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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

WE-FG-206-08: Pulmonary Functional Imaging Biomarkers of NSCLC to Guide and Optimize Functional Lung Avoidance Radiotherapy

Purpose: Functional lung avoidance radiotherapy promises optimized therapy planning by minimizing dose to well-functioning lung and maximizing dose to the rest of the lung. Patients with NSCLC commonly present with co-morbid COPD and heterogeneously distributed ventilation abnormalities stemming from emphysema, airways disease, and tumour burden. We hypothesized that pulmonary functional imaging methods may be used to optimize radiotherapy plans to avoid regions of well-functioning lung and significantly improve outcomes like quality-of-life and survival. To ascertain the utility of functional lung avoidance therapy in clinical practice, we measured COPD phenotypes in NSCLC patients enrolled in a randomized-controlled-clinical-trial prior to curative intent therapy. Methods: Thirty stage IIIA/IIIB NSCLC patients provided written informed consent to a randomized-controlled-clinical-trial ( http://clinicaltrials.gov/ct2/show/NCT02002052 ) comparing outcomes in patients randomized to standard or image-guided radiotherapy. Hyperpolarized noble gas MRI ventilation-defect-percent (VDP) (Kirby et al, Acad Radiol, 2012) as well as CT-emphysema measurements were determined. Patients were stratified based on quantitative imaging evidence of ventilation-defects and emphysema into two subgroups: 1) tumour-specific ventilation defects only (TSD), and, 2) tumour-specific and other ventilation defects with and without emphysema (TSD{sub VE}). Receiver-operating-characteristic (ROC) curves were used to characterize the performance of clinical measures as predictors of the presence of non-tumour specific ventilation defects. Results: Twenty-one out of thirty subjects (70%) had non-tumour specific ventilation defects (TSD{sub VE}) and nine subjects had ONLY tumour-specific defects (TSD). Subjects in the TSD{sub VE} group had significantly greater smoking-history (p=.006) and airflow obstruction (FEV{sub 1}/FVC) (p=.001). ROC analysis demonstrated an 87% classification rate for smoking pack-years, 90% for FEV{sub 1}/FVC, and 56% for tumour RECIST measurements for identifying patients with non-tumour and tumour-specific ventilation abnormalities. Conclusion: 70% of NSCLC patients had ventilation abnormalities stemming from emphysema, airways disease and tumour burden. Smoking-history and airflow obstruction, but not RECIST, identified NSCLC patients with ventilation abnormalities appropriate for functional lung avoidance therapy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Laser Confocal Microscopy Uncertainty Quantification Study

