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DOE OSTI2024

The hyperplane of early-type galaxies: using stellar population properties to increase the precision and accuracy of the fundamental plane as a distance indicator

ABSTRACT We use deep spectroscopy from the SAMI (Sydney-AAO Multi-object Integral) Galaxy Survey to explore the precision of the fundamental plane (FP) of early-type galaxies as a distance indicator for future single-fibre spectroscopy surveys. We study the optimal trade-off between sample size and signal-to-noise ratio (SNR), and investigate which additional observables can be used to construct hyperplanes with smaller intrinsic scatter than the FP. We add increasing levels of random noise (parametrized as effective exposure time) to the SAMI spectra to study the effect of increasing measurement uncertainties on the FP- and hyperplane-inferred distances. We find that, using direct-fit methods, the values of the FP and hyperplane best-fitting coefficients depend on the spectral SNR, and reach asymptotic values for a mean $\langle \mathrm{ SNR} \rangle =40\, \mathrm{\mathring{\rm A}}^{-1}$. As additional variables for the FP we consider three stellar-population observables: light-weighted age, stellar mass-to-light ratio, and a novel combination of Lick indices ($I_\mathrm{age}$). For an $\langle \mathrm{ SNR} \rangle =45~\mathrm{\mathring{\rm A}}^{-1}$ (equivalent to 1-h exposure on a 4-m telescope), all three hyperplanes outperform the FP as distance indicators. Being an empirical spectral index, $I_\mathrm{age}$ avoids the model-dependent uncertainties and bias underlying age and mass-to-light ratio measurements, yet yields a 10 per cent reduction of the median distance uncertainty compared to the FP. We also find that, as a by-product, the $I_\mathrm{age}$ hyperplane removes most of the reported environment bias of the FP. After accounting for the different SNR, these conclusions also apply to a 50 times larger sample from SDSS-III (Sloan Digital Sky Survey). However, in this case, only $\mathrm{ age}$ removes the environment bias.

D’Eugenio, Francesco (ORCID:0000000323888172)↗

DOE OSTI2024

Improved Statistical Analysis for the Neutrinoless Double-Beta Decay Matrix Element of 136Xe

Neutrinoless double beta decay nuclear matrix element (M0ν) for 136Xe was recently analyzed using a statistical approach (Phys. Rev. C 107, 045501 (2023)). In the analysis, three initial shell model effective Hamiltonians were randomly altered, and their results for 23 measured observables were used to infer credibility for the M0ν nuclear matrix element (NME) based on a Bayesian Model Averaging approach. In that analysis, a reasonable Gamow-Teller quenching factor of 0.7 was assumed for each starting effective Hamiltonian. Given that the result of the statistical analysis was sensible to this choice, we are here improving that analysis by assuming that the Gamow-Teller quenching factor is also randomly chosen within reasonabe limits for all three starting Hamiltonians. The outcomes are slightly higher expectation values and uncertainties for the M0ν NME.

Astronomy & Astrophysics↗

DOE OSTI2020

An Analysis of the Statistics and Systematics of Limb Anomaly Detections in HST/STIS Transit Images of Europa

Several recent studies derived the existence of plumes on Jupiter’s moon Europa. The only technique that provided multiple detections is the far-ultraviolet imaging observations of Europa in transit of Jupiter taken by the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope (HST). In this study, we reanalyze the three HST/STIS transit images in which Sparks et al. identified limb anomalies as evidence for Europa’s plume activity. After reproducing the results of Sparks et al., we find that positive outliers are similarly present in the images as the negative outliers that were attributed to plume absorption. A physical explanation for the positive outliers is missing. We then investigate the systematic uncertainties and statistics in the images and identify two factors that are crucial when searching for anomalies around the limb. One factor is the alignment between the actual and assumed locations of Europa on the detector. A misalignment introduces distorted statistics, most strongly affecting the limb above the darker trailing hemisphere where the plumes were detected. The second factor is a discrepancy between the observation and the model used for comparison, adding uncertainty in the statistics. When accounting for these two factors, the limb minima (and maxima) are consistent with random statistical occurrence in a sample size given by the number of pixels in the analyzed limb region. The plume candidate features in the three analyzed images can be explained by purely statistical fluctuations and do not provide evidence for absorption by plumes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Bayesian State-Space Modeling Framework for Understanding and Predicting Golden Eagle Movements Using Telemetry Data

