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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 OSTI2024

Uncertainty Propagation within Chained Models for Machine Learning Reconstruction of Neutrino-LAr Interactions

Sequential or chained models are increasingly prevalent in machine learning for scientific applications, due to their flexibility and ease of development. Chained models are particularly useful when a task is separable into distinct steps with a hierarchy of meaningful intermediate representations. In reliability-critical tasks, it is important to quantify the confidence of model inferences. However, chained models pose an additional challenge for uncertainty quantification, especially when input uncertainties need to be propagated. In such cases, a fully uncertainty-aware chain of models is required, where each step accepts a probability distribution over the input space, and produces a probability distribution over the output space. In this work, we present a case study for adapting a single model within an existing chain, designed for reconstruction within neutrino-Argon interactions, developed for neutrino oscillation experiments such as MicroBooNE, ICARUS, and the future DUNE experiment. We test the performance of an input uncertainty-enabled model against an uncertainty-blinded model using a method for generating synthetic noise. By comparing these two, we assess the increase in inference quality achieved by exposing models to upstream uncertainty estimates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

On the Need to Align Intent and Implementation in Uncertainty Quantification for Machine Learning

Quantifying uncertainties for machine learning (ML) models is a foundational challenge in modern data analysis. This challenge is compounded by at least two key aspects of the field: (a) inconsistent terminology surrounding uncertainty and estimation across disciplines, and (b) the varying technical requirements for establishing trustworthy uncertainties in diverse problem contexts. In this position paper, we aim to clarify the depth of these challenges by identifying these inconsistencies and articulating how different contexts impose distinct epistemic demands. We examine the current landscape of estimation targets (e.g., prediction, inference, simulation-based inference), uncertainty constructs (e.g., frequentist, Bayesian, fiducial), and the approaches used to map between them. Drawing on the literature, we highlight and explain examples of problematic mappings. To help address these issues, we advocate for standards that promote alignment between the \textit{intent} and \textit{implementation} of uncertainty quantification (UQ) approaches. We discuss several axes of trustworthiness that are necessary (if not sufficient) for reliable UQ in ML models, and show how these axes can inform the design and evaluation of uncertainty-aware ML systems. Our practical recommendations focus on scientific ML, offering illustrative cases and use scenarios, particularly in the context of simulation-based inference (SBI).

Trivedi, Shubhendu [MIT] (ORCID:0000000312374301)↗
DOE OSTI2020

EMPIRICAL VALIDATION OF MULTI-ZONE BUILDING AND HVAC SYSTEM MODELS UNDER UNCERTAINTY

This study implemented a framework of empirical validation of building energy models under uncertainty to a set of controlled experiments that aim to validate multi-zone building and HVAC system models. Energy models were created through iterative acquisitions of information and data and uses measurement data from various types of sensors as both inputs and as observations to validate predictions. Experimental and modeling uncertainties were quantified and propagated accordingly, and probabilistic accuracy metrics were used to evaluate the agreement between model predictions and observations under uncertainty. Sensitivity analysis was performed to identify the most influential uncertainties that will be prioritized to be addressed in the next steps. Current results of two cooling tests show an overall good agreement between predictions and observations on a set of HVAC system outputs despite considerable and influential uncertainty in DX cooling coil COP. Agreements on zone-level responses vary notably among individual rooms, likely because of significant uncertainties in room radiation heat gain and system supply air.

Li, Qi↗
DOE OSTI2020

Validation and Independent Uncertainty Analysis of the MIX-SOL-THERM-003 ICSBEP Benchmark

