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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Sensitivity and Uncertainty Quantification of Transition Scenario Simulations

This report documents the first collective attempt at developing and applying capabilities to quantify uncertainties, assess parametric sensitivities, and optimize multiple parameters and metrics in fuel cycle simulations generated by the SA&I Campaign. To do this, external codes that were designed to perform sensitivity analysis and uncertainty quantification (SA&UQ) needed to be coupled to the SA&I Campaign’s nuclear fuel cycle simulators (NFCS). In FY20, two approaches were pursued: 1) coupling Cyclus to an ORNL-internal code called MOT (Metaheuristic Optimization Tool) and 2) coupling DYMOND to the opensource SA&UQ tool kit Dakota. The primary objective of having these NFCS/SA&UQ coupled capabilities is to better inform DOE-NE and other stakeholders on the results generated from the NFCS. For a given set of fuel cycle strategies, policies, and technology assumptions that make up a fuel cycle scenario, these NFCS have traditionally been used by the SA&I Campaign to provide quantitative answers in terms of year-by-year mass flows, infrastructure requirements, costs, etc. With these newly developed coupled capabilities, the SA&I Campaign can now efficiently simulate hundreds or thousands of these scenarios, sample large ranges of parameters and assumptions, and use the unique features of the SA&UQ tools to process the data. This enables providing answers with known and propagated uncertainties, determining the sensitivity of important metrics to different parameters and assumptions, quantifying how much fuel cycle and technology parameters impact each other, and producing optimized fuel cycle strategies for single and multiple variables. To demonstrate these new capabilities, the Cyclus/MOT was used to model several scenarios ranging from simple fleet retirements to transitions to advanced reactors. Specifically, for a transition scenario from LWRs to SFRs and advanced LWRs, uncertainty quantification, sensitivity analysis, and optimization studies were applied to cases involving single and multiple parameter (input) and single and multiple metric (output) variations. In addition, a similar transition scenario was modeled to demonstrate how to optimize the reprocessing capacity parameter to minimize two performance metrics while taking into account uncertainties from two other parameters. Lastly, a depletion module based on SCALE/ORIGEN was added in Cyclus to simulate the third scenario that was designed to quantify the impact of the modeling assumption that all LWR used nuclear fuel have the same burnup. The newly developed DYMOND/Dakota capability was also applied to a transition scenario from the existing fleet to small modular reactors and fast reactors. This particular scenario involves not only explicit isotopic depletion via ORIGEN-2, but also includes multirecycling and utilizing the criticality search feature to determine the fresh fuel composition of recycled fuel, a feature unique to the DYMOND NFCS. A large database of simulations were run with 4 main parameters that were sampled: start date of reprocessing, reprocessing capacity, energy demand growth rate, and advanced reactor share of the fleet. The 4 main metrics were uranium consumption, enrichment requirements, waste generation, and levelized cost of electricity using data from the Cost Basis Report. The demonstrated SA&UQ results include those that inform on how to choose parameters to avoid “failed” scenarios, Sobol’ indices that inform on the importance of various parameters individually and synergistically, and Analysis of Variance (ANOVA) studies that decompose parameter ranges into groups and informs on whether variations are statistically significant.

Feng, B.↗
DOE OSTI2023

Understanding the Uncertainty in the Technical Performance Level Assessment for Wave Energy

In recent years, the design and development of wave energy converters (WECs) has been explored with intense interest, with highly varying design concepts emerging globally across both research enterprises and industry. The design space for WECs is vast - many concepts ranging in functionality, control systems, power development systems, materials, and scale have been ideated and prototyped, but WEC technology has yet to converge. One critical element of the technology trajectory that governs the speed of adoption is the performance of a WEC concept. In analogous but more-established industries (such as aerospace, and environmentally sustainable electronics design), performance assessment is a quantitative method, based on historical data, that is used as an iterative tool to improve the design of these systems early on in the design process. Though more nascent than these approaches, in wave energy R&D, WEC performance has been assessed using the Technology Performance Level (TPL) assessment, which provides designers with a quantitative score, situating a grid-scale WEC concept on a scale from 1-9 (1 being the lowest performance, and 9 being the highest, trending with the oft-used Technology Readiness Level, or TRL). The TPL assessment is designed to be used during design iteration, when a WEC concept is fully ideated, to enable designers to consider potential means of improving the downstream performance of the concept. One concern that may be slowing the adoption of TPL among WEC developers is the inherent uncertainty in the assessment, and how uncertainty in the individual questions asked as part of the assessment may contribute to perceived inaccuracies in the final score. In this work, we explore the uncertainty present in the assessment and quantify this uncertainty using both traditional mathematical operations and a Monte Carlo simulation. Results imply areas of improvement of the TPL assessment, where reducing uncertainty will be most helpful to end users, enabling both TPL practitioners and users to understand with more accuracy those design elements that can be improved to impact device performance most substantively.