Predicting raptor movements through a wind power plant under given atmospheric and topographical conditions is a crucial first step in the overall goal of quantifying the risk of turbine-related collisions and mortalities. Extracting behavioral traits of golden eagles (Aquila chrysaetos) from telemetry data requires the fusion of noisy and sparse movement data (location, heading, velocity) with a stochastic mathematical representation of the eagles' decision-making processes. In this study, we framed this problem in a Bayesian state-space framework where both observations and decision-making are assumed to be stochastic processes connected through hidden states (mode of flight, intent), and the unknown model parameters are assumed to be random variables that are calibrated using the available telemetry data. This framework allowed for rigorous consideration of underlying uncertainties while allowing for both data and prior biological knowledge to contribute to a probabilistic and predictive agent-based movement model. We implemented and applied the Bayesian framework to understand movement behavior of 23 GPS-tagged golden eagles travelling in the western US for years 2019 and 2020. Our preliminary findings show that the Bayesian state-space framework provides a robust inverse modeling apparatus to decode eagle behavioral characteristics from telemetry data. This study was primarily aimed at verifying and validating the framework with selected golden eagle tracks (both long- and short-ranged), with future research aimed at extending the framework to include multi-mode flight, consideration of atmospheric data and uplift mechanisms, eagle-to-eagle interaction, and eagle-to-turbine interaction.

Bayesian modeling↗

DOE OSTI2022

Evolving Metrics for Resource Adequacy Assessment

Resource adequacy analysis quantifies the likelihood of capacity shortfall on a power system in a probabilistic manner. Using a combination of statistical techniques and power system fundamentals, the analysis typically evaluates hundreds or thousands of stochastic random samples (replications) of varying load, generator outages, variable renewable energy availability, and other aspects of power system uncertainty. In this range of uncertainty, there are - at times - periods where the power system's available resources are insufficient to meet system demand, referred to as a shortfall event. Today's power systems' rapidly evolving generation mix is changing the types of data needed by system planners and regulators, which can often render traditional resource adequacy metrics insufficient for ensuring resource adequacy for tomorrow's grid. In this paper we provide a critical assessment of traditional measures of shortfall risk in power systems, discussing their shortcomings and how they compare to metrics used in other domains. From this analysis we propose four steps forward for improving power system resource adequacy risk metrics in the future.

ENERGY PLANNING, POLICY, AND ECONOMY,POWER TRANSMI↗

DOE OSTI2023

Beyond Expected Values Evolving Metrics for Resource Adequacy Assessment

ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2022

Coarse-Grained Density Functional Theory Predictions via Deep Kernel Learning

Scalable electronic predictions are critical for soft materials design. Recently, the Electronic Coarse-Graining (ECG) method was introduced to renormalize all-atom quantum chemical (QC) predictions to coarse-grained (CG) resolutions using deep neural networks (DNNs). While DNNs can learn complex representations that prove challenging for kernel-based methods, they are susceptible to overfitting and the overconfidence of uncertainty estimations. Here, we develop ECG within a GPU-accelerated Deep Kernel Learning (DKL) framework to enable CG QC predictions using range-separated hybrid density functional theory (DFT), obtaining a 107 speedup relative to naive all-atom QC. By treating the predicted electronic properties as random Gaussian Processes, DKL incorporates CG mapping degeneracy by learning the distribution of electronic energies as a function of CG configuration. DKL-ECG accurately reproduces molecular orbital energies from range-separated DFT while facilitating efficient training via active learning using the uncertainties provided by DKL. Further, we show that while active learning algorithms enable efficient sampling of a more diverse configurational space relative to random sampling, all explored query methods exhibit comparable performance for the examined system. We attribute this result to the significant overlap of the feature space and output property distributions across multiple temperatures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling

In the Monte Carlo many-body perturbation (MC-MP) method, the conventional correlation-correction formula, which is a long sum of products of low-dimensional integrals, is first recast into a short sum of high-dimensional integrals over electron-pair and imaginary-time coordinates. These high-dimensional integrals are then evaluated by the Monte Carlo method with random coordinates generated by the Metropolis–Hasting algorithm according to a suitable distribution. The latter algorithm, while advantageous in its ability to sample nearly any distribution, introduces autocorrelation in sampled coordinates, which in turn increases the statistical uncertainty of the integrals and thus the computational cost. It also involves wasteful rejected moves and an initial “burn-in” step as well as displays hysteresis. Here, an algorithm is proposed that directly produces a random sequence of electron-pair coordinates for the same distribution used in the MC-MP method, which is free from autocorrelation, rejected moves, a burn-in step, or hysteresis. Furthermore, this direct-sampling algorithm is shown to accelerate second- (MC-MP2) and third-order Monte Carlo many-body perturbation (MC-MP3) calculations by up to 222% and 38%, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Pre-conditioned BFGS-based uncertainty quantification in elastic full-waveform inversion

