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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A critical review on additive manufacturing of refractory alloys from a data analytics perspective- beyond nickel-based superalloys

Refractory alloys (RAs) are promising materials due to their exceptional physicochemical properties, but most research remains at the laboratory scale. For broader adoption, advancements in manufacturing are essential. Because their high stability makes conventional methods like machining and casting difficult, additive manufacturing (AM) is emerging as an effective approach for fabricating refractory alloy components. However, AM's repeated non-equilibrium thermal cycles introduce undesired features (e.g. defects, anisotropic microstructures, and residual stresses), which are magnified due to RAs’ unique properties. This paper comprehensively reviews the state-of-the-art methods of AM for refractory alloys. It explores data analytics techniques to establish design rules based on multi-fidelity experimental and computational methods. Furthermore, it investigates integrated, collaborative efforts to harmonise standalone databases, information, knowledge, and predictive models at multi-physics, multi-stage, and multi-scale. Unlike the existing literature that focuses primarily on material systems or process fundamentals, this work provides an integrated perspective on AM of refractory alloys from a data analytics standpoint, highlighting the roles of integrated computational materials engineering (ICME), verification, validation, and uncertainty quantification (VV&UQ), and digital twin-driven qualification in overcoming data scarcity and accelerating rapid qualification.

Additive manufacturing↗
DOE OSTI2025

Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks

Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov-Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation. To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion (DTEKI) with Chebyshev KANs. This gradient-free method effectively mitigates overfitting and enhances numerical stability. In addition, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results show that the new method achieves comparable or better accuracy, much higher efficiency as well as stability compared to HMC, in addition to scalability. Moreover, by leveraging the low-dimensional parameter subspace, our method preserves prediction accuracy while substantially reducing further the computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Hierarchical Gaussian Random Field Sampling for Multilevel Markov Chain Monte Carlo: Coupling Stochastic Partial Differential Equation and the Karhunen–Loève Decomposition

This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRFs) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods, such as those based on stochastic partial differential equations (SPDEs), often reduce the dimensionality of the sample space at the cost of accuracy of inference. Other approaches, such that those based on Karhunen-Loève (KL) expansions, offer sample space dimensionality reduction but sacrifice GRF representation accuracy and ergodicity of the Markov chain Monte Carlo (MCMC) sampler and are computationally expensive for high-dimensional problems. The proposed method integrates the dimensionality reduction capabilities of KL expansions with the scalability of SPDE-based sampling, thereby providing a robust, unified framework for high-dimensional uncertainty quantification (UQ) that is scalable and accurate, preserves ergodicity, and offers dimensionality reduction of the sample space. The hierarchy in our multilevel algorithm is derived from the geometric multigrid hierarchy. By constructing a hierarchical decomposition that maintains the covariance structure across the levels in the hierarchy, the approach enables efficient coarse-to-fine sampling while ensuring that all samples are drawn from the desired distribution. The effectiveness of the proposed method is demonstrated on a benchmark subsurface flow problem, demonstrating its effectiveness in improving computational efficiency and statistical accuracy. Furthermore, our proposed technique is more efficient and accurate and displays better convergence properties than existing methods for high-dimensional Bayesian inference problems.

Gaussian random fields↗
DOE OSTI2025

Decurion

Predictive UQ for Time-Valued QoIs

Harmon, Jake J. [Los Alamos National Laboratory]↗
DOE OSTI2026

TSEUQLib

TSEUQLib (Taylor Series Expansion Uncertainty Quantification Library): Conduct UQ and sensitivity analysis with the Taylor series expansion surrogate model.

Balcer, Matthew↗
DOE OSTI2024

HydraGNN_Predictive_GFM_2024 - Ensemble of predictive graph foundation models for ground state atomistic materials modeling

