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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Bayesian inference for the seismic moment tensor using regional waveforms and a data-derived distribution of velocity models

The largest source of uncertainty in any source inversion is the velocity model used to construct the transfer function employed in the forward model that relates observed ground motion to the seismic moment tensor. However, standard inverse procedures often does not quantify uncertainty in the seismic moment tensor due to error in the Green’s functions from uncertain event location and Earth structure. We attempt to incorporate this uncertainty into an estimation of the seismic moment tensor using a distribution of velocity models calculated in a prior effort based on different and complementary data sets. The posterior distribution of velocity models is then used to construct Green’s functions for use in Bayesian inference of an unknown seismic moment tensor using regional waveform data. The combined likelihood is estimated using data-specific error models and the posterior of the seismic moment tensor is estimated and can be interpreted in terms of most-probable source-type.

58 GEOSCIENCES↗
DOE OSTI2023

Investigation of 3D printed lightweight hybrid composites via theoretical modeling and machine learning

Hybrid composites combine two or more different fillers to achieve multifunctional or advanced material properties, such as lightweight and enhanced mechanical properties. The properties of the composites significantly depend on their microstructures, which can be tailored via advanced 3D printing processes. Understanding the process-structure-property relationships is critical to enable the design and engineering of novel hybrid composites for applications in aerospace, automotive, and protective coatings. Here, for this work, we develop 3D printable and lightweight hybrid composites and leverage the conventional design of experiments, a theoretical hybrid model, and an image-driven machine learning (ML) method to investigate their mechanical behaviors. The hybrid composites are formulated with elastomer matrix, microfillers, and thin-shell particles, enabling a significant degree of design freedom of microstructures with densities and mechanical properties varying up to 70% and 91%, respectively. Our statistical analysis indicates that the 3D printing path direction and the microfibers fraction are dominating process parameters with contribution percentages of 45.3% and 57.7% on the specific stiffness and strength, respectively. A hybrid mechanics model is developed based on a simple Weibull distribution function and classical single-filler models to effectively capture the variations in mechanical properties, however, it overestimates the values due to its statistical constraints and idealization of experimental uncertainty. The image-driven ML model leverages the microscale images directly without losing the structural details, shows more accurate predictions with experimental data, and has 48.6% lower root mean square error than the theoretical model.

3D printing↗
DOE OSTI2022

Towards precise and accurate calculations of neutrinoless double-beta decay

We present the results of a National Science Foundation Project Scoping Workshop, the purpose of which was to assess the current status of calculations for the nuclear matrix elements governing neutrinoless double-beta decay and determine if more work on them is required. After reviewing important recent progress in the application of effective field theory, lattice quantum chromodynamics, and ab initio nuclear-structure theory to double-beta decay, we discuss the state of the art in nuclear-physics uncertainty quantification and then construct a roadmap for work in all these areas to fully complement the increasingly sensitive experiments in operation and under development. The roadmap includes specific projects in theoretical and computational physics as well as the use of Bayesian methods to quantify both intra- and inter-model uncertainties. Here, the goal of this ambitious program is a set of accurate and precise matrix elements, in all nuclei of interest to experimentalists, delivered together with carefully assessed uncertainties. Such calculations will allow crisp conclusions from the observation or non-observation of neutrinoless double-beta decay, no matter what new physics is at play.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Observational constraints of an anisotropic boost due to the projection effects using redMaPPer clusters

Optical clusters identified from red-sequence galaxies suffer from projection effects, where interloper galaxies along the line of sight to a cluster are mistaken as genuine members of the cluster. In the previous study, we found that the projection effects cause the boost on the amplitudes of clustering and lensing on large scale compared to the expected amplitudes in the absence of any projection effects. These boosts are caused by preferential selections of filamentary structure aligned to the line of sight due to distance uncertainties in photometric surveys. We model the projection effects with two simple assumptions and develop a novel method to quantify the size of the boost using cluster-galaxy cross-correlation functions. We validate our method using mock cluster catalogues built from cosmological N-body simulations and find that we can obtain unbiased constraints on the boost parameter with our model. We then apply our analysis on the SDSS redMaPPer clusters and find that the size of the boost is roughly 20 per cent for all the richness bins except the cluster sample with the richness bin λ ∈ [30, 40]. This is the first study to constrain the boost parameter independent from cluster cosmology studies and provides a self-consistency test for the projection effects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A Grand Challenge "Uncertainty Project" to Accelerate Advances in Earth System Predictability: AI-Enabled Concepts and Applications