SUMMARY Full-waveform inversion has become an essential technique for mapping geophysical subsurface structures. However, proper uncertainty quantification is often lacking in current applications. In theory, uncertainty quantification is related to the inverse Hessian (or the posterior covariance matrix). Even for common geophysical inverse problems its calculation is beyond the computational and storage capacities of the largest high-performance computing systems. In this study, we amend the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to perform uncertainty quantification for large-scale applications. For seismic inverse problems, the limited-memory BFGS (L-BFGS) method prevails as the most efficient quasi-Newton method. We aim to augment it further to obtain an approximate inverse Hessian for uncertainty quantification in FWI. To facilitate retrieval of the inverse Hessian, we combine BFGS (essentially a full-history L-BFGS) with randomized singular value decomposition to determine a low-rank approximation of the inverse Hessian. Setting the rank number equal to the number of iterations makes this solution efficient and memory-affordable even for large-scale problems. Furthermore, based on the Gauss–Newton method, we formulate different initial, diagonal Hessian matrices as pre-conditioners for the inverse scheme and compare their performances in elastic FWI applications. We highlight our approach with the elastic Marmousi benchmark model, demonstrating the applicability of pre-conditioned BFGS for large-scale FWI and uncertainty quantification.

58 GEOSCIENCES↗

DOE OSTI2020

ROM-Based Surrogate Systems Modeling of EBR-II

We report the System Analysis Module (SAM), developed and maintained by Argonne National Laboratory, is designed to provide whole-plant transient safety analysis capabilities for a number of advanced non-light water reactors, including sodium-cooled fast reactor (SFR), lead-cooled fast reactor (LFR), and molten salt reactor (MSR)/fluoride-salt-cooled high-temperature reactor (FHR) designs. SAM is primarily constructed as a systems-level analysis tool, with the potential to incorporate reduced order models from three-dimensional computational fluid dynamics (CFD) simulations to improve characterization of complex, multidimensional physics. It is recognized that the computational expense associated with CFD can be intractable for various engineering analyses, such as uncertainty quantification, inference, and design optimization. This paper explores the reducibility of a SAM model using recent advances in randomized linear algebra techniques, which attempt to find recurring patterns in the various realizations generated by a model after randomly perturbing all its input parameters. The reduction is described in terms of fewer degrees of freedom (DOFs), referred to as the active DOFs, for the model variables such as input model parameters and model responses. The results indicate that there is significant room for additional reduction that may be leveraged for additional computational gains when employing SAM for engineering-intensive analyses that require repeated model executions. Different from physics-based reduction approaches, the proposed approach allows one to estimate upper bounds on the reduction errors, which are rigorously developed in this work. Finally, different methods for surrogate model construction, such as regression and neural network-based training, are employed to correlate the input and output active DOFs, which are related back to the original variables using matrix-based linear transformations.

42 ENGINEERING↗

DOE OSTI2024

Distributionally Robust Variational Quantum Algorithms With Shifted Noise

Given their potential to demonstrate near-term quantum advantage, variational quantum algorithms (VQAs) have been extensively studied. Although numerous techniques have been developed for VQA parameter optimization, it remains a significant challenge. A practical issue is the high sensitivity of quantum noise to environmental changes, and its propensity to shift in real time. This presents a critical problem as an optimized VQA ansatz may not perform effectively under a different noise environment. For the first time, we explore how to optimize VQA parameters to be robust against unknown shifted noise. We model the noise level as a random variable with an unknown probability density function (PDF), and we assume that the PDF may shift within an uncertainty set. This assumption guides us to formulate a distributionally robust optimization problem, with the goal of finding parameters that maintain effectiveness under shifted noise. We utilize a distributionally robust Bayesian optimization solver for our proposed formulation. This provides numerical evidence in both the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE) with hardware-efficient ansatz, indicating that we can identify parameters that perform more robustly under shifted noise. We regard this work as the first step towards improving the reliability of VQAs influenced by real-time noise.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

High-resolution leaf area index maps generated from unoccupied aerial system, Teller Mile 27, Seward Peninsula, Alaska