We provide the ensemble of fifteen pre-trained graph foundation models (GFMs) for atomistic materials modeling applications. Each one of the fifteen GFMs has been trained on five open-source datasets that (once aggregated) amount to over 154 million atomistic structures, which cover over two-thirds of the natural elements of the periodic table and that comprises a broad set of organic and inorganic compounds. This vast set of atomistic structures comprises ground state configurations that are dynamically stable (i.e., equilibrated structures with atomic forces approximately close to zero values) as well as dynamically unstable structures (i.e., non-equilibrium structures with non-negligible non-zero values of atomic forces). The ensemble of datasets aggregated does NOT include excited states. The datasets have been curated to remove atomistic structures with spectral norm of the force tensor above 100 eV/angstrom. Moreover, a linear term of the energy was computed for each dataset using a linear regression model that uses the chemical concentration of each natural element as regressor. The linear term predicted by the linear regression model has been subtracted from each original energy value to perform a re-alignment of the energy values across different electronic structures approximation theories performed to generate the diverse multi-source, multi-fidelity datasets. The folder "ADIOS_files" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "ADIOS_files" directory contains 6 sub-directories named as follows: - ANI1x-v3.bp - MPTrj-v3.bp - OC2020-20M-v3.bp - OC2020-v3.bp - OC2022-v3.bp - qm7x-v3.bp Each sub-directory contains the pre-processed datasets converted in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used to the development, training, and performance testing of the ensemble go predictive graph foundation models. Each GFM was developed using HydraGNN (https://github.com/ORNL/HydraGNN) as underlying graph neural network (GNN) architecture. The multi-task learning (MTL) capability of HydraGNN was used to simultaneously train the GFMs on labeled values for direct predictions of energy (a total system property of an atomistic structure that measures the chemical stability) and atomic forces (an atomic level property of an atomistic structure that measures the dynamical stability). The hyper parameters of the GFM have been tuned using scalable hyperparameter optimization (HPO) algorithms implemented in the software DeepHyper (https://github.com/deephyper/deephyper). The pre-training of each HPO trial was performed using distributed data parallelism (DDP) to scale the training across 128 compute nodes of the exascale OLCF supercomputer Frontier. Each HPO trial was trained only for 10 epochs and an early stopping was performed to avoid wasting significant computational resources on GNN architectures that were clearly underperforming. For each HPO trial, the 'omnistat' tool developed by (AMD Research - Advanced Micro Device) was used to measure the total energy consumption in kWh. The ensemble of GFMs was obtained by selecting the fifteen best performing HPO trials. Four models have been selected for their clear advantage in accuracy, and these are the GFMs with IDs 229, 156, 147, 260. Additional eleven models have been selected based on judicious balance between accuracy and energy consumption needed for training, and these are the GFMs with IDs 165, 78, 137, 1, 175, 171, 181, 67, 179, 167, 351. Each selected GFM of the ensemble was continued to cumulate a total of at most 30 epochs. In some cases, the total number of epochs actually performed was les than 30 due to two combined factors: (1) the size of the GFM (i.e., the number of model parameters to train) and (2) the total wall-clock time for which the computational resources could be allocated on OLCF-Frontier. The "Ensemble_of_models" directory contains 15 sub-directories named as follows: - gfm_0.229 - gfm_0.156 - gfm_0.147 - gfm_0.260 - gfm_0.165 - gfm_0.78 - gfm_0.137 - gfm_0.1 - gfm_0.175 - gfm_0.171 - gfm_0.181 - gfm_0.67 - gfm_0.179 - gfm_0.167 - gfm_0.351 Each one of these sub-directories refers to one of the fifteen HPO trials that have been selected to continue the pre-training with at most 30 epochs. With each sub-directory associated with a specific HPO trial, the following files can be found: - config.json: file for argument parsing to develop and train an HydraGNN architecture - gfm_0.ID_epoch_N.pk: file with model parameters for HPO ID trial after N epochs of training The ensemble of fifteen GFM architectures was used for (1) ensemble averaging to stabilize the predictions of energy and atomic forces after pre-training for post-processing analysis and (2) ensemble uncertainty quantification (UQ). The code used to develop, pre-train, and load the pre-trained models for post-processing analysis is available on the ORNL-GitHub at the following link: https://github.com/ORNL/HydraGNN/tree/Predictive_GFM_2024

36 MATERIALS SCIENCE↗
DOE OSTI2024

Model Validation and Uncertainty Quantification on the KRUSTY Microreactor Design Using GRIFFIN Neutron Transport Code [Poster]