techno-economic analysis↗
DOE OSTI2025

Uncertainty based Online Ensemble on Non-Stationary Data for Fusion Science

Machine Learning (ML) is poised to play a pivotal role in the development and operation of next-generation fusion devices. Fusion data shows non-stationary behavior due to drifts in the data. The drifts can arise from both experimental evolution and machine wear-and-tear. ML models assume stationary distribution and fail to maintain performance when encountered with non-stationary data streams.Online learning can be used to continuously adapt the models with new data as it is acquired. However, traditional online learning can suffer from short-term performance degradation, as ground truth are not available before making the prediction. To address this challenge, we propose uncertainty aware ensemble approach for online learning. We use Deep Gaussian Process Approximation (DGPA) technique for calibrated uncertainty estimation and use the uncertainty values to guide a meta-algorithm that produces predictions based on ensemble of learners. Moreover, DGPA also provides uncertainty estimation along with the predictions for decision makers. This paper demonstrates that the proposed method outperforms traditional online learning approach, and a naive ensemble without uncertainty guidance by about 7% and 6%, respectively, on B-coil deflection prediction at DIII-D Fusion Facility.

Rajput, Kishansingh [Thomas Jefferson National Acc↗
DOE OSTI2021

Robust vehicle routing under uncertainty via branch-price-and-cut

Here, this paper contemplates how branch-price-and-cut solvers can be employed along with the robust optimization paradigm to address parametric uncertainty in the context of vehicle routing problems. In this setting, given postulated uncertainty sets for customer demands and vehicle travel times, one aims to identify a set of cost-effective routes for vehicles to traverse, such that the vehicle capacities and customer time window constraints are respected under any anticipated demand and travel time realization, respectively. To tackle such problems, we propose a novel approach that combines cutting-plane techniques with an advanced branch-price-and-cut algorithm. Specifically, we use deterministic pricing procedures to generate "partially robust" vehicle routes and then utilize robust versions of rounded capacity inequalities and infeasible path elimination constraints to guarantee complete robust feasibility of routing designs against demand and travel time uncertainty. In contrast to recent approaches that modify the pricing algorithm, our approach is both modular and versatile. It permits the use of advanced branch-price-and-cut technologies without significant modification, while it can admit a variety of uncertainty sets that are commonly used in robust optimization but could not be previously employed in a branch-price-and-cut setting.

42 ENGINEERING↗
DOE OSTI2020

Bottom-up and Top-Down Uncertainty Quantification for Measurements

Several recent papers address improved uncertainty quantification (UQ) for measurements used in nuclear safeguards. This paper reviews progress and presents new results for bottom-up (first principles) and top-down (empirical) UQ for safeguards, where the main quantitative measure of uncertainty is the total measurement error standard deviation (SD), which includes both random and systematic error components. The five main UQ topics addressed here include: (1) impact of making data-driven choices in SD estimation; (2) use of approximate Bayesian computation (ABC) for both bottom-up and top-down UQ; (3) computational calibration; (4) revisions to the guide to the expression of uncertainty in measurement (GUM), and (5) critique of a recently-suggested “Unified Theory of Measurement Errors and Uncertainties.”