Leaf area index (LAI), a measure of the amount of one-side leaf area per ground unit, is an important indicator of plant carbon, energy, and water cycle. In the heterogeneous Arctic landscapes, it has been challenging to accurately measure LAI across species and space needed for Earth system model validation. Here, we use multispectral unoccupied aerial systems (UASs) to scale up and map leaf area index (LAI) , in a low-Arctic tundra landscape on the Seward Peninsula, Alaska. We linked previous published LAI measurements with high-resolution, UAS-collected multispectral data collected over the region of Next Generation Ecosystem Experiments in the Arctic (NGEE Arctic)’s Teller Mile Maker 27 site in 2022 to develop random forest (RF) machine learning models to predict and map LAI. 100 RF models were developed to account for uncertainties in ground LAI plot measurements and process scaling. This dataset includes a raster (*.tif) map of the mean LAI value of the 100 RF models, a raster (*.tif) map of the standard deviation of the RF-modeled LAI data, and a user guide (*.pdf).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

How to estimate soil organic carbon stocks of agricultural fields? perspectives using ex-ante evaluation

Estimating soil organic carbon (SOC) stocks of agricultural fields has a range of important applications from development of sustainable management practices to monitoring carbon stocks. There are many estimation strategies with the potential for more reliable estimates of SOC stock and more efficient use of soil sampling and analysis resources, especially by leveraging readily available auxiliary information such as remote sensing. However, concrete guidance for strategy selection is lacking. This study narrows this gap with a comparison of strategies for estimating deep SOC stock (0–60 cm) in a prototypical field. Using high density SOC stock measurements and simulation, we built on past studies by 1) ex-ante evaluating a large number of strategy options, 2) using a Bayesian approach to quantify the uncertainty of the comparison, and 3) considering multiple Bayesian models to assess sensitivity to this modeling choice. We found that, using readily available auxiliary information, both balanced and stratified sampling offer substantial improvements over simple random sampling. The auxiliary information most important for this improvement is a Sentinel-2 SOC index = blue / (green × red), followed by the topographic wetness index. We found that these results are robust to the choice of mapping method, but that there is uncertainty in the magnitude of improvement. Here, we recommend future studies implement this Bayesian approach for simulated ex-ante evaluation of SOC stock estimation strategies across more fields to investigate the generalizability of these findings.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Computational materials reliability assessment of hydrogen fueled gas turbine power generation engines

The use of blended fuel sources in land based gas turbine engines drives variations in the resulting operational profile (temperatures and pressures) which can impact engine reliability. Furthermore, variability in the manufacture of components affects the resulting microstructure which directly impacts material performance and reliability. Currently, data-driven models are typically used for maintaining and inspecting fleets of engines. Without explicitly capturing material and operational sources of variability conservatism must be used in developing component-level reliability models. Therefore, there exists an opportunity to use information from materials-scale physics models to better inform reliability modeling and reduce conservatism; the impact is more cost-efficient operation and maintenance of current and future fleets. Specifically, this work establishes a computational framework for evaluating the probabilistic high temperature creep performance of hot-section Ni-based superalloys where uncertainty comes from both microstructural and operational variability. A novel high-fidelity physics model which phenomenologically captures grain-boundary sensitive phenomena has been established. A probabilistic calibration procedure was used to calibrate the model and capture uncertainty in the parameterized model coefficients. A design of experiments methodology was established for identifying informative microstructural digital representations for suitable for forward model evaluation. Results show that training a machine-learning surrogate using this design criteria outperforms random selection of microstructural representations. Finally, two surrogate models were developed: (1) a deterministic surrogate model which predicts the local field response given microstructure, constitutive model parameters, and operating conditions (stress, temperature) and (2) a probabilistic model, where uncertainty comes from constitutive law uncertainty, built using denoising diffusion probabilistic models which samples responses given (1) microstructure and (2) operating conditions. These surrogate models enable partner Siemens Energy to rapidly perform UQ analysis specific to creep deformation across a range of microstructures and operating conditions. The impact is that these ML and physics codes can be used to establish more advanced reliability models for the inspection, servicing, and maintenance of land based gas turbine engines.

36 MATERIALS SCIENCE↗

DOE OSTI2020

UQpy: A general purpose Python package and development environment for uncertainty quantification

In this paper, we present the UQpy software toolbox, an open-source Python package for general uncertainty quantification (UQ) in mathematical and physical systems. The software serves as both a user-ready toolbox that includes many of the latest methods for UQ in computational modeling and a convenient development environment for Python programmers advancing the field of UQ. The paper presents an introduction to the software's architecture and existing capabilities, divided in the code in a set of modules centered around different UQ tasks such as sampling methods, generation of random processes and random fields, probabilistic inverse modeling, reliability analysis, surrogate modeling, and active learning. The paper also highlights the importance of the RunModel module, which is used to drive simulations in the uncertainty analyses performed in UQpy. This module conveniently allows the user to define computational models directly in Python, or to run simulations from a third-party software in serial or in parallel. To illustrate the various capabilities, two examples are tracked throughout the paper and analyzed repeatedly for various UQ tasks. The first is a Python model solving a nonlinear structural dynamics problem, used to illustrate UQpy's capabilities in sampling and forward propagation of high dimensional random vectors (stochastic processes), and probabilistic inference. The second model is a third-party Abaqus finite element model solving the thermomechanical response of a beam structure. This example is used to illustrate UQpy's capabilities in variance reduction sampling techniques, reliability analysis, surrogate modeling and active learning techniques.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling

