Uncertainty Quantification and Propagation in Computational Materials Science and Simulation-Assisted Materials Design

Honarmandi, Pejman; Arróyave, Raymundo

doi:10.1007/s40192-020-00168-2

Cited by 46 publications

(23 citation statements)

References 112 publications

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“…The effective properties for each microstructure occupying Ω RVE were computed using finite element simulations and Hill's averaging theorem [41,42] (see Supplementary Information: Structure-Property linkage). We assumed a contrast ratio of 50 in the properties of the two phases, i.e., E 1 /E 0 = 50 (where E 0 , E 1 are the elastic moduli of phases 0 and 1) 5 and a 1 /a 0 = 50 (where a 0 , a 1 are the conductivities of phases 0 and 1). In the following plots, phase 1 is always shown as white and phase 0 always as black.…”

Section: Resultsmentioning

confidence: 99%

“…While significant progress has been made in the forward and backward modeling of the process-structure and structureproperty linkages and in capturing the nonlinear and multiscale processes involved [3], much fewer efforts have attempted to integrate uncertainties which are an indispensable component of materials' analysis and design [4,5] since a) process variables do not fully determine the resulting microstructure but rather a probability distribution on microstructures [6], b) noise and incompleteness are characteristic of experimental data that are used to capture process-structure (most often) and structure-property relations [7], c) models employed for the process-structure or structure-property links are often stochastic and there is uncertainty in their parameters or form, especially in multiscale formulations [8], and d) model compression and dimension reduction employed in order to gain efficiency unavoidably leads to some loss of information which in turn gives rise to predictive uncertainty [9]. As a result, microstructure-sensitive properties can exhibit stochastic variability which should be incorporated in the design objectives.…”

Section: Introductionmentioning

confidence: 99%

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Self-supervised optimization of random material microstructures in the small-data regime

Rixner¹,

Koutsourelakis²

2021

Preprint

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While the forward and backward modeling of the process-structure-property chain has received a lot of attention from the materials community, fewer efforts have taken into consideration uncertainties. Those arise from a multitude of sources and their quantification and integration in the inversion process are essential in meeting the materials design objectives. The first contribution of this paper is a flexible, fully probabilistic formulation of such optimization problems that accounts for the uncertainty in the process-structure and structure-property linkages and enables the identification of optimal, high-dimensional, process parameters. We employ a probabilistic, data-driven surrogate for the structure-property link which expedites computations and enables handling of non-differential objectives. We couple this with a novel active learning strategy, i.e. a self-supervised collection of data, which significantly improves accuracy while requiring small amounts of training data. We demonstrate its efficacy in optimizing the mechanical and thermal properties of two-phase, random media but envision its applicability encompasses a wide variety of microstructure-sensitive design problems.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Self-supervised optimization of random material microstructures in the small-data regime

Rixner¹,

Koutsourelakis²

2021

Preprint

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“…As computing efficiency increased, several authors identified Markov Chain Monte Carlo (MCMC) as a powerful technique for optimizing Calphad model parameters and simultaneously determining their uncertainty with respect to the data [2,3]. Readers interested in further discussion of recent developments in Bayesian UQ for ICME, with application to Calphad, are directed to a recent review [4].…”

Section: Introductionmentioning

confidence: 99%

Sensitivity estimation for calculated phase equilibria

Otis

Bocklund

Liu

2021

Journal of Materials Research

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The development of a consistent framework for Calphad model sensitivity is necessary for the rational reduction of uncertainty via new models and experiments. In the present work, a sensitivity theory for Calphad was developed, and a closed‐form expression for the log‐likelihood gradient and Hessian of a multi‐phase equilibrium measurement was presented. The inherent locality of the defined sensitivity metric was mitigated through the use of Monte Carlo averaging. A case study of the Cr–Ni system was used to demonstrate visualizations and analyses enabled by the developed theory. Criteria based on the classical Cramér–Rao bound were shown to be a useful diagnostic in assessing the accuracy of parameter covariance estimates from Markov Chain Monte Carlo. The developed sensitivity framework was applied to estimate the statistical value of phase equilibria measurements in comparison with thermochemical measurements, with implications for Calphad model uncertainty reduction.

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“…So far, parameter calibration has been mostly uncertaintyagnostic and computational predictions have been rarely provided with an error bar. However, approaches based on Bayesian inference provide a convenient framework for uncertainty quantification, which is crucial in the verification of simulation results [2]. We will demonstrate how such a methodology can be applied to calibrate a thermodynamic model to experimental data of binary W-Ti alloys and to determine their degree of uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Applications of Data Driven Methods in Computational Materials Design

Dösinger

Spitaler

Reichmann

et al. 2021

Berg Huettenmaenn Monatsh

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In today’s digitized world, large amounts of data are becoming available at rates never seen before. This holds true also for materials science where high-throughput simulations and experiments continuously produce new data. Data driven methods are required which can make best use of the information stored in large data repositories. In the present article, two of such data driven methods are presented. First, we apply machine learning to generalize and extend the results obtained from computationally intense density functional theory (DFT) simulations. We show how grain boundary segregation energies can be trained with gradient boosting regression and extended to many more positions in the grain boundary for a complete description. The second method relies on Bayesian inference, which can be used to calibrate models to give data and quantification of the model uncertainty. The method is applied to calibrate parameters in thermodynamic models of the Gibbs energy of Ti-W alloys. The uncertainty of the model parameters is quantified and propagated to the phase boundaries of the Ti-W system.

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Uncertainty Quantification and Propagation in Computational Materials Science and Simulation-Assisted Materials Design

Cited by 46 publications

References 112 publications

Self-supervised optimization of random material microstructures in the small-data regime

Self-supervised optimization of random material microstructures in the small-data regime

Sensitivity estimation for calculated phase equilibria

Applications of Data Driven Methods in Computational Materials Design

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