Bayesian uncertainty quantification and information fusion in CALPHAD-based thermodynamic modeling

Honarmandi, Pejman; Duong, Thien; Ghoreishi, Seyede Fatemeh; Allaire, Douglas; Arróyave, Raymundo

doi:10.1016/j.actamat.2018.11.007

Cited by 50 publications

(32 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While deterministic, this work demonstrates the advantages of using phase fractions over phase boundaries for quantifying phase diagrams. Finally, in 2019, Honarmandi et al developed a method to fuse CALPHAD models with different parameterizations and obtain uncertainty estimates that were potentially more reliable than those of a single parameterization [4]. This work also introduced uncertainty in invariants, though it was limited to the uncertainty with respect to temperature.…”

Section: A C C E P T E D Accepted Manuscriptmentioning

confidence: 99%

Quantified uncertainty in thermodynamic modeling for materials design

et al. 2019

View full text Add to dashboard Cite

Phase fractions, compositions and energies of the stable phases as a function of macroscopic composition, temperature, and pressure (X-T-P) are the principle correlations needed for the design of new materials and improvement of existing materials. They are the outcomes of thermodynamic modeling based on the CALculation of PHAse Diagrams (CALPHAD) approach. The accuracy of CALPHAD predictions vary widely in X-T-P space due to experimental error, model inadequacy and unequal data coverage. In response, researchers have developed frameworks to quantify the uncertainty of thermodynamic property model parameters and propagate it to phase diagram predictions. In most previous studies, uncertainty was represented as intervals on phase boundaries (with respect to composition or temperature) or invariant reactions (with respect to temperature) and was unable to represent the uncertainty in eutectoid invariant reactions or in the stability of phase regions. In this work, we propose a suite of tools that leverages samples from the multivariate model parameter distribution to represent uncertainty in forms that surpass previous limitations and are well suited to materials design. These representations include the distribution of phase diagrams and their features, as well as the dependence of phase stability and the distributions of phase fraction, composition, activity and Gibbs energy on X-T-P location -irrespective of the total number of components. Most critically, the new methodology allows the material designer to interrogate a certain composition and temperature domain and get in return the probability of different phases to be stable, which can positively impact materials design.

show abstract

Section: A C C E P T E D Accepted Manuscriptmentioning

confidence: 99%

Quantified uncertainty in thermodynamic modeling for materials design

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Uncertainty quantification of phase diagrams is the first step required to provide confidence for decision making in property-or performance-based design. In work that was the first of its kind (Honarmandi et al, 2019), the authors independently generated four CALPHAD models describing Gibbs free energies for the Hf − Si system. The calculation of the Hf − Si binary phase diagram and its uncertainties is of great importance since adding Hafnium to Niobium silicide based alloys (as promising turbine airfoil materials with high operating temperature) increases their strength, fracture toughness, and oxidation resistance significantly (Zhao et al, 2001).…”

Section: Bayesian Model Averaging and Information Fusion: Calphad-basmentioning

confidence: 99%

“…Optimum Hf-Si phase diagrams and their 95% Bayesian credible intervals (BCIs) obtained from models 1-4 (A-D) after uncertainty propagation of the MCMC calibrated parameters in each case. Reproduced with permission fromHonarmandi et al (2019).…”

mentioning

confidence: 99%

See 1 more Smart Citation

Experiment Design Frameworks for Accelerated Discovery of Targeted Materials Across Scales

et al. 2019

View full text Add to dashboard Cite

Over the last decade, there has been a paradigm shift away from labor-intensive and time-consuming materials discovery methods, and materials exploration through informatics approaches is gaining traction at present. Current approaches are typically centered around the idea of achieving this exploration through high-throughput (HT) experimentation/computation. Such approaches, however, do not account for the practicalities of resource constraints which eventually result in bottlenecks at various stage of the workflow. Regardless of how many bottlenecks are eliminated, the fact that ultimately a human must make decisions about what to do with the acquired information implies that HT frameworks face hard limits that will be extremely difficult to overcome. Recently, this problem has been addressed by framing the materials discovery process as an optimal experiment design problem. In this article, we discuss the need for optimal experiment design, the challenges in it's implementation and finally discuss some successful examples of materials discovery via experiment design.

show abstract

“…Surrogate models are then developed based on the scattered samples and serve as the basis for further optimization and uncertainty quantification. With development in the past decades, surrogate models have proved to be a major scheme for effective design optimization and uncertainty quantification of various mechanical systems including but not limited to composite laminates [4], thermodynamic modeling [5], chemo-thermal modeling of composites [6], computational fluid dynamics [7], high-performance computing [8], structural prognosis [9], crashworthiness-based lightweight design [10], time-dependent reliability design optimization [11], flapping wing design [12]. The accuracy of the surrogate model relies on the sampling scheme which systematically determines the location and number of samples.…”

Section: Introductionmentioning

confidence: 99%

A Strategy for Adaptive Sampling of Multi-Fidelity Gaussian Processes to Reduce Predictive Uncertainty

Ghosh

Kristensen

Zhang

et al. 2019

Volume 2B: 45th Design Automation Conference

View full text Add to dashboard Cite

Multi-fidelity Gaussian process is a common approach to address the extensive computationally demanding algorithms such as optimization, calibration and uncertainty quantification. Adaptive sampling for multi-fidelity Gaussian process is a changing task due to the fact that not only we seek to estimate the next sampling location of the design variable, but also the level of the simulator fidelity. This issue is often addressed by including the cost of the simulator as an another factor in the searching criterion in conjunction with the uncertainty reduction metric. In this work, we extent the traditional design of experiment framework for the multi-fidelity Gaussian process by partitioning the prediction uncertainty based on the fidelity level and the associated cost of execution. In addition, we utilize the concept of Believer which quantifies the effect of adding an exploratory design point on the Gaussian process uncertainty prediction. We demonstrated our framework using academic examples as well as a industrial application of steady-state thermodynamic operation point of a fluidized bed process

show abstract

Bayesian uncertainty quantification and information fusion in CALPHAD-based thermodynamic modeling

Cited by 50 publications

References 46 publications

Quantified uncertainty in thermodynamic modeling for materials design

Quantified uncertainty in thermodynamic modeling for materials design

Experiment Design Frameworks for Accelerated Discovery of Targeted Materials Across Scales

A Strategy for Adaptive Sampling of Multi-Fidelity Gaussian Processes to Reduce Predictive Uncertainty

Contact Info

Product

Resources

About