At Los Alamos National Laboratory (LANL), the Storage Safety and Engineering (SSE) team completes annual surveillance on a subset of in-use interim nuclear material storage containers in fulfilment of requirements outlined in DOE Manual M 441.1-1. The containers are selected through several methods, such as subject matter expert judgement, random selection, and trending items. Following these selections, the SSE team has the capacity to complete surveillance on 15-20 containers each fiscal year, composed of a combination of SAVY-4000 and Hagan storage containers. Through previous work, the stainless-steel components of the containers have been identified as life limiting components, with an emphasis on the thin-walled bodies. The team is focused on understanding the extent of general and pitting corrosion, due to observations of extensive corrosion from stored contents and bag-out-bag degradation. Quantifying corrosion effects on the thin-walled stainless steel container bodies, and understanding potential impacts to the respective design release rates and design qualification release rates is paramount to the team. To date, destructive examination (DE) has proven to be the most insightful method for developing an understanding on the extent of corrosion on used containers. To standardize this process, the SSE team developed a destructive examination guide for analyzing stainless steel components of the containers. Corroded containers of interest are identified during surveillance activities and set aside for sectioning and characterization. Following sectioning, a major step in the DE workflow is the utilization of laser confocal microscopy for scanning corroded samples of interest and extracting data on pits, such as count, depth, and equivalent diameter. Adhering to the techniques outlined in the DE guide, analysis has been completed on two Hagans and one SAVY-4000 container, with the maximum pit depth recorded as 139.1 ± 22.82 μm on a 17.5 year old Hagan. The findings from the completed destructive examinations will be utilized to support lifetime extension efforts of the SAVY-4000 as the team can better estimate corrosion rates and effects over time based on stored contents and age. Due to the implications of observing extreme pit depths that approach the nominal container body thickness of .0299 inches (0.759 mm) or minimum container thickness of 0.236” (0.6 mm), high confidence in the LCM measurements is desired. Through testing outlined in, it was concluded that the total error ascribed to the 20x objective when conducting large image mapping on the Keyence VK-X3050 laser confocal microscope (LCM) relative to a 50x objective (reference) is 16.4% (± 8.73%). For shallow features on the order of pristine SAVY surface defects (i.e. 5 μm), this uncertainty is appropriate. However, this conservative estimate of total error poses a fundamental concern for pit depths that approach the thickness of the measured samples. That is, with the measurement uncertainty currently employed on all measurements, the LCM would be unable to resolve if a pit with a depth of 515 μm is through wall. Standard step height samples were procured and used in the present study to assess the resolution and repeatability of height measurements. Understanding the resolution and repeatability of height measurements was the first focus of the team as it relates directly to pit depth, which is of primary concern. Calibration gratings were procured to evaluate the resolution and repeatability of measurements in the X and Y axes of the LCM stage. The results of the depth uncertainty study were conducted first and presented in the subsequent sections. The planar uncertainty study is appended to the depth study with conclusions from both summarized at the end of the report.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Machine learning based job status prediction in scientific clusters

Large high-performance computing systems are built with increasing number of components with more CPU cores, more memory, and more storage space. At the same time, scientific applications have been growing in complexity. Together, they are leading to more frequent unsuccessful job statuses on HPC systems. From measured job statuses, 23.4% of CPU time was spent to the unsuccessful jobs. Here, we set out to study whether these unsuccessful job statuses could be anticipated from known job characteristics. To explore this possibility, we have developed a job status prediction method for the execution of jobs on scientific clusters. The Random Forests algorithm was applied to extract and characterize the patterns of unsuccessful job statuses. Experimental results show that our method can predict the unsuccessful job statuses from the monitored ongoing job executions in 99.8% the cases with 83.6% recall and 94.8% precision. Lastly, this prediction accuracy can be sufficiently high that it can be used to mitigation procedures of predicted failures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Optimal Energy Management for Microgrid with Stationary and Mobile Storage

This paper studies energy management in a Microgrid (MG) with solar generation, Battery Energy Management System (BESS) and gridable (V2G) EVs. A two-stage stochastic optimization method is proposed to capture the intermittent solar generation and random EV user behaviors. It is subsequently formulated as a Mixed Integer Linear Programming (MILP) problem. To evalutate the proposed method, real solar generation, loads, BESS and EV data is used in Sample Average Approximation (SAA). Computational results show the correctness of the proposed method as well as steady and tightly bounded optimality gap. Comparisons demonstrate that the proposed stochastic method outperforms its deterministic counterpart at the expense of higher computational cost. It is also observed that moderate number of EVs helps to reduce the overall operational cost of the MG, which sheds light on future EV integration to the smart grid.