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2026

An uncertainty visualization framework for large-scale cardiovascular flow simulations: A case study on aortic stenosis

We present a generalizable uncertainty quantification (UQ) and visualization framework for lattice Boltzmann method simulations of high Reynolds number vascular flows, demonstrated on a patient-specific stenosed aorta. The framework combines EasyVVUQ for parameter sampling with large-eddy simulation turbulence modeling in HemeLB, and executes ensembles on the Frontier exascale supercomputer. Spatially resolved metrics, including entropy and isosurface-crossing probability, are used to map uncertainty in pressure and wall shear stress fields directly onto vascular geometries. Two sources of model variability are examined: inlet peak velocity and the Smagorinsky constant. Inlet velocity variation produces high uncertainty downstream of the stenosis where turbulence develops, while upstream regions remain stable. Smagorinsky constant variation has little effect on the large-scale pressure field but increases WSS uncertainty in localized high-shear regions. In both cases, the stenotic throat manifests low entropy, indicative of robust identification of elevated WSS. By linking quantitative UQ measures to three-dimensional anatomy, the framework improves interpretability over conventional 1D UQ plots and supports clinically relevant decision-making, with broad applicability to vascular flow problems requiring both accuracy and spatial insight.

Hemodynamics↗
DOE OSTI2025

Decision-Dependent Uncertainty-Aware Distribution System Planning Under Wildfire Risk

The interaction between power systems and wildfires can be dangerous and costly. Distribution grids can be liable for the outbreak of wildfires during extreme weather. In wildfire-prone areas, investment planning should consider the impact of operational actions on wildfire-related uncertainties affecting line failure likelihood. Here, in this case, endogenous-based uncertainty modeling should comprise the backbone of the investment planning model viz-a-viz the inability of standard exogenous-based uncertainty modeling. Therefore, we propose a decision-dependent uncertainty (DDU) aware methodology to optimize investment portfolios for distribution systems, considering that high power-flow levels in high-threat areas can ignite wildfires and increase line failure probability. The methodology identifies the best combination of upgrades (new lines, hardening existing lines, and placing switching devices). Methodologically, we propose a two-stage distributionally robust planning optimization problem with DDU that considers the distribution system's multiperiod operation. The first stage determines optimal switching actions and line investments, and the second stage evaluates the worst-case expected operational cost under a DDU framework designed to account for the endogenous impact of power-flow levels and hardening investment decisions in the line failure probabilities. An iterative method is tailored to handle the problem and numerical experiments demonstrate a more prepared grid to deal with wildfire risk.

Power systems investment planning↗
DOE OSTI2025

Deliverable 6.7-Final Technical Report: Development Summary and Evaluation of the Solar Uncertainty Integrator (SUNI) Software

The Data Quality and Uncertainty Integration Project was a three-year effort to address stakeholder needs for assessing solar radiation resource data quality based on existing tools for estimating radiometer measurement uncertainties and assessing post-measurement data quality. The annual research objectives for the project addressed a logical progression of effort needed to achieve the ultimate project goal of developing the Solar Uncertainty Integrator (SUNI) software. This final technical report summarizes the development process for achieving these key research objectives and addresses the outreach and code development efforts in the final year of the project to develop a new solar irradiance data uncertainty integration software package.

14 SOLAR ENERGY↗
NASA NTRSDate not supplied

Design Under Uncertainty with Design-Dependent Uncertain Variables

Uncertainty quantification (UQ) can provide a more robust understanding of a system, leading to better informed decisions earlier in the design process. The additional information that UQ provides can be leveraged during a design optimization process known as design under uncertainty that, when incorporated with multidisciplinary design and optimization, can become computationally infeasible due to the large number of responses required for meaningful results. Previous work addressed reducing the computational expense in design under uncertainty by incorporating analytic derivatives throughout polynomial chaos expansion. Although this allows design under uncertainty to be feasible for more systems, some multidisciplinary systems have design-dependent uncertain variables. This paper details an implementation of design dependent uncertain variables in a manner than preserves derivatives required for efficient gradient-based optimization throughout the process. Two analytic examples of design-dependent uncertain variables are given: the first transforms a uniform uncertain variable with one design variable and the second transforms a normal uncertain variable with two design variables. The polynomial chaos expansion (PCE) results are comparable to both the Monte Carlo (MC) results and the analytic results for the two examples. A case study that maximizes the lift-to-drag ratio with a design-dependence between the wing leading edge sweep angle and uncertain parameter percentage of laminar flow is compared to a MC and alternative optimization formulations. This paper demonstrates that design-dependent uncertain variables are valid and hold throughout PCE.

