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At least 379 records · Page 21

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

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

97 MATHEMATICS AND COMPUTING↗

A multistage distributionally robust optimization approach to water allocation under climate uncertainty

This paper investigates a Multistage Distributionally Robust Optimization (MDRO) approach to water allocation under climate uncertainty. The MDRO is formed by creating sets of conditional distributions (called conditional ambiguity sets) on a finite scenario tree. The distributions in the conditional ambiguity sets remain close to a nominal conditional distribution according a ø-divergence (e.g., Kullback-Leibler divergence, Hellinger distance, Burg entropy, etc.). Here, the paper discusses a decomposition algorithm to solve the resulting MDRO with ø-divergences, which uses the dual formulation and solves only linear subproblems instead of convex ones. Some properties of the algorithm such as generating feasible policies and valid upper/lower bounds are established. The paper then applies the modeling and solution techniques to allocate water in a rapidly-developing area of Tucson, Arizona. Tucson, like many arid and semi-arid regions around the world, faces considerable uncertainty in its ability to provide water for its citizens in the future. The primary sources of uncertainty in the Tucson region include (1) unpredictable population growth, (2) the availability of water from the Colorado River, and (3) the effects of climate variability on water consumption. This paper integrates forecasts for all these sources of uncertainty into a single optimization model for robust and sustainable water allocation. Then, it uses this model to analyze the value of constructing additional treatment facilities to reduce future water shortages. The results indicate that the MDRO approach can be very valuable for water managers by providing insights to minimize their risks and help them plan for the future.

54 ENVIRONMENTAL SCIENCES↗

Uncertainty analysis for techno-economic and life-cycle assessment of wet waste hydrothermal liquefaction with centralized upgrading to produce fuel blendstocks

Wet waste hydrothermal liquefaction is a promising technology for producing transportation fuels with much lower greenhouse gases emissions than petroleum-based fuels. However, its techno-economic and life cycle assessment are primarily based on laboratory scale testing data, subject to considerable uncertainties, and even bias, due to knowledge gaps. Here, a preliminary uncertainty analysis of key economic measures was conducted based on the 2019 state-of-technology model for biocrude production. Building on the preliminary analysis, this work presents a comprehensive uncertainty analysis in both economic and environmental measures of the entire supply chain of wet waste hydrothermal liquefaction to fuel blendstocks including biocrude upgrading based on the 2021 state-of-technology model. The analysis includes the most recent developments in hydrothermal liquefaction and biocrude upgrading technologies and Monte Carlo simulation based on an integrated model system including an improved reactor yield model, reduced-order process model, discounted cash flow economic model and simplified life-cycle assessment model. The estimated biocrude yield ranges from 42.2% to 52.4% with a median of 47.3%. The estimated fuel yield ranges from 34.7% to 42.7% with a median of 38.7%. The estimated minimum fuel selling price ranges from $\$ $2.28/gge to $\$ $3.45/gge with a median of $\$ $2.80/gge. Relative to petroleum-derived diesel, the estimated reduction in supply chain greenhouse gas emissions ranges from 73.4% to 81.8% with a median of 77.7%. Compared to the 2019 state-of-technology analysis, a significant improvement in biocrude selectivity and economic measures and reduction in uncertainties were achieved due to the incorporation of additional continuous experimental data sets, technology development and de-risking, and improvement in model accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-resolution modeling of indoor radon exposure with uncertainty quantification in Utah

Indoor radon accounts for 37% of population-level exposure to ionizing radiation in the United States. However, radon metrics are typically reported at coarse spatial scales, potentially obscuring meaningful local variation. We developed a high-resolution modeling framework to estimate indoor radon concentrations across Utah while explicitly quantifying predictive uncertainty. A total of 19,497 residential radon measurements collected between 2006 and 2017 were combined with environmental and housing characteristics and analyzed using a geospatial neural network that accommodates spatial dependence and nonlinear associations. Predictions were generated on a uniform hexagonal grid at 0.73 km2 resolution (H3 level 8). Out-of-sample predictions aggregated to the H3 level 8 grid showed good agreement with observed concentrations (Pearson r=0.64), while household-level predictions exhibited more moderate agreement (r=0.45). The model produced well-calibrated uncertainty estimates, with 24.1% of held-out observations exceeding the predicted 75th-percentile threshold. Maps of predicted radon concentrations and the probability of exceeding the U.S. EPA action level of 148 Bq/m3 (4 pCi/L) revealed substantial fine-scale spatial heterogeneity that was not apparent in conventional coarse-resolution summaries, with greater local variability observed in densely monitored urban counties than in sparsely sampled regions. High-resolution radon models that explicitly quantify uncertainty provide a useful framework for characterizing the spatial distribution of indoor radon and identifying areas of elevated exceedance risk. These findings highlight the value of fine-scale monitoring data and uncertainty-aware modeling approaches for radon exposure assessment, environmental risk characterization, and radon-related health research.