Battery Energy Management System (BESS)↗
DOE OSTI2023

Projective Hedging Algorithms for Multistage Stochastic Programming, Supporting Distributed and Asynchronous Implementation

Here we propose a decomposition algorithm for multistage stochastic programming that resembles the progressive hedging method of Rockafellar and Wets but is provably capable of several forms of asynchronous operation. We derive the method from a class of projective operator splitting methods fairly recently proposed by Combettes and Eckstein, significantly expanding the known applications of those methods. Our derivation assures convergence for convex problems whose feasible set is compact, subject to some standard regularity conditions and a mild “fairness” condition on subproblem selection. The method’s convergence guarantees are deterministic and do not require randomization, in contrast to other proposed asynchronous variations of progressive hedging. Computational experiments described in an online appendix show the method to outperform progressive hedging on large-scale problems in a highly parallel computing environment.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Predicting the Effect of Single and Multiple Mutations on Protein Structural Stability

Predicting how a point mutation alters a protein’s stability can guide pharmaceutical drug design initiatives which aim to counter the effects of serious diseases. Conducting mutagenesis studies in physical proteins can give insights about the effects of amino acid substitutions, but such wet-lab work is prohibitive due to the time as well as financial resources needed to assess the effect of even a single amino acid substitution. Computational methods for predicting the effects of a mutation on a protein structure can complement wet-lab work, and varying approaches are available with promising accuracy rates. In this work we compare and assess the utility of several machine learning methods and their ability to predict the effects of single and double mutations. We in silico generate mutant protein structures, and compute several rigidity metrics for each of them. We use these as features for our Support Vector Regression (SVR), Random Forest (RF), and Deep Neural Network (DNN) methods. We validate the predictions of our in silico mutations against experimental ΔΔG stability data, and attain Pearson Correlation values upwards of 0.71 for single mutations, and 0.81 for double mutations. We perform ablation studies to assess which features contribute most to a model’s success, and also introduce a voting scheme to synthesize a single prediction from the individual predictions of the three models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Stochastic Modeling in a Multimaterial Continuum Mixture Shock Physics Code

Stochastic modelling approaches are presented to capture random effects at multiple time and length scales. Random processes that occur at the microscale produce nondeterministic effects at the macroscale. Here we present three stochastic modeling approaches that describe random processes at microscopic length scales and map these processes to the macroscopic length scale. The first stochastic modeling approach is based upon a particle based numerical technique to solve a Stochastic Differential Equation (SDE) using an arbitrary diffusion process to capture random processes at the microstructural level. The second approach prescribes a Probability Density Function (PDF) for the drift and diffusion of the random variable derived using the forward and backward Kolmogorov equations. This method requires mean and drift evolution PDF transport equations. The third approach is the coupling of multiple random variables which are dependent on each other. The relationship of the PDFs and a coupling function, known as a copula, produces a Joint Probability Density Function (JPDF). These stochastic modeling approaches are implemented into a Multiple Component (MC) shock physics computational code and used to model statistical fracture and reactive flow applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Rigorous Data Fusion for Computationally Expensive Simulations

This manuscript comprises the final report for the 1-year, FY19 LDRD project "Rigorous Data Fusion for Computationally Expensive Simulations," wherein an alternative approach to Bayesian calibration was developed based a new sampling technique called VoroSpokes. Vorospokes is a novel quadrature and sampling framework defined with respect to Voronoi tessellations of bounded domains in $R^d$ developed within this project. In this work, we first establish local quadrature and sampling results on convex polytopes using randomly directed rays, or spokes, to approximate the quantities of interest for a specified target function. A theoretical justification for both procedures is provided along with empirical results demonstrating the unbiased convergence in the resulting estimates/samples. The local quadrature and sampling procedures are then extended to global procedures defined on more general domains by applying the local results to the cells of a Voronoi tessellation covering the domain in consideration. We then demonstrate how the proposed global sampling procedure can be used to define a natural framework for adaptively constructing Voronoi Piecewise Surrogate (VPS) approximations based on local error estimates. Finally, we show that the adaptive VPS procedure can be used to form a surrogate model approximation to a specified, potentially unnormalized, density function, and that the global sampling procedure can be used to efficiently draw independent samples from the surrogate density in parallel. The performance of the resulting VoroSpokes sampling framework is assessed on a collection of Bayesian inference problems and is shown to provide highly accurate posterior predictions which align with the results obtained using traditional methods such as Gibbs sampling and random-walk Markov Chain Monte Carlo (MCMC). Importantly, the proposed framework provides a foundation for performing Bayesian inference tasks which is entirely independent from the theory of Markov chains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