This proposal is emerging from GISS ModelE3 ESM development in the area of cloud physics, so we begin with an example of research needs/gaps from that work. Here, some of our greatest development concerns arise where we lack fundamental process-level understanding, as in ice formation. Namely, it is currently unclear what is the main process that is forming the majority of ice crystals in commonly occurring convection, apparently via secondary ice production at warm temperatures. We are keenly awaiting laboratory data for candidate mechanisms, which is not yet in hand to crucially establish their efficiency. Our progress is also hampered by a lack of uncertainty characterization in currently available measurements of ice crystal number size distributions. Furthermore, the same multiplication process may be responsible for a majority of ice crystals in many extratropical mixed-phase clouds, whose variable representation in CMIP6 ESMs may be a leading cause of differences in cloud phase feedback and ECS. Yet we have been required to deliver an ESM with the cloud physics knowledge at hand. The proposed grand challenge project is AI-enabled via application of machine learning (ML) to climate model and observational data streams (focal area 3), and applications include AI-guided observing system design and model/component/parameterization selection (areas 1 and 2). The project is structurally agnostic as to whether model or observing system components use AI approaches or not, but uncertainties must be estimated and propagatable in both.

58 GEOSCIENCES↗
DOE OSTI2026

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Reconstruction and uncertainty quantification of lattice Hamiltonian model parameters from observations of microscopic degrees of freedom

The emergence of scanning probe and electron beam imaging techniques has allowed quantitative studies of atomic structure and minute details of electronic and vibrational structure on the level of individual atomic units. These microscopic descriptors, in turn, can be associated with local symmetry breaking phenomena, representing the stochastic manifestation of the underpinning generative physical model. In this work, we explore the reconstruction of exchange integrals in the Hamiltonian for a lattice model with two competing interactions from observations of microscopic degrees of freedom and establish the uncertainties and reliability of such analysis in a broad parameter-temperature space. In contrast to other approaches, we specifically specify a loss function inherent to thermodynamic systems and utilize it to estimate uncertainty in simulated realizations of different models. As an ancillary task, we develop a machine learning approach based on histogram clustering to predict phase diagrams efficiently using a reduced descriptor space. We further demonstrate that reconstruction is possible well above the phase transition and in the regions of parameter space when the macroscopic ground state of the system is poorly defined due to frustrated interactions. This suggests that this approach can be applied to the traditionally complex problems of condensed matter physics such as ferroelectric relaxors and morphotropic phase boundary systems, spin and cluster glasses, and quantum systems once the local descriptors linked to the relevant physical behaviors are known.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Supporting hierarchical soil biogeochemical modeling: version 2 of the Biogeochemical Transport and Reaction model (BeTR-v2)

Abstract. Reliable soil biogeochemical modeling is a prerequisite for credible projections of climate change and associated ecosystem feedbacks. This recognition has called for frameworks that can support flexible and efficient development and application of new or alternative soil biogeochemical modules in Earth system models (ESMs). The the Biogeochemical Transport and Reaction model version 1 (BeTR-v1) code (i.e., CLM4-BeTR) is one such framework designed to accelerate the development and integration of new soil biogeochemistry formulations into ESMs and to analyze structural uncertainty in ESM simulations. With a generic reactive transport capability, BeTR-v1 can represent multiphase (e.g., gaseous, aqueous, and solid), multi-tracer (e.g., nitrate and organic carbon), and multi-organism (e.g., plants, bacteria, and fungi) dynamics. Here, we describe the new version, Biogeochemical Transport and Reaction model version 2 (BeTR-v2), which adopts more robust numerical solvers for multiphase diffusion and advection and coupling between biogeochemical reactions and improves code modularization over BeTR-v1. BeTR-v2 better supports different mathematical formulations in a hierarchical manner by allowing the resultant model be run for a single topsoil layer or a vertically resolved soil column, and it allows the model to be fully coupled with the land component of the Energy Exascale Earth System Model (E3SM). We demonstrate the capability of BeTR-v2 with benchmark cases and example soil biogeochemical (BGC) implementations. By taking advantage of BeTR-v2's generic structure integrated in E3SM, we then found that calibration could not resolve biases introduced by different numerical coupling strategies of plant–soil biogeochemistry. These results highlight the importance of numerically robust implementation of soil biogeochemistry and coupling with hydrology, thermal dynamics, and plants – capabilities that the open-source BeTR-v2 provides. We contend that Earth system models should strive to minimize this uncertainty by applying better numerical solvers.