robust design↗
DOE OSTI2020

Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models

We use a conditional Karhunen-Lo` eve (KL) model to quantify and reduce uncertainty in a stochastic partial differential equation (SPDE) problem with partially-known space-dependent coefficient, Y (x). We assume that a small number of Y (x) measurements are available and model Y (x) with a KL expansion. We achieve reduction in uncertainty by conditioning the KL expansion coefficients on measurements. We consider two approaches for conditioning the KL expansion: In Approach 1, we condition the KL model first and then truncate it. In Approach 2, we first truncate the KL expansion and then condition it. We employ the conditional KL expansion together with Monte Carlo and sparse grid collocation methods to compute the moments of the solution of the SPDE problem. Uncertainty of the problem is further reduced by adaptively selecting additional observation locations using two active learning methods. Method 1 minimizes the variance of the PDE coefficient, while Method 2 minimizes the variance of the solution of the PDE. We demonstrate that conditioning leads to dimension reduction of the KL representation of Y (x). For a linear diffusion SPDE with uncertain log-normal coefficient, we show that Approach 1 provides a more accurate approximation of the conditional log-normal coefficient and solution of the SPDE than Approach 2 for the same number of random dimensions in a conditional KL expansion. Furthermore, Approach 2 provides a good estimate for the number of terms of the truncated KL expansion of the conditional field of Approach 1. Finally, we demonstrate that active learning based on Method 2 is more efficient for uncertainty reduction in the SPDE’s states (i.e., it leads to a larger reduction of the variance) than active learning using Method 2.

Conditioned Karhunen-Lo` eve expanion, machine lea↗
DOE OSTI2023

Automated Generation of Microkinetics for Heterogeneously Catalyzed Reactions Considering Correlated Uncertainties**

Abstract The study presents an ab‐initio based framework for the automated construction of microkinetic mechanisms considering correlated uncertainties in all energetic parameters and estimation routines. 2000 unique microkinetic models were generated within the uncertainty space of the BEEF‐vdW functional for the oxidation reactions of representative exhaust gas emissions from stoichiometric combustion engines over Pt(111) and compared to experiments through multiscale modeling. The ensemble of simulations stresses the importance of considering uncertainties. Within this set of first‐principles‐based models, it is possible to identify a microkinetic mechanism that agrees with experimental data. This mechanism can be traced back to a single exchange‐correlation functional, and it suggests that Pt(111) could be the active site for the oxidation of light hydrocarbons. The study provides a universal framework for the automated construction of reaction mechanisms with correlated uncertainty quantification, enabling a DFT‐constrained microkinetic model optimization for other heterogeneously catalyzed systems.

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

Quantifying subsurface parameter and transport uncertainty using surrogate modelling and environmental tracers

Here, we combine physics-based groundwater reactive transport modelling with machine-learning techniques to quantify hydrogeological model and solute transport predictive uncertainties. We train an artificial neural network (ANN) on a dataset of groundwater hydraulic heads and 3 H concentrations generated using a high-fidelity groundwater reactive transport model. Using the trained ANN as a surrogate model to reproduce the input–output response of the high-fidelity reactive transport model, we quantify the posterior distributions of hydrogeological parameters and hydraulic forcing conditions using Markov chain Monte Carlo calibration against field observations of groundwater hydraulic heads and 3 H concentrations. We demonstrate the methodology with a model application that predicts Chlorofluorocarbon-12 (CFC-12) solute transport at a contaminated field site in Wyoming, United States. Our results show that including 3 H observations in the calibration dataset reduced the uncertainty in the estimated permeability field and infiltration rates, compared to calibration against hydraulic heads alone. However, predictive uncertainty quantification shows that CFC-12 transport predictions conditioned to the parameter posterior distributions cannot reproduce the field measurements. We found that calibrating the model to hydraulic head and 3 H observations results in groundwater mean ages that are too large to explain the observed CFC-12 concentrations. The coupling of the physics-based reactive transport model with the machine-learning surrogate model allows us to efficiently quantify model parameter and predictive uncertainties, which is typically computationally intractable using reactive transport models alone.