Argonne National Laboratory (ANL) and INL have developed a GRIFFIN steady state neutronics model for the multiphysics simulations of the Kilopower Reactor Using Sterling TechnologY (KRUSTY) microreactor in the Multiphysics Object Oriented Simulation Environment (MOOSE). The reliability of such deterministic neutronics models can be validated by comparing with computations from Monte Carlo codes (e.g. MCNP, SERPENT, OpenMC, Shift, etc). Furthermore, potential modeling/design improvements can be identified by incorporating uncertainty quantification (UQ), which can be performed by MOOSE’s Stochastic Tools Module (STM). KRUSTY is a prototype for a 5-kW thermal nuclear-powered space reactor. Its primary components consist of nuclear fuel, heat pipes, a control rod, a reflector, and the shielding. The fuel consists of 3 stacked U-7.65Mo cylinders with a hole in the center for the control rod. 8 liquid sodium heat pipes transfer fission energy from the solid fuel block to the Sterling power conversion system where the energy is extracted, and the cooled sodium flows back to the core via capillary action . The movable Boron Carbide control rod regulates the neutron population during startup or when a reactor temperature boost is needed . The beryllium oxide reflector is in 3 places in the reactor; it surrounds the core axially, it lies beneath the core on a platen, and it is present in the shim. The axial and lower reflectors rest on an adjustable stainless-steel platen that moves upward to cover the fuel and help the reactor reach criticality. Lastly, radial stainless steel surrounds the core offering protection from radiation exposure .

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Partnership Center for High-Fidelity Boundary Plasma Simulation (Final Report)

Within the Partnership Center for High-Fidelity Boundary Plasma Simulation (HBPS), work at UT-Austin was aimed at improved verification, validation, and uncertainty quantification (VVUQ) for edge plasma simulations and on performing gyrokinetics simulations of pedestal instabilities and turbulence in order to expand foundational understanding of pedestal transport. Regarding VVUQ, the accomplishments can be summarized as follows. First, it was shown that the Moment Preserving Constrained Resampling technique, when applied periodically in particle-in-cell simulations in the XGC code, can dramatically improve the accuracy of the simulation at essentially equivalent computational cost. Second, a technique for estimating model correlations, which are required to solve the model selection and sample allocation problem in multifidelity UQ techniques, without sampling the highest fidelity, most computationally expensive model, was developed and demonstrated. Third, previously developed methods for estimating statistical and discretization errors were applied to numerical methods relevant to edge plasma simulations, namely in particle-in-cell-based approaches, and shown to work. Finally, benchmark studies for comparing gyrokinetic codes were developed and performed, leading to reasonable agreement between four commonly used codes. Regarding physics studies, gyrokinetic simulations to investigate microtearing modes in the DIII-D pedestal were performed using the GENE code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A Quantum Leap for Dynamic Radiography

Dynamic radiography techniques have been instrumental in advancing the National Nuclear Security Administration's (NNSA) mission since WWII. This paper explores the transformative potential of quantum information science (QIS) to revolutionize dynamic radiography through enhanced image processing, tomographic reconstruction, statistics and uncertainty quantification (UQ), and artificial intelligence integration. By leveraging quantum algorithms to extract previously inaccessible information from existing datasets, this interdisciplinary approach promises unprecedented insights at the intersection of dynamic imaging, artificial intelligence, and quantum information technologies.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
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 OSTI2025

Probabilistic Predictions for Fastener Failure in the Sandia Mechanics Challenge Using the Discrete-Direct Uncertainty Quantification Approach

This paper documents the blind and post-blind analysis predictions for the 2023 Sandia Mechanics Challenge (SMC), which involved predicting the behavior of a threaded fastener joint structure subjected to shock loading. Utilizing repeat sets of fastener calibration data from various experimental configurations including tension, double shear, and joint tension, we developed a library of calibrated models which were propagated through the application model using the Discrete-Direct (DD) uncertainty quantification (UQ) approach. Although the initial blind predictions did not incorporate spare-sample processing to quantify fastener failure probabilities, the analyses yielded reasonable conclusions aligned with experimental results. In the post-blind analysis phase, we focused on enhancing the fidelity of the aluminum constitutive model and innovating the DD approach to obtain probabilistic predictions for fastener failure, particularly when quantities of interest (QoIs) approach their bounds. The improved aluminum model captures the behavior of the cantilever under shock loading more accurately, predicting both partial and complete cracks, although it tends to underpredict failure propagation. The enhanced DD approach facilitates probabilistic predictions that reflect the interdependent failure mechanisms of the fasteners and the cantilever, revealing that while certain fasteners are more likely to fail, the failure does not necessarily follow a progressive pattern. Overall, the post-blind analyses significantly improved the predictive capabilities of the model, providing valuable insights into the SMC application and establishing a robust foundation for informed engineering decisions. The methodology demonstrates a cost-effective and extensible approach suitable for a wide range of applications, highlighting the importance of uncertainty quantification to provide context for engineering decision making.