Wu, Yunhan [ORNL] (ORCID:0000000178842994)↗

Uncertainty quantification for Joule heating processes in fibrous pore-resolved media

Joule heating (JH) is an energy-efficient and sustainable technique for heating materials. Its application for industrial heating, particularly, has been gaining attention due to its potential for increasing the yield of various chemical products. The process involves the use of heating elements (materials that are highly conductive electrically and thermally) to heat up other materials or substances. These conductors, however, can exhbit varying degrees of uncertainty due to non-linearities in their temperature-dependent properties, which could result in variable material behavior. In this work, we carry out uncertainty quantification (UQ) at the pore scale to describe the uncertainty of such materials. In so doing, we applied the non-intrusive polynomial chaos expansion (PCE) technique to quantify the uncertainty within the system. The steady state Joule heating equation was solved numerically at the pore scale mimicking conditions within a heating chamber for propane dehydrogenation, and various electro-thermal profiles were obtained. We also examined the effect of the number of sampling points (20 – 100) and order of the PCE coefficients (2 – 5) on the accuracy of the temperature evaluations. The results were then benchmarked with the standard Monte Carlo (MC) method. The average temperature of the 4th-order global PCE showed good agreement with the MC results (which were positively skewed). Orders greater than 4 gave an underestimation of the temperatures while predictions for the peak temperature improved as the number of sampling points increased.

Fagbemi, Samuel [ORNL] (ORCID:0000000236995025)↗

Uncertainty quantification for competing failure mechanisms in unidirectionally reinforced carbon–carbon composites

Microstructure-informed finite element models play a key role in the carbon–carbon composite design process. Variability in manufacturing process parameters and experimental limitations introduce model parameter uncertainty. This study quantifies the effect of model parameter uncertainty on transverse tensile fracture behavior and proposes a methodology to predict the failure mode based on competing microscale damage mechanisms. Finite element simulations incorporate fiber–matrix interface debonding with cohesive zones and matrix damage with a smeared crack band approach in a unidirectional carbon–carbon composite. Results from a variance-based global sensitivity analysis identifies interfacial and matrix damage parameters as the primary source of variability in fracture behavior. Sobol’ indices indicate that matrix and cohesive zone strengths contribute 94% of the variance in the effective ultimate stress. A local analysis elucidates the relationship between these constituent strength parameters and failure mode by estimating the probability of cohesive, matrix, and mixed-mode dominated failure. Based on the results for 4000 simulations, 93% exhibit mixed-mode or interfacial dominated failure, which underscores the crucial role of fiber–matrix interface debonding in the transverse tensile failure of carbon–carbon composites. These uncertainty quantification results facilitate more efficient model calibration and provide a framework for microstructure-informed failure predictions in the face of manufacturing-induced uncertainty.

36 MATERIALS SCIENCE↗

Unrecognized Sources of Uncertainties ( USU ) in Experimental Nuclear Data

Evaluated nuclear data uncertainties reported in the literature or archived in data libraries are often perceived as unrealistic, most often because they are thought to be too small. The impact of this issue in applied nuclear science has been discussed widely in recent years. Commonly suggested causes are: poor estimates of specific error components, neglect of uncertainty correlations, and overlooked known error sources. However, instances have been reported where very careful, objective assessments of all known error sources have been made with realistic error magnitudes and correlations provided, yet the resulting evaluated uncertainties still appear to be inconsistent with observed scatter of predicted mean values. These discrepancies might be attributed to significant unrecognized sources of uncertainty ( USU ) that limit the accuracy to which these physical quantities can be determined. The objective of our work reported herein has been to develop qualitative and quantitative procedures for revealing and including USU estimates in nuclear data evaluations involving experimental input data. This paper identifies several specific clues that can be explored by evaluators in identifying the existence of USU . It then describes numerical procedures we have introduced to generate quantitative estimates of USU magnitudes. Key requirements for these procedures to be viable are that sufficient numbers of data points be available, for statistical reasons, and that additional supporting information about the measurements be provided by the experimenters. Several realistic examples are described here to illustrate these procedures and demonstrate their outcomes and limitations. Our work strongly supports the view that USU is an important issue in nuclear data evaluation, with significant consequences for applications, and that this topic warrants further investigation by the nuclear science community.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Sensitivity of the simulation of passive neutron emission from UF 6 cylinders to the uncertainties in both 19 F(α,n) energy spectrum and thick target yield of 234 U in UF 6