58 GEOSCIENCES↗
DOE OSTI2021

Lowering post‐construction yield assessment uncertainty through better wind plant power curves

Abstract Many operational analyses of wind power plants require a statistical relationship, which can be called the wind plant power curve, to be developed between wind plant energy production and concurrent atmospheric variables. Currently, a univariate linear regression at monthly resolution is the industry standard for post‐construction yield assessments. Here, we evaluate the benefits in augmenting this conventional approach by testing alternative regressions performed with multiple inputs, at a finer time resolution, and using nonlinear machine‐learning algorithms. We utilize the National Renewable Energy Laboratory's open‐source software package OpenOA to assess wind plant power curves for 10 wind plants. When a univariate generalized additive model at daily or hourly resolution is used, regression uncertainty is reduced, in absolute terms, by up to 1.0 % and 1.2 % (corresponding to a −59 % and −80 % relative change), respectively, compared to a univariate linear regression at monthly resolution; also, a more accurate assessment of the mean long‐term wind plant production is achieved. Additional input variables also reduce the regression uncertainty: when temperature is added as an input to the conventional monthly linear regression, the operational analysis uncertainty connected to regression is reduced, in absolute terms, by up to 0.5 % (−43 % relative change) for wind power plants with strong seasonal variability. Adding input variables to the machine‐learning model at daily resolution can further reduce regression uncertainty, with up to a −10 % relative change. Based on these results, we conclude that a multivariate nonlinear regression at daily or hourly resolution should be recommended for assessing wind plant power curves.

17 WIND ENERGY↗
DOE OSTI2023

Multi-fidelity Uncertainty Quantification for Homogenization Problems in Structure-Property Relationships from Crystal Plasticity Finite Elements

Crystal plasticity finite element method (CPFEM) has been an integrated computational materials engineering (ICME) workhorse to study materials behaviors and structure-property relationships for the last few decades. These relations are mappings from the microstructure space to the materials properties space. Due to the stochastic and random nature of microstructures, there is always some uncertainty associated with materials properties, for example, in homogenized stress-strain curves. For critical applications with strong reliability needs, it is often desirable to quantify the microstructure-induced uncertainty in the context of structure-property relationships. However, this uncertainty quantification (UQ) problem often incurs a large computational cost because many statistically equivalent representative volume elements (SERVEs) are needed. In this article, we apply a multi-level Monte Carlo (MLMC) method to CPFEM to study the uncertainty in stress-strain curves, given an ensemble of SERVEs at multiple mesh resolutions. By using the information at coarse meshes, we show that it is possible to approximate the response at fine meshes with a much reduced computational cost. We focus on problems where the model output is multi-dimensional, which requires us to track multiple quantities of interest (QoIs) at the same time. In conclusion, our numerical results show that MLMC can accelerate UQ tasks around 2.23x, compared to the classical Monte Carlo (MC) method, which is widely known as ensemble average in the CPFEM literature.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Quantifying Uncertainties in Modeling Wind Resource Data from Different PBL Schemes in the WRF Model: A Case Study Over the Puerto Rico Region

This study examines the modeling uncertainty of wind resource data stemming from the use of various planetary boundary layer (PBL) parameterizations available in the Weather Research and Forecasting (WRF) model. WRF-based wind simulations spanning 20 years at 3-km resolution using 11 different PBL schemes are used to objectively investigate the uncertainty in modeling wind speed for land-based wind (LBW) and offshore wind (OSW) locations in Puerto Rico. The uncertainty in the wind modeling for the 20-year dataset is quantified using the spread index (SI) and standard deviation (SD). For virtual LBW and OSW sites, the SI and SD values are analyzed as calculated across various spatial and temporal scales. Because the PBL's atmospheric stability conditions can be characterized into two dominant categories, the study focuses on analyzing the SI and SD for daytime (mainly unstable PBL conditions) and nighttime (mainly stable PBL conditions). For wind shear (10 m-200 m) at the OSW and LBW sites, WRF-based numerical experiments indicate the following SI (or SD) ranges: 39%-94% (0.74 m/s-1.44 m/s) during the daytime for OSW, 50%-75% (0.68 m/s-1.19 m/s) during the daytime for LBW, 37%-60% (0.73 m/s-1.12 m/s) during the nighttime for OSW, and 57%-143 % (0.65 m/s-1.43 m/s) during the nighttime for LBW. While a high SI is observed when modeling LBW during the nighttime, there are notable modeling uncertainties during the daytime on the leeward side of the orographic barriers for Puerto Rico.

