands the two-moment, M 1 , radiation treatment from gray to multi-frequency transport, including Doppler and gravitational frequency shifts. The solver accommodates either photon (Bose–Einstein) or neutrino (Fermi–Dirac) statistical distribution functions with absorption, emission, and elastic scattering processes. An implicit scheme is implemented to simultaneously solve the primitive inversion problem together with the radiation–matter coupling source terms, providing stability over a broad range of opacities and optical depths where the interaction terms can be stiff. We discuss our formulations and numerical methods, and validate our methods against a wide variety of test problems spanning optically thin to thick regimes in flat, weakly curved, and strongly curved spacetimes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Quantification of hydraulic trait control on plant hydrodynamics and risk of hydraulic failure within a demographic structured vegetation model in a tropical forest (FATES–HYDRO V1.0)

Abstract. Vegetation plays a key role in the global carbon cycle and thus is an important component within Earth system models (ESMs) that project future climate. Many ESMs are adopting methods to resolve plant size and ecosystem disturbance history, using vegetation demographic models. These models make it feasible to conduct more realistic simulation of processes that control vegetation dynamics. Meanwhile, increasing understanding of the processes governing plant water use, and ecosystem responses to drought in particular, has led to the adoption of dynamic plant water transport (i.e., hydrodynamic) schemes within ESMs. However, the extent to which variations in plant hydraulic traits affect both plant water stress and the risk of mortality in trait-diverse tropical forests is understudied. In this study, we report on a sensitivity analysis of an existing hydrodynamic scheme (HYDRO) model that is updated and incorporated into the Functionally Assembled Terrestrial Ecosystem Simulator (FATES) (FATES–HYDRO V1.0). The size- and canopy-structured representation within FATES is able to simulate how plant size and hydraulic traits affect vegetation dynamics and carbon–water fluxes. To better understand this new model system, and its functionality in tropical forest systems in particular, we conducted a global parameter sensitivity analysis at Barro Colorado Island, Panama. We assembled 942 observations of plant hydraulic traits on 306 tropical plant species for stomata, leaves, stems, and roots and determined the best-fit statistical distribution for each trait, which was used in model parameter sampling to assess the parametric sensitivity. We showed that, for simulated leaf water potential and loss of hydraulic conductivity across different plant organs, the four most important traits were associated with xylem conduit taper (buffers increasing hydraulic resistance with tree height), stomatal sensitivity to leaf water potential, maximum stem hydraulic conductivity, and the partitioning of total hydraulic resistance above vs. belowground. Our analysis of individual ensemble members revealed that trees at a high risk of hydraulic failure and potential tree mortality generally have a lower conduit taper, lower maximum xylem conductivity, lower stomatal sensitivity to leaf water potential, and lower resistance to xylem embolism for stem and transporting roots. We expect that our results will provide guidance on future modeling studies using plant hydrodynamic models to predict the forest responses to droughts and future field campaigns that aim to better parameterize plant hydrodynamic models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Stochastic Analysis for Long Term Capital Structures, Systems, and Components Refurbishment and Replacement

As commercial Nuclear Power Plants (NPPs) pursue extended plant operation in the form of Second License Renewal (SLR), opportunities exist for these plants to provide capital investments to ensure long-term safe and economic performance. At the current time, several utilities have announced an intention to pursue extended operation for one or more of their NPPs via SLR . The goal of this research is to develop a risk-informed approach to evaluate and prioritize plant capital investments made in preparation for, and during the period of, extended plant operations to support decisions for NPP operations. Since the capital investments are influenced by various factors, such as markets, safety and regulatory, the decision-making process of NPP operations should take into account relevant factors for balancing risks, costs and profits. The traditional method of capital budgeting is based on the priority list of candidate projects using economic measures such as benefit-investment ratio, net present value (NPV) and internal rate of return. In the literatures, the problem of capital budgeting or the variant can be represented by an appropriate knapsack problem. The knapsack approach to capital budgeting takes as input as investment, along with the cost and profit of each project. The objective of capital budgeting is to find the combination of the binary decisions for every investment such that the overall profit is as large as possible. The output is a collection of projects to be carried out, and we refer this selected collection of projects as a project portfolio. One limitation of traditional optimization models for capital budgeting is that they do not account for risk/uncertainty in profit and cost streams associated with individual projects, they do not account for risk in resource availability in future years [1,2,3]. Projects can incur cost over-runs, especially when projects are large, performed infrequently, and when there is risk regarding technical viability, external contractors, and/or suppliers of requisite parts and materials. Occasionally, projects are performed ahead of schedule and with cost savings. Planned budgets for capital improvements can be cut and key personnel may be lost. Or, there may be surprise windfalls in budgets for maintenance activities due to decreased costs for “unplanned” maintenance. In these cases, how should we resolve capital budgeting when we have risk forecasts for costs, profits and budgets? One approach we proposed in this summary is to re-solve the optimization models based on assumed statistical distributions of given parameters. If these distributions were not available, a two-stage stochastic optimization approach can be used to provide priority lists to decision-makers to support better risk-informed decisions [4, 5]. In this summary, we will only focus on the first approach.