58 GEOSCIENCES↗
DOE OSTI2020

Azimuthally averaged wind and thermodynamic structures of tropical cyclones in global climate models and their sensitivity to horizontal resolution

Characteristics of tropical cyclones (TCs) in global climate models (GCMs) are known to be influenced by details of the model configurations, including horizontal resolution and parameterization schemes. Understanding model-to-model differences in TC characteristics is a prerequisite for reducing uncertainty in future TC activity projections by GCMs. This study performs a process-level examination of TC structures in eight GCM simulations that span a range of horizontal resolutions from 1° to 0.25°. A recently developed set of process-oriented diagnostics is used to examine the azimuthally averaged wind and thermodynamic structures of the GCM-simulated TCs. Results indicate that the inner-core wind structures of simulated TCs are more strongly constrained by the horizontal resolutions of the models than are the thermodynamic structures of those TCs. As expected, the structures of TC circulations become more realistic with smaller horizontal grid spacing, such that the radii of maximum wind (RMW) become smaller, and the maximum vertical velocities occur off the center. However, the RMWs are still too large, especially at higher intensities, and there are rising motions occurring at the storm centers, inconsistently with observations. The distributions of precipitation, moisture, radiative and surface turbulent heat fluxes around TCs are diverse, even across models with similar horizontal resolutions. At the same horizontal resolution, models that produce greater rainfall in the inner-core regions tend to simulate stronger TCs. Further, when TCs are weak, the radial gradient of net column radiative flux convergence is comparable to that of surface turbulent heat fluxes, emphasizing the importance of cloud-radiative feedbacks during the early developmental phases of TCs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Active Learning Surrogates for Integrating Electron Microscopy and Computational Insights from Simulations in Autonomous Experiments

Artificial Intelligence (AI) combined with simulations and experiments has great potential to accelerate scientific discovery across technology and pharmaceuticals. However, the gap between simulations and experiments is challenging due to disparities in time and scale, making it difficult to estimate properties like energy and electronic states from experiments, and to provide feedback based on theoretical insights.Our research addresses the challenge by developing unique deep kernel based surrogate models that learns from microscopic images, mapping structural features to energy differences from defect formation. We start with full-training using simulated images to determine optimal settings, establishing a baseline for active learning. Using these settings from the baseline, active learning is trained, and predicts structures along simulation trajectories based on uncertainty and energetic stability, thus reducing data requirements, simulation time and computational costs. The results demonstrate that the model achieves a low average error margin of approximately 0.03 meV, indicating good performance. To enhance feature extraction and reconstruction capabilities, we developed an autoencoder-decoder as additional surrogate to create latent space to capture essential features, enabling precise comparisons between simulations and experiments. The results from this model achieved a reconstruction loss of around 0.2 and accurately reconstructed molecular structures.Overall, this work advances the steering of experiments through computational simulations by employing a surrogate models that actively predicts the trajectories of structural evolution, achieving time-to-solution comparable to experimental measurements.

Saranathan, Gayathri [Hewlett-Packard]↗
DOE OSTI2020

Jet substructure from dark sector showers

We examine the robustness of collider phenomenology predictions for a dark sector scenario with QCD-like properties. Pair production of dark quarks at the LHC can result in a wide variety of signatures, depending on the details of the new physics model. A particularly challenging signal results when prompt production induces a parton shower that yields a high multiplicity of collimated dark hadrons with subsequent decays to Standard Model hadrons. The final states contain jets whose substructure encodes their non-QCD origin. This is a relatively subtle signature of strongly coupled beyond the Standard Model dynamics, and thus it is crucial that analyses incorporate systematic errors to account for the approximations that are being made when modeling the signal. We estimate theoretical uncertainties for a canonical substructure observable designed to be sensitive to the gauge structure of the underlying object, the two-point energy correlator $ {e}_2^{\left(\beta \right)} $ , by computing envelopes between resummed analytic distributions and numerical results from Pythia. We explore the separability against the QCD background as the confinement scale, number of colors, number of flavors, and dark quark masses are varied. Additionally, we investigate the uncertainties inherent to modeling dark sector hadronization. Simple estimates are provided that quantify one’s ability to distinguish these dark sector jets from the overwhelming QCD background. Such a search would benefit from theory advances to improve the predictions, and the increase in statistics using the data to be collected at the high luminosity LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Bayesian force fields from active learning for simulation of inter-dimensional transformation of stanene

Abstract We present a way to dramatically accelerate Gaussian process models for interatomic force fields based on many-body kernels by mapping both forces and uncertainties onto functions of low-dimensional features. This allows for automated active learning of models combining near-quantum accuracy, built-in uncertainty, and constant cost of evaluation that is comparable to classical analytical models, capable of simulating millions of atoms. Using this approach, we perform large-scale molecular dynamics simulations of the stability of the stanene monolayer. We discover an unusual phase transformation mechanism of 2D stanene, where ripples lead to nucleation of bilayer defects, densification into a disordered multilayer structure, followed by formation of bulk liquid at high temperature or nucleation and growth of the 3D bcc crystal at low temperature. The presented method opens possibilities for rapid development of fast accurate uncertainty-aware models for simulating long-time large-scale dynamics of complex materials.