17 WIND ENERGY↗
DOE OSTI2020

Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics

Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. Here, we propose an efficient uncertainty quantification framework utilizing a multilevel multifidelity Monte Carlo (MLMF) estimator to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. This is achieved by leveraging three cardiovascular model fidelities, each with varying spatial resolution to rigorously quantify the variability in hemodynamic outputs. We employ two low-fidelity models (zero- and one-dimensional) to construct several different estimators. Our goal is to investigate and compare the efficiency of estimators built from combinations of these two low-fidelity model alternatives and our high-fidelity three-dimensional models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. Our goal is to demonstrate that for this application it is possible to accelerate the convergence of the estimators by utilizing a MLMF paradigm. Therefore, we compare our approach to single fidelity Monte Carlo estimators and to a multilevel Monte Carlo approach based only on three-dimensional simulations, but leveraging multiple spatial resolutions. We demonstrate significant, on the order of 10 to 100 times, reduction in total computational cost with the MLMF estimators. We also examine the differing properties of the MLMF estimators in healthy versus diseased models, as well as global versus local quantities of interest. As expected, global quantities such as outlet pressure and flow show larger reductions than local quantities, such as those relating to wall shear stress, as the latter rely more heavily on the highest fidelity model evaluations. Similarly, healthy models show larger reductions than diseased models. In all cases, our workflow coupling Dakota’s MLMF estimators with the SimVascular cardiovascular modeling framework makes uncertainty quantification feasible for constrained computational budgets.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Uncertainty quantification of graph convolution neural network models of evolving processes

The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural networks have proved to be adept at modeling processes with spatial–temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there is a need to find uncertainty quantification methods that are suitable for neural networks. In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial–temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant. Specifically we apply these methods to graph convolutional neural network models of evolving systems modeled with recurrent neural network and neural ordinary differential equations architectures. We show that Stein variational inference is a viable alternative to Monte Carlo methods with some clear advantages for complex neural network models. For our exemplars, Stein variational interference gave similar pushed forward uncertainty profiles through time compared to Hamiltonian Monte Carlo, albeit with generally more generous variance. As a result, projected Stein variational gradient descent also produced similar uncertainty profiles to the non-projected counterpart, but large reductions in the active weight space were confounded by the stability of the neural network predictions and the convoluted likelihood landscape.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Effects of cluster expansion on the locations of phase transition boundary as a first step to quantify uncertainty in first principles statistical mechanics framework

Predicting phase diagrams from first principle calculations eliminates the need of tedious experimental trials and errors. Fully automating first principle phase diagram calculations without any sort of human intervention has been a long daunting task and troubling scientific communities for decades. This grand problem remains not fully resolved, largely due to the vastly high-dimensional parameter space associated with density functional theory, cluster expansion, lattice Monte Carlo, and the substantial uncertainty propagating through a set of complex simulations. As a first step to tackle this grand problem, we reported a first demonstration of how sensitive phase boundary locations can be to various cluster expansion fittings and input DFT training data. To the best knowledge of the authors, this study reported the first ever attempt to quantify uncertainty in first principles statistical mechanics framework. In addition, a semi-automated phase transition detection algorithm has been devised in this paper to deal with the associated statistical errors and uncertainties from Monte Carlo method and its predecessor DFT calculations and cluster expansions. This algorithm has been applied in a classical cluster expansion Mg-Cd binary alloy system to detect phase transitions at various locations of phase diagram using different cluster expansions to demonstrate its predictive power and quantify uncertainties. The results suggested that using Chebyshev basis function shifted the transition locations toward the dilute solid solution phase and expanded the phase stability of concentrated ordered phases to wider composition range. The addition of perturbed defect configurations into training data set lowered the order-disorder transition temperature to be away from true transition temperature, suggesting the transition nature is indeed configurational disorder dominated rather than defect assisted. Finally, we found that the weighting has negligible effect on the transition locations, except for the case of using Chebyshev basis function to fit all non-weighted configurations that can be susceptible to Monte Carlo sampling hysteresis.

36 MATERIALS SCIENCE↗