42 ENGINEERING↗
DOE OSTI2026

New approaches to Bayesian uncertainty quantification for Nuclear Science (Final Technical Report)

Inverse problems play a central role in experimentation and theory/data comparisons for many areas of modern Nuclear Physics (NP) and High-Energy Physics (HEP). Bayes’s Theorem is a powerful tool for solving Inverse Problems, providing conceptually transparent and unbiased constraints on theoretical parameters and their uncertainties (“Bayesian Inference”) and enabling the quantification of agreement or tension between models and data. However, analyses based on Bayesian Inference are often challenging for NP and HEP applications, either because of the large number of parameters in the problem, the high computational cost, or both. We propose a multi-institutional collaboration to develop and deploy novel Bayesian analysis tools that advance the scientific scope of a broad range of current and future NP experiments. This project brings together NP domain scientists working on several high-profile NP projects for which new, high-performance Bayesian Uncertainty Quantification (“Bayesian UQ”) methods are essential to carry out the science, and data scientists who are developing state-of-the-art methods applicable to these problems. The NP projects in this proposal comprise measurements of the mass and fundamental nature of the neutrino; study of the Quark-Gluon Plasma that filled the early universe; and mapping of natural and anthropogenic radiation environments. While these NP projects have very different scientific goals, with datasets and analysis approaches that differ significantly, they share common requirements for improving computationally intensive Bayesian analyses using advanced Machine Learning algorithms and will benefit strongly from a coherent effort to develop general solutions. This proposal brings together these projects and forefront ML-based data science algorithms to develop such general solutions. The methods developed in this project will also be more widely applicable, thereby advancing science in the larger Nuclear Physics portfolio.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Quantum surrogate models for uncertainty quantification

Surrogate models are a critical ingredient to computation-based design and validation of many DOE mission-relevant physical systems. When first-principles computation of properties of a physical systems becomes pro hibitive, surrogate models are the only path towards achieving tasks such as uncertainty quantification (UQ), exploration of design space, and validation of design choices. In this project we have developed and demonstrated a new surro gate modeling paradigm for complex models that is data-driven, non-intrusive, and has the potential to be versatile and equipped with performance guaran tees. This combination of features is absent in existing surrogate modeling tools. The framework we have developed in this project exploits a quantum-classical correspondence to establish a quantum system that mimics the dynamics of the classical Hamiltonian system from which data in the form of temporal snapshots is provided. Since quantum dynamics propagates distributions over observables, the framework is naturally suited to propagation of epistemic uncertainties in the form of distributions over initial state and parametric uncertainties. In this project, we take the first step in establishing this novel framework by deriving a quantization and de-quantization procedure, demonstrating the accuracy of the quantum surrogate models these define using two model systems, and defining the next steps in maturing the framework towards a tool applicable to Sandia mission-relevant problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Fracture Analysis of Cohesive Zone Models for Modeling Residual Stress Induced Delamination in Composite Structures

A fracture study of coupon-scale composite cylinders with embedded defects was conducted with an objective to assess and validate a modeling approach using two available cohesive material models. The study included experimental and simulation evaluations of initiation of crack growth and progression. Interrupted thermal experiments used acoustic emissions monitoring to identify the onset of crack progression during each cooling interval and ultrasonic scanning provided images of defect growth. Verification, validation, and uncertainty quantification (VVUQ) processes were performed in the assessment of the simulation predicted temperature at which crack propagation begins (quantity of interest). The Sobol sensitivity analysis identified the hoop direction elastic modulus in the carbon fiber reinforced polymer (CFRP) plies as the most influential parameter for simulations using both cohesive models, accounting for at least 70% of the variation in the temperature at crack propagation. The UQ temperature range for the Tvergaard-Hutchinson model was higher (more conservative) than the experimental acoustic measurement indicators of crack progression, while the temperature range for the Thouless-Parmigiani model enveloped the experimental data points for the primary defect size of 0.75 x 1 in. The simulations could not capture the stable crack growth indicated in the experiments. This is likely due to the models’ inability to represent anisotropic fracture toughness attributed to the structure of the orthotropic fiber weave in a woven composite laminate.