Interest in safeguards verification measurements using passive thermal neutron counting to assay 235 U content in large 30B UF 6 canisters has grown in recent years. Here, the prohibitively high cost and impracticality of using reference 30B calibration cylinders extensively will likely make accurate simulations of increasing interest. Accuracy of the simulated response will define the confidence in the predicted response and the extent to which simulations can reasonably be relied upon. With 234 U driven 19 F(α, n) reactions being the main neutron source in low enriched UF 6 the uncertainties of the 19 F(α, n) energy spectrum and the thick target yield of 234 U in UF 6 propagate into the uncertainty in the predicted response and represent a major influence of basic nuclear data. Here sensitivity of the simulated total (Singles) and coincidence (Doubles) count rates are assessed for the Passive Neutron Enrichment Meter using six potential 19 F(α, n) neutron energy spectra over a range of enrichments and material distributions. The results indicate that variations in the Singles and Doubles due to simulated (α, n) neutron spectrum are less than 1.5% for this set of simulated neutron spectra, with dependence varying inversely with enrichment. Singles uncertainty is only slightly less than that of the thick target 19 F(α, n) yield corresponding to the primary neutron source, whereas the 19 F(α, n) yield dependence of the Doubles is reduced by the non-negligible 238 U(SF) coincident neutron emissions. Based on available thick target 19 F(α, n) yield estimates the uncertainty is on the order of 5%, establishing this as the main nuclear data limitation when simulating thermal neutron detectors response for 30B UF 6 storage cylinders. Based on these findings, it appears that the measurement and evaluation of the thick target 19 F(α, n) yield for uranium hexafluoride is due.

19F(α,n) neutron spectrum↗

Uncertainty analysis of PIV measurements in bubbly flows considering sampling and bubble effects with ray optics modeling

In this report, a modeling-based approach is developed to investigate the external sources of uncertainty in particle image velocimetry (PIV) measurements for two-phase bubbly flows. Primarily relied on ray optics modeling, this study focuses on the uncertainty in PIV measurements due to bubble-induced light distortion. In addition, the uncertainty due to sampling is also considered through synthetic PIV images generated from Monte Carlo sampling. Based on a PIV-planar laser induced florescence (PLIF) measurement system, three case studies are performed and discussed, considering respectively the sampling effect, bubble effect, and the combination of these two effects. These case studies confirm the validity of the ray optics modeling in obtaining accurate particle images through a benchmark test. Furthermore, it is also found that the bubble effect could significantly influence the particle images. On the other hand, the result of the case study with synthetic PIV images indicates that the bubble effect on particle images can be minimized by removing “outliers” in the obtained velocity vector field through a multi-pass post-processing procedure. However, the uncertainty of the velocity measurements will still increase.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

On the uncertainty of estimating photovoltaic soiling using nearby soiling data

The accumulation of dust on the surface of photovoltaic modules can reduce their performance and affect the cost competitiveness of this technology. This phenomenon is known as soiling and can be mitigated through appropriate corrective and/or preventive actions. In order to maximize its effectiveness, it is important to plan the soiling mitigation strategy even before the PV system is operational. This is typically done through a nearest neighbor approach, by estimating soiling using data from the nearest operational photovoltaic system. This work focuses on understanding the uncertainty related to this practice. For this purpose, the semi-variance function is used to study the dissimilarity between the soiling losses of two locations in California depending on their distance. The results show that, when the soiling loss at a nearby system is used to estimate soiling of a site, the uncertainty can be approximated to increase linearly at a rate of 0.08-0.10%/km up to 60 or 80 km. After this distance, the use of a nearest neighbor approach is no longer justified, as it produces an uncertainty as big as the average soiling loss of the sites in the dataset used in this study. In some conditions, uncertainties > 0% are found also for sites located within 25 km, meaning that even close-by systems might soil differently.