The International Criticality Safety Benchmark Evaluation Project (ICSBEP) was started in 1992 by the United States Department of Energy and later in 1995 became an international project with contributions from 22 countries. The project is now organized by the OECD (Organisation for Economic Co-operation and Development) Nuclear Energy Agency (NEA). In its most recent iteration, the ICSBEP handbook contains over five thousand evaluations of critical, near-critical, and subcritical experiments conducted in facilities all around the world. These benchmarks serve as valuable information for criticality safety engineers who can use them to validate calculation techniques and establish minimum subcritical margins for operations with fissionable materials. The benchmarks in the handbook are categorized by their fissile material composition, material form (oxide, solution, or metal), and fission energy spectra. This is especially useful for those looking for benchmarks similar to a system they are working on to compare methods and identify trends. The ICSBEP Handbook Uncertainty Guide is document outlining recommended practices and methods for determining uncertainties in these benchmarks. Quantifying these uncertainties thoroughly is crucial as it allows a higher degree of confidence that data used from them is valid and relevant. The guide stresses the importance of a thorough and well documented uncertainty analysis when evaluating an experiment. All measured values of a system, whether they be dimensions or material compositions, have a certain amount of uncertainty associated with them and can be analyzed one by one to determine their effects on the system. Many evaluated benchmarks in the handbook present this in detail, however some do not, mostly earlier evaluations performed in the 1990’s and early 2000’s. Recently at Los Alamos National Laboratory (LANL), the Nuclear Criticality Safety Division (NCSD) of LANL has been validating MCNP6.2 ® input files of criticality benchmarks for use by Whisper, a criticality safety code developed at LANL. This effort is also part of the OECD NEA Working Party on International Nuclear Data Evaluation Co-operation (WPEC) Subgroup 45, also known as Validation of Nuclear Data Libraries (VaNDaL). The goal of VaNDaL is to compile a set of validated simulation inputs for use in validating nuclear data and simulation codes. As part of these efforts, one of the benchmarks reviewed was the MIX SOL-THERM-003 ICSBEP benchmark. This paper provides an independent uncertainty analysis of this benchmark experiment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Calibration and Uncertainty Estimation Using the Ensemble Kalman Filter with a Large Subsurface Flow and Transport Model - 20321

At routinely monitored groundwater contamination sites, periodically measured environmental conditions such as groundwater levels and contaminant concentrations are used to inform and confirm a conceptual site model (CSM) and guide the development and calibration of a numerical groundwater flow and transport model. The calibration of groundwater flow and transport models after each measurement (sampling) event can illuminate deficiencies in a CSM, identify areas where additional monitoring is warranted, and predict the behavior of the system to guide decision making. However, manual and automated (e.g. PEST) model calibration tools can be time-consuming and computationally expensive to implement after each sampling event. Perhaps as a result, such calibration tools generally utilize all available monitoring data simultaneously rather than sequentially assimilating monitoring data one sampling event at a time as the results from sampling become available. A more real-time data assimilation approach may reduce parameter uncertainty, quantify the value of additional monitoring data, and produce a usable model more quickly and with less effort. To mitigate the potential time-consuming aspects of manual and widely applied automated calibration techniques, a data assimilation algorithm called the ensemble Kalman filter (EnKF) was evaluated as a relatively efficient method of model calibration and uncertainty assessment via the sequential integration of monitoring data into a model. The EnKF was able to successfully and efficiently assimilate monitoring and modeling data to calibrate a complex flow and transport model at a real-world site with significant subsurface heterogeneity, uncertainty, and 12 years of monitoring data (over 4,000 individual measurements of groundwater levels and over 2,500 measurements of contaminant concentrations). Starting with an uncalibrated model data from annual sampling events were sequentially assimilated, and the resultant predication errors and estimated parameter uncertainties were tracked. After all monitoring data were assimilated, both flow and transport residuals at the end of the EnKF process were comparable to those produced via a concurrent PEST calibration effort but required fewer model simulations. Both uncertainty and prediction errors decreased over time. In a real-time application, the adequacy of the model could be assessed after each sampling event. The benefits of such a real-time approach to utilizing monitoring data include reduced costs (in the form of model updates or site characterization efforts), early flagging of possible errors in the CSM, and a reduced risk of overfitting and corresponding increased confidence in model predictions. This tool may be particularly useful compared to other calibration techniques (e.g. manual, PEST) when model runtimes are long, calibration parameters are many, or parameter uncertainty is large. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Impact of fission yield covariance matrices on decay heat uncertainty quantification with the DARWIN2 package