van der Waals Correction to the Physisorption of Graphene on Metal Surfaces

Adsorption is a scientifically and technologically important interfacial phenomenon, which however presents challenges to conventional density functional theory (DFT) due to the long-range van der Waals (vdW) interactions. We have developed a model of long-range vdW correction for physisorption of graphene (G) on metals with the Lifshitz–Zaremba–Kohn second-order perturbation theory, by incorporating dipole- and quadrupole-surface interactions and screening effects. The physisorption energies calculated by the model between graphene and eight metal surfaces (Al, Ni, Co, Pd, Pt, Cu, Ag, and Au), and the adsorption energies for the same G/metal structures from self-consistent DFT PBE (Perdew–Burke–Ernzerhof) calculations, are obtained in a range of distances between G and the metal surfaces. The sum of these two parts is the total adsorption energy as a function of the distance, from which the equilibrium distance and the binding energy are determined simultaneously. The results show high accuracy, with the mean absolute error (MAE) of binding energy of 7 meV and the MAE of equilibrium distance of 0.2 Å, significantly improving upon other vdW methods. Here, the PBE + vdW binding energy curves give better fits to the random phase approximation curves around the equilibrium distances than do the curves of other methods considered here. The higher-order quadrupole-surface correction is important and accounts for about 30% of the total vdW correction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

A four‐alternative forced choice (4AFC) methodology for evaluating microcalcification detection in clinical full‐field digital mammography (FFDM) and digital breast tomosynthesis (DBT) systems using an inkjet‐printed anthropomorphic phantom

Purpose The advent of three‐dimensional breast imaging systems such as digital breast tomosynthesis (DBT) has great promise for improving the detection and diagnosis of breast cancer. With these new technologies comes an essential need for testing methods to assess the resultant image quality. Although randomized clinical trials are the gold standard for assessing image quality, phantom‐based studies can provide a simpler and less burdensome approach. In this work, a complete framework is presented for task‐based evaluation of microcalcification (MCs) detection performance for DBT imaging systems. Methods The framework consists of three parts. The first part is a realistic anthropomorphic physical breast phantom created through inkjet printing, with parchment paper and iodine‐doped ink. The second is a method for inserting realistic MCs fabricated from calcium hydroxyapatite. The reproducibility and stability of the phantom materials were investigated through multiple samples of parchment and ink over 6 months. The final part is an analysis using a four‐alternative forced choice (4AFC) reader study. To demonstrate the framework, a task‐based 4AFC study was conducted using a clinical system to compare performance from DBT, synthetic mammography (SM), and full‐field digital mammography (FFDM). Nine human observers read images containing MC clusters imaged with all three modalities and tried to correctly locate the MCs. The proportion correct (PC) was measured as the number of correctly detected clusters out of all trials. Results Overall, readers scored the highest with FFDM, (PC = 0.95 ± 0.03) then DBT (0.85 ± 0.04), and finally SM (0.44 ± 0.06). For the parchment and ink samples, the linear attenuation properties were very stable over 6 months. In addition, little difference was found between the various parchment and ink samples, indicating good reproducibility. Conclusions This framework presents a promising methodology for evaluating diagnostic task performance of clinical breast DBT systems.