42 ENGINEERING↗

DOE OSTI2024

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

The statistics of velocity and density fields are crucial for cosmic structure formation and evolution. Here, this paper extends our previous work on the two-point second-order statistics for the velocity field [Phys. Fluids 35, 077105 (2023)] to one-point probability distributions for both density and velocity fields. The scale and redshift variation of density and velocity distributions are studied by a halo-based non-projection approach. First, all particles are divided into halo and out-of-halo particles so that the redshift variation can be studied via generalized kurtosis of distributions for halo and out-of-halo particles, respectively. Second, without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: (i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; (ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade on small scales with a constant rate $\varepsilon_u$; (iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}$; (iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{'}$-$u_L$ and velocity sum $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; (v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the entropy of the system. The distribution of $\Delta u_L$ can be different; (vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution, while $u_L$ has a different distribution; (vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha(z)$ decreasing with time.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Determination of a most representative cycle from cylinder pressure ensembles via statistical method using distribution skewness

In internal combustion engine research, cylinder pressure measurements provide valuable information about the underlying thermodynamic and combustion processes, and are typically collected in ensembles of several 100 traces. Although in some particular fields of combustion research all traces are analyzed, in most cases only one trace is studied because analyzing all the traces is impractical due to the large number of collected samples. Instead, an ensemble-averaged pressure trace is commonly calculated and used for analysis. However, this pressure trace is highly smoothed and dynamic information is lost during the averaging process. With the average trace, pressure rise rates are lower and pressure oscillations such as the ones resulting from combustion knock are lost. In this work, a statistical method was developed to determine the “most representative cycle,” which is the cycle from the ensemble that has the pressure trace most representative of the engine operating condition. Eleven characteristic parameters are computed from each pressure trace and probabilistic distributions are obtained for each of the parameters using all the traces in the ensemble. Finally, the most representative cycle is selected by means of a cost function minimization. The benefits of this method are illustrated using experimental data from four very different engine platforms, under four different combustion modes and over a range of operating conditions.

42 ENGINEERING↗

DOE OSTI2022

Time-Based CAN IDS Paper Results Code

Modern vehicles are complex cyber-physical systems made of hundreds of electronic control units (ECUs) that communicate over controller area networks (CANs). This inherited complexity has expanded the CAN attack surface which is vulnerable to message injection attacks. These injections change the overall timing characteristics of messages on the bus, and thus, to detect these malicious messages, time-based intrusion detection systems (IDSs) have been proposed. However, time-based IDSs are usually trained and tested on low-fidelity datasets with unrealistic, labeled attacks. This makes difficult the task of evaluating, comparing, and validating IDSs. Here we detail and benchmark four time-based IDSs against the newly published ROAD dataset, the first open CAN IDS dataset with real (non-simulated) stealthy attacks with physically verified effects. We found that methods that perform hypothesis testing by explicitly estimating message timing distributions have lower performance than methods that seek anomalies in a distribution related statistic. In particular, these “distribution-agnostic” based methods outperform “distribution-based” methods by at least 55% in area under the precision-recall curve (AUC-PR). Our results expand the body of knowledge of CAN time-based IDSs by providing details of these methods and reporting their results when tested on datasets with real advanced attacks. Finally, we develop an after-market plug-in detector using lightweight hardware, which can be used to deploy the best performing IDS method on nearly any vehicle.