Although fission yields are strongly correlated, correlations between them are usually not taken into account when performing decay heat uncertainty calculations with the CEA DARWIN2 package due to the lack of reference covariance matrices associated to the JEFF-3.1.1 evaluation. However, covariance matrices for {sup 235}U and {sup 239}Pu thermal fission yields have been produced recently by the subgroup 37 of OECD/NEA Working Party on International Nuclear Data Evaluation Cooperation (WPEC). The study presented in this paper evaluates the effect of those covariances on the decay heat uncertainty calculation, both on fission burst experiments and on integral decay heat measurements that are part of the DARWIN2 experimental validation database. Although some differences are observed, partly due to the variety of models used to produce the matrices, the propagation of fission yield covariances always leads to a reduction of the decay heat uncertainty for cooling time above 10 seconds, indicating that not taking them into account is a conservative hypothesis from a safety point of view. Nevertheless, the strong impact of those covariances on the decay heat uncertainty also highlights the need of documented and consistent fission yield uncertainties and correlation data. On top of that, all the covariance matrices used for this study represent the correlation between the physical model parameters, but none of them includes the experimental correlations. An evaluation of the experimental correlations would also be of strong interest for decay heat uncertainty calculations. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Data-Driven Computation of Probabilistic Marching Cubes for Efficient Visualization of Level-Set Uncertainty

Uncertainty visualization is an important emerging research area. Being able to visualize data uncertainty can help scientists improve trust in analysis and decision-making. However, visualizing uncertainty can add computational overhead, which can hinder the efficiency of analysis. In this paper, we propose novel data-driven techniques to reduce the computational requirements of the probabilistic marching cubes (PMC) algorithm. PMC is an uncertainty visualization technique that studies how uncertainty in data affects level-set positions. However, the algorithm relies on expensive Monte Carlo (MC) sampling for the multivariate Gaussian uncertainty model because no closed-form solution exists for the integration of multivariate Gaussian. In this work, we propose the eigenvalue decomposition and adaptive probability model techniques that reduce the amount of MC sampling in the original PMC algorithm and hence speed up the computations. Our proposed methods produce results that show negligible differences compared with the original PMC algorithm demonstrated through metrics, including root mean squared error, maximum error, and difference images. We demonstrate the performance and accuracy evaluations of our data-driven methods through experiments on synthetic and real datasets.

Athawale, Tushar↗
DOE OSTI2020

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

Uncertainty quantification (UQ) includes the characterization, integration, and propagation of uncertainties that result from stochastic variations and a lack of knowledge or data in the natural world. Monte Carlo (MC) method is a sampling-based approach that has widely used for quantification and propagation of uncertainties. However, the standard MC method is often time-consuming if the simulation-based model is computationally intensive. This article gives an overview of modern MC methods to address the existing challenges of the standard MC in the context of UQ. Specifically, multilevel Monte Carlo (MLMC) extending the concept of control variates achieves a significant reduction of the computational cost by performing most evaluations with low accuracy and corresponding low cost, and relatively few evaluations at high accuracy and corresponding high cost. Multifidelity Monte Carlo (MFMC) accelerates the convergence of standard Monte Carlo by generalizing the control variates with different models having varying fidelities and varying computational costs. Multimodel Monte Carlo method (MMMC), having a different setting of MLMC and MFMC, aims to address the issue of UQ and propagation when data for characterizing probability distributions are limited. Multimodel inference combined with importance sampling is proposed for quantifying and efficiently propagating the uncertainties resulting from small data sets. All of these three modern MC methods achieve a significant improvement of computational efficiency for probabilistic UQ, particularly uncertainty propagation. Finally, an algorithm summary and the corresponding code implementation are provided for each of the modern MC methods. The extension and application of these methods are discussed in detail.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Stochastic scheduling for commercial building cooling systems: considering uncertainty in zone temperature prediction