Chemistry↗
DOE OSTI2022

Understanding Uncertainty in Microstructure Evolution and Constitutive Properties in Additive Process Modeling

Coupled process–microstructure–property modeling, and understanding the sources of uncertainty and their propagation toward error in part property prediction, are key steps toward full utilization of additive manufacturing (AM) for predictable quality part development. The OpenFOAM model for process conditions, the ExaCA model for as-solidified grain structure, and the ExaConstit model for constitutive mechanical properties are used as part of the ExaAM modeling framework to examine a few of the various sources of uncertainty in the modeling workflow. In addition to “random” uncertainty (due to random number generation in the orientations and locations of grains present), the heterogeneous nucleation density N 0 and the mean substrate grain spacing S 0 are varied to examine their impact of grain area development as a function of build height in the simulated microstructure. While mean grain area after 1 mm of build is found to be sensitive to N 0 and S 0 , particularly at small N 0 and large S 0 (despite some convergence toward similar values), the resulting grain shapes and overall textures develop in a reasonably similar manner. As a result of these similar textures, ExaConstit simulation using ExaCA representative volume elements (RVEs) from various permutations of N 0 , S 0 , and location within the build resulted in similar yield stress, stress–strain curve shape, and stress triaxiality distributions. It is concluded that for this particular material and scan pattern, 15 layers is sufficient for ExaCA texture and ExaConstit predicted properties to become relatively independent of additional layer simulation, provided that reasonable estimates for N 0 and S 0 are used. However, additional layers of ExaCA will need to be run to obtain mean grain areas independent of build height and baseplate structure.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Atmospheric Structure Prediction for Infrasound Propagation Modeling Using Deep Learning

Abstract Infrasound is generated by a variety of natural and anthropogenic sources. Infrasonic waves travel through the dynamic atmosphere, which can change on the order of minutes to hours. Infrasound propagation largely depends on the wind and temperature structure of the atmosphere. Numerical weather prediction models are available to provide atmospheric specifications, but uncertainties in these models exist and they are computationally expensive to run. Machine learning has proven useful in predicting tropospheric weather using Long Short‐Term Memory (LSTM) networks. An LSTM network is utilized to make atmospheric specification predictions up to ∼30 km for three different training and testing scenarios: (a) the model is trained and tested using only radiosonde data from the Albuquerque, NM, USA station, (b) the model is trained on radiosonde stations across the contiguous US, excluding the Albuquerque, NM, USA station, which was reserved for testing, and (c) the model is trained and tested on radiosonde stations across the contiguous US. Long Short‐Term Memory predictions are compared to a state‐of‐the‐art reanalysis model and show cases where the LSTM outperforms, performs equally as well, or underperforms in comparison to the state‐of‐the‐art. Regional and temporal trends in model performance across the US are also discussed. Results suggest that the LSTM model is a viable tool for predicting atmospheric specifications for infrasound propagation modeling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

LandScan mosaic enables high-resolution gridded population estimates with explicit uncertainty

Gridded population datasets represent high-resolution distributions of human occupancy, enabling informed decision-making across a broad range of fields. These data products are valuable for assessing environmental risk, urban development, disaster preparedness and resource allocation—areas where accurate population estimates directly enhance policy effectiveness and optimize resource distribution. Despite the importance of gridded population datasets, traditional population modeling approaches often overlook inherent uncertainties in the estimation process. This limitation can create a false sense of certainty in population estimates, potentially leading to flawed decisions by those who rely on the data. To address this methodological gap, we introduce a probabilistic machine learning modeling framework, LandScan Mosaic, that explicitly incorporates uncertainty into the population modeling process. Our approach systematically quantifies uncertainty in three key modeling parameters of the LandScan HD gridded population dataset: building use types, floor counts, and occupancy rates. By employing Monte Carlo simulations, we propagate these uncertainties through the modeling process, yielding probability distributions of population counts in place of deterministic point estimates. We demonstrate the practical application of this framework in Iloilo City, Philippines, using structured decision-making techniques and our probabilistic estimates to identify and prioritize areas most affected by projected flooding, supporting targeted interventions that address both economic and social risks. In doing so, we propose a population-specific approach for incorporating confidence into structured decision making processes. Through a comparative analysis with conventional deterministic approaches and point estimate approaches, including LandScan HD and WorldPop, we evaluate how the incorporation of machine learning and uncertainty influences decision rankings. This research advances population distribution modeling by offering a robust, quantitative approach that explicitly accounts for uncertainty in the underlying data, along with guidance for how users can apply uncertainty in their decision-making.