Abstract. Uncertainties in an output of interest that depends on the solution of a complex system (e.g., of partial differential equations with random inputs) are often, if not nearly ubiquitously, determined in practice using Monte Carlo (MC) estimation. While simple to implement, MC estimation fails to provide reliable information about statistical quantities (such as the expected value of the output of interest) in application settings such as climate modeling, for which obtaining a single realization of the output of interest is a costly endeavor. Specifically, the dilemma encountered is that many samples of the output of interest have to be collected in order to obtain an MC estimator that has sufficient accuracy – so many, in fact, that the available computational budget is not large enough to effect the number of samples needed. To circumvent this dilemma, we consider using multifidelity Monte Carlo (MFMC) estimation which leverages the use of less costly and less accurate surrogate models (such as coarser grids, reduced-order models, simplified physics, and/or interpolants) to achieve, for the same computational budget, higher accuracy compared to that obtained by an MC estimator – or, looking at it another way, an MFMC estimator obtains the same accuracy as the MC estimator at lower computational cost. The key to the efficacy of MFMC estimation is the fact that most of the required computational budget is loaded onto the less costly surrogate models so that very few samples are taken of the more expensive model of interest. We first provide a more detailed discussion about the need to consider an alternative to MC estimation for uncertainty quantification. Subsequently, we present a review, in an abstract setting, of the MFMC approach along with its application to three climate-related benchmark problems as a proof-of-concept exercise.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Uncertainty-aware mixed-variable machine learning for materials design

Abstract Data-driven design shows the promise of accelerating materials discovery but is challenging due to the prohibitive cost of searching the vast design space of chemistry, structure, and synthesis methods. Bayesian optimization (BO) employs uncertainty-aware machine learning models to select promising designs to evaluate, hence reducing the cost. However, BO with mixed numerical and categorical variables, which is of particular interest in materials design, has not been well studied. In this work, we survey frequentist and Bayesian approaches to uncertainty quantification of machine learning with mixed variables. We then conduct a systematic comparative study of their performances in BO using a popular representative model from each group, the random forest-based Lolo model (frequentist) and the latent variable Gaussian process model (Bayesian). We examine the efficacy of the two models in the optimization of mathematical functions, as well as properties of structural and functional materials, where we observe performance differences as related to problem dimensionality and complexity. By investigating the machine learning models’ predictive and uncertainty estimation capabilities, we provide interpretations of the observed performance differences. Our results provide practical guidance on choosing between frequentist and Bayesian uncertainty-aware machine learning models for mixed-variable BO in materials design.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Flow-driven spectral chaos (FSC) method for simulating long-time dynamics of arbitrary-order non-linear stochastic dynamical systems

Uncertainty quantification techniques such as the time-dependent generalized polynomial chaos (TD-gPC) use an adaptive orthogonal basis to better represent the stochastic part of the solution space (aka random function space) in time. However, because the random function space is constructed using tensor products, TD-gPC-based methods are known to suffer from the curse of dimensionality. Here, we introduce a new numerical method called the flow-driven spectral chaos (FSC) which overcomes this curse of dimensionality at the random-function-space level. The proposed method is not only computationally more efficient than existing TD-gPC-based methods but is also far more accurate. The FSC method uses the concept of enriched stochastic flow maps to track the evolution of a finite-dimensional random function space efficiently in time. To transfer the probability information from one random function space to another, two approaches are developed and studied herein. In the first approach, the probability information is transferred in the mean-square sense, whereas in the second approach the transfer is done exactly using a new theorem that was developed for this purpose. The FSC method can quantify uncertainties with high fidelity, especially for the long-time response of stochastic dynamical systems governed by ODEs of arbitrary order. Six representative numerical examples, including a nonlinear problem (the Van-der-Pol oscillator), are presented to demonstrate the performance of the FSC method and corroborate the claims of its superior numerical properties. Finally, a parametric, high-dimensional stochastic problem is used to demonstrate that when the FSC method is used in conjunction with Monte Carlo integration, the curse of dimensionality can be overcome altogether.

(nonlinear) stochastic dynamical systems↗