Moriano, Pablo [Oak Ridge National Lab. (ORNL), Oa↗

DOE OSTI2021

Statistical analysis of spatial distribution of pores in metal additive manufacturing

We report mechanical properties of additively manufactured parts are sensitive to the presence of pores form during the manufacturing process. The impact of pores on the mechanical performance has been investigated extensively with respect to different parameters, such as pore volume fraction, shape, and size. However, statistical investigations focusing on the relationships between the spatial distribution of pores and process parameters; and consequently, the performance of the manufactured parts are scattered and limited. Also, these sparse investigations usually suffer from an ambiguous definition of terminologies. For instance, the required criteria to consider a point pattern as complete spatial randomness (CSR) are generally not clarified. Moreover, no numerical formalism is yet developed to show how much the observed spatial results are statistically significant. To address these shortcomings, the statistical definition of CSR in a point pattern and the procedure to quantitatively determine the deviation of a pattern from CSR were discussed. The explained statistical approach was used to investigate the effect of scanning speed parameter on the spatial distribution of gas pores in laser powder bed fusion manufactured stainless steel parts. Furthermore, and to highlight the impact of the spatial distribution of pores on mechanical properties, fatigue performances of parts with clustered and randomly distributed pores were simulated by finite element analysis. It is shown that by reducing the scanning speed, the spatial distribution of gas pores deviated more from CSR, and correspondingly fatigue performance deteriorated.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Statistical analysis of S—N type environmental fatigue data of Ni-base alloy welds using weibull distribution

In this study, the probabilistic fatigue life model for Ni-base alloys was developed based on the Weibull distribution using statistical analysis of fatigue data reported in NUREG/CR-6909 and the new fatigue data of Alloy 52M/152 and 82/182. The developed Weibull model can consider right-censored data (i.e., non-failed data) and quantify the improved safety (or reliability) based on the level of failure probability. The overall margin in the current fatigue design limit model (ASME design curve + NUREG/CR-6909 F en model) is similar to that of the Weibull model with a cumulative failure probability of approximately 2.5%. The margin in the current fatigue design limit model demonstrated inconsistencies for the Ni-base alloy weld data, whereas the Weibull model showed a consistent margin. Therefore, the Weibull model can systematically mitigate the excessive safety margin.

36 MATERIALS SCIENCE↗

DOE OSTI2020

How “hot” are hotspots: Statistically localizing the high-activity areas on soil and rhizosphere images

The topic of microbial hotspots in soil requires not only visualizing their spatial distribution and biochemical analyses, but also statistical approaches to identify these hotspots and separate them from the surrounding activities (background). We hypothesized that each hotspot type (e.g. enzyme activities in the rhizosphere, root exudation, localization of herbicide accumulation) is a result of local process driven by biotic and/or abiotic factors, and the process rates in the hotspots are much faster than those in the soil background. We further hypothesized that the background and hotspot activities in soil belong to different statistical distributions. Consequently, hotspot determination should be based on statistical separation of activities significantly higher than the background. We analyzed for the statistical distributions of grey values on three groups of published images: 1) 14 C images of carbon input by roots into the rhizosphere, 2) 14 C glyphosate accumulation in the plant, and 3) zymogram of leucine aminopeptidase activity in rooted soil. The two Gaussian distributions were fit (the first representing the background, the second the hotspots) to the distribution of grey values in the images, the parameters (means and standard deviations, SD) of the fitted distributions were calculated, and the background was removed. Thus, we identified hotspots as areas outside of the Mean+2SD image intensity (corresponding to the upper ~ 2.5% of activity, being over 97.5% of background values) and finally, visualized images of solely hotspot locations. Finally, these results were compared with previously used decisions on hotspot intensity thresholding (i.e. Top-25% and 17 standard thresholding approaches in ImageJ) and discussed the advantages of the Mean+2SD as well as Mean+3SD approaches. These advantages include: i) simple unification of the thresholding approach for several imaging methods with various principles of activity distribution, ii) identification of hotspots with various activity levels, iii) analysis of “time-specific” hotspots in temporal sequences of images. Compared with 17 standard thresholding methods, we concluded that objectively elucidating and separating the hotspots should be based on statistical distribution analysis, e.g. using the Mean+2SD or Mean+3SD approaches. Furthermore, this simple Mean+2SD approach delivered suitable results for three groups of images and so, helps to understand the processes responsible for the highest activities and elucidate hotspots.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

DefectTrack: a deep learning-based multi-object tracking algorithm for quantitative defect analysis of in-situ TEM videos in real-time

Abstract In-situ irradiation transmission electron microscopy (TEM) offers unique insights into the millisecond-timescale post-cascade process, such as the lifetime and thermal stability of defect clusters, vital to the mechanistic understanding of irradiation damage in nuclear materials. Converting in-situ irradiation TEM video data into meaningful information on defect cluster dynamic properties (e.g., lifetime) has become the major technical bottleneck. Here, we present a solution called the DefectTrack , the first dedicated deep learning-based one-shot multi-object tracking (MOT) model capable of tracking cascade-induced defect clusters in in-situ TEM videos in real-time. DefectTrack has achieved a Multi-Object Tracking Accuracy (MOTA) of 66.43% and a Mostly Tracked (MT) of 67.81% on the test set, which are comparable to state-of-the-art MOT algorithms. We discuss the MOT framework, model selection, training, and evaluation strategies for in-situ TEM applications. Further, we compare the DefectTrack with four human experts in quantifying defect cluster lifetime distributions using statistical tests and discuss the relationship between the material science domain metrics and MOT metrics. Our statistical evaluations on the defect lifetime distribution suggest that the DefectTrack outperforms human experts in accuracy and speed.