Environmental sciences↗
DOE OSTI2022

Evaluating alternative ebullition models for predicting peatland methane emission and its pathways via data–model fusion

Abstract. Understanding the dynamics of peatland methane (CH4) emissions and quantifying sources of uncertainty in estimating peatland CH4 emissions are critical for mitigating climate change. The relative contributions of CH4 emission pathways through ebullition, plant-mediated transport, and diffusion, together with their different transport rates and vulnerability to oxidation, determine the quantity of CH4 to be oxidized before leaving the soil. Notwithstanding their importance, the relative contributions of the emission pathways are highly uncertain. In particular, the ebullition process is more uncertain and can lead to large uncertainties in modeled CH4 emissions. To improve model simulations of CH4 emission and its pathways, we evaluated two model structures: (1) the ebullition bubble growth volume threshold approach (EBG) and (2) the modified ebullition concentration threshold approach (ECT) using CH4 flux and concentration data collected in a peatland in northern Minnesota, USA. When model parameters were constrained using observed CH4 fluxes, the CH4 emissions simulated by the EBG approach (RMSE = 0.53) had a better agreement with observations than the ECT approach (RMSE = 0.61). Further, the EBG approach simulated a smaller contribution from ebullition but more frequent ebullition events than the ECT approach. The EBG approach yielded greatly improved simulations of pore water CH4 concentrations, especially in the deep soil layers, compared to the ECT approach. When constraining the EBG model with both CH4 flux and concentration data in model–data fusion, uncertainty of the modeled CH4 concentration profiles was reduced by 78 % to 86 % in comparison to constraints based on CH4 flux data alone. The improved model capability was attributed to the well-constrained parameters regulating the CH4 production and emission pathways. Our results suggest that the EBG modeling approach better characterizes CH4 emission and underlying mechanisms. Moreover, to achieve the best model results both CH4 flux and concentration data are required to constrain model parameterization.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Bayesian Inference for the Seismic Moment Tensor Using Regional Waveforms and Teleseismic- P Polarities with a Data-Derived Distribution of Velocity Models and Source Locations

The largest source of uncertainty in any source inversion is the velocity model used in the transfer function that relates observed ground motion to the seismic moment tensor. However, standard inverse procedure often does not quantify uncertainty in the seismic moment tensor due to error in the Green’s functions from uncertain event location and Earth structure. Here, we incorporate this uncertainty into an estimation of the seismic moment tensor using a data-derived distribution of velocity models based on complementary geophysical data sets, including thickness constraints, velocity profiles, gravity data, surface-wave group velocities, and regional body-wave travel times. The data-derived distribution of velocity models is then used as a prior distribution of Green’s functions for use in Bayesian inference of an unknown seismic moment tensor using regional and teleseismic-P waveforms. The use of multiple data sets is important for gaining resolution to different components of the moment tensor. The combined likelihood is estimated using data-specific error models and the posterior of the seismic moment tensor is estimated and interpreted in terms of the most probable source type.

58 GEOSCIENCES↗
DOE OSTI2021

Discrete-Direct Model Calibration and Uncertainty Propagation Method Confirmed on Multi-Parameter Plasticity Model Calibrated to Sparse Random Field Data

A discrete direct (DD) model calibration and uncertainty propagation approach is explained and demonstrated on a 4-parameter Johnson-Cook (J-C) strain-rate dependent material strength model for an aluminum alloy. The methodology's performance is characterized in many trials involving four random realizations of strain-rate dependent material-test data curves per trial, drawn from a large synthetic population. The J-C model is calibrated to particular combinations of the data curves to obtain calibration parameter sets which are then propagated to “Can Crush” structural model predictions to produce samples of predicted response variability. These are processed with appropriate sparse-sample uncertainty quantification (UQ) methods to estimate various statistics of response with an appropriate level of conservatism. This is tested on 16 output quantities (von Mises stresses and equivalent plastic strains) and it is shown that important statistics of the true variabilities of the 16 quantities are bounded with a high success rate that is reasonably predictable and controllable. The DD approach has several advantages over other calibration-UQ approaches like Bayesian inference for capturing and utilizing the information obtained from typically small numbers of replicate experiments in model calibration situations—especially when sparse replicate functional data are involved like force–displacement curves from material tests. The DD methodology is straightforward and efficient for calibration and propagation problems involving aleatory and epistemic uncertainties in calibration experiments, models, and procedures.

42 ENGINEERING↗