14 SOLAR ENERGY↗

Optimization problems governed by systems of PDEs with uncertainties

This paper reviews current theoretical and numerical approaches to optimization problems governed by partial differential equations (PDEs) that depend on random variables or random fields. Such problems arise in many engineering, science, economics and societal decision-making tasks. This paper focuses on problems in which the governing PDEs are parametrized by the random variables/fields, and the decisions are made at the beginning and are not revised once uncertainty is revealed. Examples of such problems are presented to motivate the topic of this paper, and to illustrate the impact of different ways to model uncertainty in the formulations of the optimization problem and their impact on the solution. A linear–quadratic elliptic optimal control problem is used to provide a detailed discussion of the set-up for the risk-neutral optimization problem formulation, study the existence and characterization of its solution, and survey numerical methods for computing it. Different ways to model uncertainty in the PDE-constrained optimization problem are surveyed in an abstract setting, including risk measures, distributionally robust optimization formulations, probabilistic functions and chance constraints, and stochastic orders. Furthermore, approximation-based optimization approaches and stochastic methods for the solution of the large-scale PDE-constrained optimization problems under uncertainty are described. Some possible future research directions are outlined.

Heinkenschloss, Matthias [Rice Univ., Houston, TX ↗

Lightning Interferometry Uncertainty, Beam Steering Interferometry, and Evidence of Lightning Being Ignited by a Cosmic Ray Shower

Abstract We present an uncertainty analysis on correlation‐based time delay estimate, the basis for broadband lightning interferometry. A normal interferometry would yield much higher uncertainties than the theoretically predicted lower bound due to finite correlation window lengths. However, if the signals are aligned in time, the uncertainties approach the lower bound and can be used to indicate the interferometric uncertainties. Based on this, we introduce a beam steering interferometry technique. It first estimates a direction centroid for the lightning sources with a normal interferometry and computes the time delays among the signals. It then shifts the raw data with the time delays to align the signals roughly in time and reprocess the aligned signals. It finally pushes the reprocessed results to their correct positions, based on the time delays estimated in the first step. We apply this technique on a fast positive breakdown (FPB) process that started a normal intracloud lightning. The FPB process is shown to have a much more complex structure and development than a normal interferometry would provide. More importantly, from both interferometric and polarization analyses, the FPB appears to be ignited by a cosmic ray shower (CRS). We estimate the radio frequency strength and frequency content related to a presumed CRS in a thunderstorm electric field and find that they are in agreement with the observations. We examine the electric field effect of the CRS front and find that it could raise the field above the threshold for positive breakdown and is capable of igniting the FPB (and the lightning).

Shao, Xuan‐Min↗

Exploiting SMILEs and the CMIP5 Archive to Understand Arctic Climate Change Seasonality and Uncertainty

Arctic Amplification (AA) exhibits a distinct seasonal dependence; it is weakest in boreal summer and strongest in winter. Here, we analyze simulations from single-model initial-condition large ensembles and Coupled Model Intercomparison Project Phase 5 to decipher the seasonal evolution of Arctic climate change. Models agree that the annual maximum AA shifts from autumn into winter over the 21st century, accompanied by similar shifts in sea-ice loss and surface turbulent heat fluxes, whereas the maximum precipitation shifts only into late autumn. However, the exact seasonal timing and magnitude of these shifts are highly uncertain. Decomposing the uncertainty into model structural differences, emission scenarios, and internal variability reveals that model differences dominate the total uncertainty, which also undergo autumn-to-winter shifts. We also find that the scenario uncertainty is unimportant for projections of AA. These results highlight that understanding model differences is critical to reducing uncertainty in projected Arctic climate change.