42 ENGINEERING↗
DOE OSTI2025

Advancements on Multi-Fidelity Random Fourier Neural Networks: Application to Hurricane Modeling for Wind Energy

Multi-fidelity approaches are emerging as effective strategies in computational science to handle otherwise intractable tasks like Uncertainty Quantification (UQ), training of Machine Learning (ML) models, and optimization, for expensive high-fidelity applications in which the amount of available simulations or data is limited. The main idea is simple: large datasets generated for low-fidelity approximations of the problem at hand are fused with a much sparser dataset for the target (high-fidelity) system. In this paper, we build on our recent success in designing random Fourier Neural Networks (rFNNs) [1] to target problems arising in wind energy applications and in particular problems of interest for hurricane modeling. In this context, data for the high-fidelity models are limited and lower fidelity alternatives are needed. In this work, we introduce a novel multi-fidelity training approach for our rFNNs and demonstrate its use on a simple verification problem and on a hurricane modeling problem in which high-fidelity data are generated via Large-Eddy Simulations (LES), while low-fidelity data are given by a mesoscale model. Initial results demonstrate how the multi-fidelity training approach can improve the quality of the resulting surrogate.

Fourier Neural Networks↗
DOE OSTI2025

Producing High-fidelity Synthetic Population Ensembles at Scale

Used within social simulations, synthetic population ensembles enable uncertainty quantification (UQ) methods for obtaining more robust model inference and prediction. A synthetic population ensemble is a series of plausible virtual reconstructions of an area’s population at the granularity of people and residences, generated stochastically to preserve privacy of the source population survey’s respondents. In this paper, we demonstrate the production of large synthetic population ensembles for the US via Oak Ridge National Laboratory’s UrbanPop framework to support modeling of high spatial resolution energy affordability metrics from nationwide social surveys in collaboration with the fusionACS project. Our initial task involves creating ensembles for 17 US metropolitan areas, each consisting of 41 population instances (a base realization and 40 replicates). To accomplish this task at scale, we configured an integrated system comprised of a research cloud, virtual containerization, GPU-enhanced functionality, and a dual API/CLI to interact with UrbanPop’s maturing Likeness Python ecosystem. We observe a reduction in theoretical execution time while maintaining high-fidelity approximations of residential totals by metropolitan area and the demographic characteristics of neighborhoods. We discuss expansion of our approach to produce synthetic population ensembles for the entire US, particularly plans to establish automated workflows for job orchestration to increase computational efficiency, as well as provide outlook for broadening applications of the ensembles.

Gaboardi, James [ORNL] (ORCID:0000000247766826)↗
NASA NTRS1997

Development of Plant Gene Vectors for Tissue-Specific Expression Using GFP as a Reporter Gene

Reporter genes are widely employed in plant molecular biology research to analyze gene expression and to identify promoters. Gus (UidA) is currently the most popular reporter gene but its detection requires a destructive assay. The use of jellyfish green fluorescent protein (GFP) gene from Aequorea Victoria holds promise for noninvasive detection of in vivo gene expression. To study how various plant promoters are expressed in sweet potato (Ipomoea batatas), we are transcriptionally fusing the intron-modified (mGFP) or synthetic (modified for codon-usage) GFP coding regions to these promoters: double cauliflower mosaic virus 35S (CaMV 35S) with AMV translational enhancer, ubiquitin7-intron-ubiquitin coding region (ubi7-intron-UQ) and sporaminA. A few of these vectors have been constructed and introduced into E. coli DH5a and Agrobacterium tumefaciens EHA105. Transient expression studies are underway using protoplast-electroporation and particle bombardment of leaf tissues.

Jackson, Jacquelyn↗
NASA NTRS2007

Numerical Uncertainty Quantification for Radiation Analysis Tools

Recently a new emphasis has been placed on engineering applications of space radiation analyses and thus a systematic effort of Verification, Validation and Uncertainty Quantification (VV&UQ) of the tools commonly used for radiation analysis for vehicle design and mission planning has begun. There are two sources of uncertainty in geometric discretization addressed in this paper that need to be quantified in order to understand the total uncertainty in estimating space radiation exposures. One source of uncertainty is in ray tracing, as the number of rays increase the associated uncertainty decreases, but the computational expense increases. Thus, a cost benefit analysis optimizing computational time versus uncertainty is needed and is addressed in this paper. The second source of uncertainty results from the interpolation over the dose vs. depth curves that is needed to determine the radiation exposure. The question, then, is what is the number of thicknesses that is needed to get an accurate result. So convergence testing is performed to quantify the uncertainty associated with interpolating over different shield thickness spatial grids.

Anderson, Brooke↗