Here, this paper presents the first attempt to address the uncertainty in zone temperature prediction with stochastic optimization. The uncertain zone temperature is a process uncertainty and has not been considered in the existing stochastic optimization for building control. To fill this gap, we proposed a novel formulation of stochastic optimization to handle process uncertainty in building control. Specifically, we first examined the accuracy of a typical linear model for predicting zone temperature. We then formulated the scheduling of the building cooling system as a stochastic optimization problem over a 24-hour look-ahead period to minimize the electricity cost of the studied building cooling system. After that, we applied the proposed stochastic load scheduling (SLS) to a direct expansion (DX) cooling system that serves a medium office building. Through simulation with a detailed building energy simulation software, EnergyPlus, we evaluated the operational cost and the thermal comfort compared with a deterministic load scheduling. The operation cost of scheduling was found to vary with the level of zone temperature prediction uncertainty. The proposed SLS can mitigate the impacts of uncertain zone temperature predictions on both operational cost and thermal comfort. The evaluation results indicate that the proposed SLS works better when the uncertainty level is more significant.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Multilevel Monte Carlo Estimators For Derivative-Free Optimization Under Uncertainty

Optimization is a key tool for scientific and engineering applications; however, in the presence of models affected by uncertainty, the optimization formulation needs to be extended to consider statistics of the quantity of interest. Optimization under uncertainty (OUU) deals with this endeavor and requires uncertainty quantification analyses at several design locations; i.e., its overall computational cost is proportional to the cost of performing a forward uncertainty analysis at each design location. An OUU workflow has two main components: an inner loop strategy for the computation of statistics of the quantity of interest, and an outer loop optimization strategy tasked with finding the optimal design, given a merit function based on the inner loop statistics. Here, in this work, we propose to alleviate the cost of the inner loop uncertainty analysis by leveraging the so-called multilevel Monte Carlo (MLMC) method, which is able to allocate resources over multiple models with varying accuracy and cost. The resource allocation problem in MLMC is formulated by minimizing the computational cost given a target variance for the estimator. We consider MLMC estimators for statistics usually employed in OUU workflows and solve the corresponding allocation problem. For the outer loop, we consider a derivative-free optimization strategy implemented in the SNOWPAC library; our novel strategy is implemented and released in the Dakota software toolkit. We discuss several numerical test cases to showcase the features and performance of our approach with respect to its Monte Carlo single fidelity counterpart.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Neural correspondence to spectrum of environmental uncertainty in multiple-cue probability judgment system with time delay

Despite state-of-the-art technologies like artificial intelligence, human judgment is critically essential in cooperative systems, such as the multi-agent system (MAS), which collect information among agents based on multiple-cue judgment. Human agents can prevent impaired situational awareness of automated agents by confirming situations under environmental uncertainty. System error caused by uncertainty can result in an unreliable system environment, and this environment affects the human agent, resulting in non-optimal decision-making in MAS. Thus, it is necessary to know how human behavior is changed to capture system reliability under uncertainty. Another issue affecting MAS is time delay, which can delay agent information transfer, resulting in low performance and instability. However, it is difficult to find studies on the influence of time delay on human agents. This study is about understanding the human decision-making process under a specific system reliability environment by uncertainty with time delay. We used concepts of expected and unexpected uncertainty to implement reliability of the system usage environment with three types of time delay conditions: no time delay, regular time delay, and irregular time delay conditions. We used electroencephalogram (EEG) for human cognitive neural mechanisms in multiple-cue judgment systems to understand human decision-making. In the reliability of system usage environment, the unreliable system environment significantly creates less memory load by less utilization of system rules for decision-making. In terms of time delay, delayed information delivery does not significantly affect memory load for decision-making.

cognitive process↗
DOE OSTI2022

Quantifying the impact of temporal analysis of products reactor initial state uncertainties on kinetic parameters

The temporal analysis of products (TAP) reactor, a transient kinetic tool, provides users with information as the catalyst state evolves. However, the state of the art for TAP uncertainty quantification only considers the experimental noise present in the outlet flow signal. Additional sources of uncertainty, including, but not limited to, initial surface coverages, the catalyst zone location, the inert void fraction, and the gas pulse intensity and pulse delay, are not included. For this reason, a framework for quantifying all uncertainty sources present in TAP experiments is presented and applied to a carbon monoxide oxidation case study. Herein, two methods for quantifying these sources of uncertainty are introduced. The first utilizes initial state sensitivities to approximate the parameter variances, as well as to provide insights into the structural certainty of the model. The second generates parameter confidence distributions through an ensemble-based sampling algorithm. This initial state covariance matrix can ultimately be merged with the experimental noise covariance matrix, providing a unified description of the parameter uncertainties for a single TAP experiment.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Preliminary investigation of an uncertainty budget for uranium isotope ratio analysis using a liquid sampling—atmospheric pressure glow discharge—orbitrap mass spectrometer system