54 ENVIRONMENTAL SCIENCES↗

A Framework for Parametric and Predictive Uncertainty Quantification in the E3SM Land Model: Assessing Site and Observable Generalizability

Quantifying parametric uncertainty using observations from individual sites provides a critical foundation for Earth system modeling, serving as a necessary first step before scaling up to regional or global applications. This study introduces a novel computational framework designed to enhance model predictability by reducing parametric uncertainty and assessing site and observable generalizability using various observational constraints. The framework integrates five components: Model Simulation, Statistical Emulation, Global Sensitivity Analysis (GSA), Model Calibration, and Model Prediction. Using the E3SM land model, we simulated site-level land-atmosphere carbon and energy fluxes from 2003 to 2007 across five evergreen needleleaf FLUXNET sites, perturbing 26 vegetation-related model parameters. Gaussian process emulators were employed to expedite GSA and model calibration. Four critical parameters that strongly influence selected land-atmosphere fluxes were identified by GSA. Bayesian approaches were used to infer parameter probability distributions leveraging synthetic data and FLUXNET observations. The results reveal that posterior parameter distributions vary significantly across different sites and observables within the same plant functional type. Probabilistic predictions indicate that parameters calibrated at one site can enhance predictive accuracy at other sites, although site heterogeneity may sometimes outweigh parametric uncertainty. Additionally, the probabilistic predictions demonstrate that calibration for one variable can also improve predictability for other variables, thereby maximizing predictive capabilities with limited observations. This framework provides a powerful approach for reducing parametric uncertainty in Earth system models and deepening our understanding of carbon dynamics and energy cycles. Its adaptability makes it a valuable tool for broader applications in Earth system modeling.

54 ENVIRONMENTAL SCIENCES↗

Uncertainty in El Niño-like warming and California precipitation changes linked by the Interdecadal Pacific Oscillation

Abstract Marked uncertainty in California (CA) precipitation projections challenges their use in adaptation planning in the region already experiencing severe water stress. Under global warming, a westerly jet extension in the North Pacific analogous to the El Niño-like teleconnection has been suggested as a key mechanism for CA winter precipitation changes. However, this teleconnection has not been reconciled with the well-known El Niño-like warming response or the controversial role of internal variability in the precipitation uncertainty. Here we find that internal variability contributes > 70% and > 50% of uncertainty in the CA precipitation changes and the El Niño-like warming, respectively, based on analysis of 318 climate simulations from several multi-model and large ensembles. The Interdecadal Pacific Oscillation plays a key role in each contribution and in connecting the two via the westerly jet extension. This unifying understanding of the role of internal variability in CA precipitation provides critical guidance for reducing and communicating uncertainty to inform adaptation planning.

54 ENVIRONMENTAL SCIENCES↗

Vegetation biogeography is a main source of uncertainty in modelling the land carbon cycle

The terrestrial biosphere exchanges a large amount of CO 2 with the atmosphere through photosynthesis and respiration, determining the magnitude of land carbon sink and consequently influencing the rate of global warming. The magnitudes of global photosynthesis and respiration, however, vary widely across models (100-200 PgC/year), constituting a key and persistent source of uncertainty in carbon cycle and climate modelling. Here, we argue that the uncertainty in the land carbon cycle modelling is largely attributable to the uncertainty in biogeography – the distribution of plant functional types (PFTs). Using an ensemble of dynamic global vegetation models (DGVMs), we find a strong dependence of total photosynthesis on total area for each PFT. The dependence allows us to reduce the spread of land carbon cycle estimates by ~75% using remote sensing-based PFT maps. We further find that 56 ± 21% of climate-driven changes in global photosynthesis modelled by DGVMs are caused by changes in PFT distribution in the last two decades. Our study identifies vegetation biogeography as a main controlling factor of uncertainty in land carbon cycle modelling and highlights the importance of biogeography-climate interactions in carbon cycle and climate studies.

Zhao, Ruiying [National Univ. of Singapore (Singap↗

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↗

Uncertainty-driven dynamics for active learning of interatomic potentials

Machine learning (ML) models, if trained to data sets of high-fidelity quantum simulations, produce accurate and efficient interatomic potentials. Active learning (AL) is a powerful tool to iteratively generate diverse data sets. In this approach, the ML model provides an uncertainty estimate along with its prediction for each new atomic configuration. If the uncertainty estimate passes a certain threshold, then the configuration is included in the data set. Here we develop a strategy to more rapidly discover configurations that meaningfully augment the training data set. The approach, uncertainty-driven dynamics for active learning (UDD-AL), modifies the potential energy surface used in molecular dynamics simulations to favor regions of configuration space for which there is large model uncertainty. The performance of UDD-AL is demonstrated for two AL tasks: sampling the conformational space of glycine and sampling the promotion of proton transfer in acetylacetone. The method is shown to efficiently explore the chemically relevant configuration space, which may be inaccessible using regular dynamical sampling at target temperature conditions.

97 MATHEMATICS AND COMPUTING↗