Ikejimba, Lynda C.↗
DOE OSTI2022

A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Physics-informed neural networks (PINNs) have shown to be effective tools for solving both forward and inverse problems of partial differential equations (PDEs). PINNs embed the PDEs into the loss of the neural network using automatic differentiation, and this PDE loss is evaluated at a set of scattered spatio-temporal points (called residual points). The location and distribution of these residual points are highly important to the performance of PINNs. However, in the existing studies on PINNs, only a few simple residual point sampling methods have mainly been used. Here, we present a comprehensive study of two categories of sampling for PINNs: non-adaptive uniform sampling and adaptive nonuniform sampling. We consider six uniform sampling methods, including (1) equispaced uniform grid, (2) uniformly random sampling, (3) Latin hypercube sampling, (4) Halton sequence, (5) Hammersley sequence, and (6) Sobol sequence. We also consider a resampling strategy for uniform sampling. To improve the sampling efficiency and the accuracy of PINNs, we propose two new residual-based adaptive sampling methods: residual-based adaptive distribution (RAD) and residual-based adaptive refinement with distribution (RAR-D), which dynamically improve the distribution of residual points based on the PDE residuals during training. Hence, we have considered a total of 10 different sampling methods, including six non-adaptive uniform sampling, uniform sampling with resampling, two proposed adaptive sampling, and an existing adaptive sampling. We extensively tested the performance of these sampling methods for four forward problems and two inverse problems in many setups. Our numerical results presented in this study are summarized from more than 6000 simulations of PINNs. Here, we show that the proposed adaptive sampling methods of RAD and RAR-D significantly improve the accuracy of PINNs with fewer residual points for both forward and inverse problems. Furthermore, the results obtained in this study can also be used as a practical guideline in choosing sampling methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Random Alloyed versus Intermetallic Nanoparticles: A Comparison of Electrocatalytic Performance

As synthetic methods advance for metal nanoparticles, more rigorous studies of structure–function relationships can be made. Many electrocatalytic processes depend on the size, shape, and composition of the nanocatalysts. Here, the properties and electrocatalytic behavior of random alloyed and intermetallic nanoparticles are compared. Beginning with an introduction of metallic nanoparticles for catalysis and the unique features of bimetallic compositions, the discussion transitions to case studies of nanoscale electrocatalysts where direct comparisons of alloy and intermetallic compositions are undertaken for methanol electrooxidation, formic acid electrooxidation, the oxygen reduction reaction, and the electroreduction of carbon dioxide (CO2). Design and synthesis strategies for random alloyed and intermetallic nanoparticles are discussed, with an emphasis on Pt–M and Cu–M compositions as model systems. The differences in catalytic performance between alloys and intermetallic nanoparticles are highlighted in order to provide an outlook for future electrocatalyst design.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Delay-induced stochastic bifurcations in a bistable system under white noise

In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Long history of Cl-36 Assessment of Graphite Waste by EDF Engineering and the Latest Suggested Developments - 17043

Prior to 2005, the EDF initial version for the radiological inventory of graphite was based on the maximum values of the measures, namely a very pessimistic way. In 2008, a scientific method was developed by EDF to evaluate the inventory by reverse activation calculation, in order to limit the overestimation. The radiological inventory computation principles can be compared to those of all engineering studies. First, the calculation is simplified by taking margins, and if the results are not satisfactory enough, some simplifications are suppressed to reduce these margins even if computation becomes more complicated. On EDF piles, the gain obtained in 2008 represented a factor 50 relative to the initial version of Cl-36, even with a very penalizing multiplicative factor for uncertainty. Today, the accurate calculation of the uncertainty no longer justifies such a factor. A gain of about 150 now occurs compared to the initial version of Cl-36. It is more than 2 orders of magnitude, which is already enough to assess again the necessary type of disposal because Cl-36 is one of the key radionuclides. After global presentation of graphite waste management in France, the paper focuses on the inventory scientific process of EDF nuclear graphite, the purity of graphite and its consequences, its particular sampling, the lessons learned, the initial method description, the link with the demonstration of the completely random point process of chlorine in nuclear graphite and the last suggested precise uncertainty computation of inventory of Cl-36. The method confirmation for concentration assessment, the history of the EDF method development and its benefits are also emphasized. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2017

Comparison of Experimental Methods for Estimating Matrix Diffusion Coefficients for Contaminant Transport Modeling

Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2018

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

Here, diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

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↗