The liquid sampling-atmospheric pressure glow discharge (LS-APGD) ionization source has proven to be an effective analysis tool for making uranium isotope ratio measurements when coupled to high-resolution mass spectrometers, such as the Orbitrap. While previous studies have shown the capabilities of the LS-APGD for isotope ratio determination, a systematic evaluation of the measurement uncertainty of the technique has not been conducted. To this end, the International Standards Organizations (ISO) guidelines to the expression of uncertainty in measurement (GUM analysis) have been applied to generate an uncertainty budget. For this work, a preliminary assessment derived from the GUM analysis was performed. The uncertainty in the instrument blank determination has been identified as a primary factor contributing to measurement uncertainty for the LS-APGD-Orbitrap method. These findings for the specific test case of uranium isotopic analysis will be invaluable in applications across the breadth of isotope ratio mass spectrometry performed on this unique instrumental platform.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2025

Uncertainty improvement of 22 Na based radioactive tracer dilution for determining total mass of pyroprocessing molten salt systems by 154 Eu removal

To determine the total salt mass of the molten salt systems for pyroprocessing spent nuclear fuels, a 22 Na based radioactive tracer dilution was studied in Idaho National Laboratory in recent years. This 22 Na based RTD technique was deemed feasible, but due to the gamma energy peak of 22 Na coinciding with one of the energy peaks of 154 Eu radioisotope in the molten salt, the uncertainty of the 22 Na radioactivity in the 22 Na-spiked salt samples was quite high. To improve the uncertainty of the 22 Na based RTD technique, we proposed to chemically remove the 154 Eu of the salt samples by DGA resin for gamma spectroscopy. The effectiveness of removing 154 Eu on uncertainty improvement was evaluated. Furthermore, it was found that (1) the 154 Eu fission product effect on the uncertainty and detection limit can be effectively eliminated by chemically removing the 154 Eu during the salt sample preparation and (2) the uncertainty of 22 Na radioactivity in the salt samples for electrorefining was significantly improved from 13% to 2%, showing the potential of practical engineering application of 22 Na based RTD as a safeguards technique for molten salt systems for pyroprocessing spent nuclear fuels.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Uncertainty Quantification Framework for Predicting Material Response with Large Number of Parameters: Application to Creep Prediction in Ferritic-Martensitic Steels Using Combined Crystal Plasticity and Grain Boundary Models

This paper presents an uncertainty quantification (UQ) framework for the physics-based model prediction of material response with a large number of parameters. The application problem presented in this work is that of predicting creep in Grade 91 steel at 600°C. The material response is defined with a physically based microstructural model with constitutive equations emulating several observed phenomena in Grade 91 and embodied into an explicit geometry mesoscale finite element model for prior austenite grains and grain boundaries. Creep within the grains and in grain boundaries are represented by crystal plasticity for dislocation motion and a physics-based model for cavity growth and nucleation, respectively. The creep behavior of this material is influenced by several parameters, some of which have a wide range of variation based on experimental data. UQ combined with microstructural modeling can discover the core microstructural causes of experimental variability, leading to improved materials with lower variability in critical long-term material properties. In this study, we investigate the model's uncertainty to identify material properties that may be modified during production to increase creep life and analyze different components of the crystal plasticity model for improvements. For this purpose, a quantity of interest is defined as time to minimum creep rate, which correlates well to the creep failure of the material. A deep neural network model was trained and validated to be used as a surrogate for the finite element model. Then, a variance-based sensitivity analysis is performed on the surrogate model to find the Sobol indices of the input parameters in respect to the output quantity of interest. The Sobol indices are used to reduce the dimensionality of the model. Generalized polynomial chaos expansion is used on the reduced basis models to propagate the uncertainty from the input parameters to the quantity of interest using the deep neural network surrogate model. These results are benchmarked against uncertainty propagation using Monte Carlo simulations. In conclusion, the UQ performed through the reduced basis model captures almost all the uncertainty in the model with significantly fewer simulations, making it possible to perform the UQ directly via simulations with the finite element model rather than surrogate machine-learned models.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Catalytic resonance theory for parametric uncertainty of programmable catalysis