42 ENGINEERING↗

DOE OSTI2025

Cosmic Reionization on Computers: Statistical Properties of the Distributions of Mean Opacities

Quasar absorption lines provide a unique window to the relationship between galaxies and the intergalactic medium during the Epoch of Reionization. In particular, high redshift quasars enable measurements of the neutral hydrogen content of the universe. However, the limited sample size of observed quasar spectra, particularly at the highest redshifts, hampers our ability to fully characterize the intergalactic medium during this epoch from observations alone. In this work, we characterize the distributions of mean opacities of the intergalactic medium in simulations from the Cosmic Reionization on Computers (CROC) project. We find that the distribution of mean opacities along sightlines follows a non-trivial distribution that cannot be easily approximated by a known distribution. When comparing the cumulative distribution function of mean opacities measurements in subsamples of sample sizes similar to observational measurements from the literature, we find consistency between CROC and observations at redshifts $z\lesssim 5.7$. However, at higher redshifts ($z\gtrsim5.7$), the cumulative distribution function of mean opacities from CROC is notably narrower than those from observed quasar sightlines implying that observations probe a systematically more opaque intergalactic medium at higher redshifts than the intergalactic medium in CROC boxes at these same redshifts. This is consistent with previous analyses that indicate that the universe is reionized too early in CROC simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Investigating the influence of particle distribution on force and torque statistics using hierarchical machine learning

An accurate representation of hydrodynamic force and torque experienced by every particle in a distribution can be obtained from particle resolved (PR) simulations. These unique quantities are influenced by the deterministic position of surrounding particles. However, systems simulated with this methodology are typically limited to particles due to the involved computational cost. This resource requirement is a major bottleneck in analyzing the effect of variations in particle distribution. Here, this article attempts to address this bottleneck by availing relatively inexpensive deep learning models. The surrogate models that we employ in this article use a physics‐based hierarchical framework and symmetry‐preserving neural networks to achieve robustness with limited training data. This article first performs additional generalizability tests on PR data of distinct distributions that are not involved in the training process. The models are then deployed on several different particle distributions. Impact of clustering and structure on the observed statistics are investigated.

42 ENGINEERING↗

DOE OSTI2021

Penetration Through Slots in Overmoded Cavities

A resonant cavity undergoes three distinct behaviors with increasing frequency: 1) fundamental modes, localized in frequency with well defined modal distribution; 2) undermoded region, where modes are still separated, but are sufficiently perturbed by small imperfections that their spectral positions (and distributions) are statistical in nature; and 3) overmoded region, where modes overlap, field distributions follow stochastic distributions, and the slot acts as if in free space. Understanding the penetration through slots in the overmoded region is of great interest, and is the focus of this article. Since full-wave solvers may not be able to provide a timely answer for very high frequencies due to a lack of memory and/or computation resources, we develop bounding methods to estimate worst-case average and maximum fields within the cavity. Finally, after discussing the bounding formulation, we compare its results to full-wave simulations at the first, second, and third resonance supported by the slot in the case of a cylindrical cavity. Note that the bounding formulation indicates that results are nearly independent of cavity shape: only the cavity volume, frequency, and cavity quality factor affect the overmoded region, making this formulation a powerful tool to assess electromagnetic interference and electromagnetic compatibility effects within cavities.

overmoded cavity↗

DOE OSTI2025

Convex relaxation for Fokker–Planck equation

We propose an approach to directly estimate the moments or marginals for a high-dimensional equilibrium distribution in statistical mechanics by solving the high-dimensional Fokker–Planck equation in terms of low-order cluster moments or marginals. With this approach, we bypass the exponential complexity of estimating the full high-dimensional distribution and directly solve the simplified partial differential equations for low-order moments/marginals. Moreover, the proposed moment/marginal relaxation is fully convex and can be solved via off-the-shelf solvers. We further propose a time-dependent version of the convex programs to study non-equilibrium dynamics. In a specific setting, we show the proposed method can recover a mean-field-type equilibrium density. Numerical results are provided to demonstrate the performance of the proposed algorithm for high-dimensional systems.

Chen, Yian↗