Microkinetic models are useful tools for screening catalytic materials; however, errors in their input parameters can lead to significant uncertainty in model predictions of catalyst performance. Here, in this work, we investigate the impact of linear scaling and Brønsted-Evans-Polanyi relation parametric uncertainty on microkinetic predictions of programmable-catalyst performance. Two case studies are considered: a generic A-to-B prototype reaction and the oxygen evolution reaction (OER). The results show that error-unaware models can accurately predict trends and, for the prototype reaction, values of optimal waveform parameters. The specific model parameters driving output uncertainty are identified via variance-based global sensitivity analysis. However, predictions of dynamic rate enhancement can decrease when uncertainty is propagated into the models. In both cases, we identify operating conditions where the programmable catalyst achieves a rate enhancement of at least one order of magnitude despite parametric uncertainty in the model, supporting programmable catalysis as a viable strategy for exceeding the Sabatier limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Bayesian prior construction for uncertainty quantification in first-principles statistical mechanics

First-principles statistical mechanics enables the prediction of thermodynamic and kinetic properties of materials, but is computationally expensive. Many approaches require surrogate models to calculate energies within Monte Carlo or molecular dynamics simulations. Inexpensive surrogates such as cluster expansions enable otherwise intractable calculations by interpolating data from higher accuracy methods, such as Density Functional Theory (DFT). Surrogate models introduce uncertainty into downstream calculations, in addition to any uncertainty inherent to DFT calculations. Bayesian frameworks address this by quantifying uncertainty and incorporating expert knowledge through priors. However, constructing effective priors remains challenging. This work introduces and describes practical strategies for building Bayesian cluster expansions, focusing on basis truncation, hyperparameter selection, and ground state replication. We analyze multiple basis truncation schemes, compare cross-validation to the evidence-approximation for hyperparameter optimization, and provide methods to find and enforce ground-state-preserving models through priors. Additionally, we compare the uncertainties between different approximations to DFT (LDA, PBE, SCAN) against the uncertainty introduced with the use of cluster expansion surrogate models. These approaches are demonstrated on the BCC Li x Mg 1-x and Li x Al 1-x alloys, which are both of interest for solid-state Li batteries. Our results provide guidelines for constructing and utilizing Bayesian cluster expansions, thereby improving the transparency of materials modeling. Furthermore, the approaches and insights developed in this work can be transferred to a wide range of cluster expansion surrogate models, including the atomic cluster expansion and related machine-learned interatomic potential architectures.

Alloy theory↗
DOE OSTI2021

A predictive discrete-continuum multiscale model of plasticity with quantified uncertainty

Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of uncertainty in the computational predictions delivered by them. In this work, a sequential multiscale model has been developed, incorporating discrete dislocation dynamics (DDD) simulations and a strain gradient plasticity (SGP) model to predict the size effect in plastic deformations of metallic micro-pillars. The DDD simulations include uniaxial compression of micro-pillars with different sizes and over a wide range of initial dislocation densities and spatial distributions of dislocations. An SGP model is employed at the continuum level that accounts for the size-dependency of flow stress and hardening rate. Sequences of uncertainty analyses have been performed to assess the predictive capability of the multiscale model. The variance-based global sensitivity analysis determines the effect of parameter uncertainty on the SGP model prediction. The multiscale model is then constructed by calibrating the continuum model using the data furnished by the DDD simulations. A Bayesian calibration method is implemented to quantify the uncertainty due to microstructural randomness in discrete dislocation simulations (density and spatial distribution of dislocations) on the macroscopic continuum model prediction (size effect in plastic deformation). Here, the outcomes of this study indicate that the discrete-continuum multiscale model can accurately simulate the plastic deformation of micro-pillars, despite the significant uncertainty in the DDD results. Additionally, depending on the macroscopic features represented by the DDD simulations, the SGP model can reliably predict the size effect in plasticity responses of the micropillars with below 10% of error.

36 MATERIALS SCIENCE↗