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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Extending the accuracy of the SNAP interatomic potential form.

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Updated: Dec 11, 2025

Knowledge Based Cloud FE Simulation of Sheet Metal Forming Processes
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Multi-fidelity machine-learning with uncertainty quantification and Bayesian optimization for materials design:

Anh Tran1, Julien Tranchida2, Tim Wildey1

  • 1Optimization and Uncertainty Quantification, Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87123, USA.

The Journal of Chemical Physics
|August 24, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a machine learning framework that combines high-accuracy (density functional theory) and fast (machine learning interatomic potential) atomistic simulations. This approach efficiently predicts materials properties and quantifies prediction uncertainty for faster materials design.

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Area of Science:

  • Computational Materials Science
  • Machine Learning in Materials Discovery
  • Atomistic Simulations

Background:

  • Accurate prediction of materials properties often requires computationally expensive high-fidelity methods like density functional theory (DFT).
  • Lower-fidelity methods, such as machine learning interatomic potentials (MLIPs), offer speed but lack accuracy and reliable uncertainty quantification.
  • Bridging these fidelity gaps is crucial for efficient materials design and discovery.

Purpose of the Study:

  • To develop and demonstrate a scale-bridging, multi-fidelity machine learning framework for atomistic materials simulations.
  • To integrate predictions from high-fidelity (DFT) and low-fidelity (MLIP) models.
  • To enable efficient materials property prediction and uncertainty quantification across alloy composition spaces.

Main Methods:

  • A multi-fidelity Gaussian process (MFGP) machine learning framework was developed to fuse predictions from DFT and MLIPs.
  • Uncertainty quantification was achieved through the posterior variance of the MFGP predictions.
  • The framework was coupled with Bayesian optimization for efficient on-the-fly materials property optimization.

Main Results:

  • The MFGP framework successfully reproduced the ternary composition dependence of the bulk modulus for aluminum-niobium-titanium random alloys.
  • The approach demonstrated computational efficiency by performing an on-the-fly search for the global optimum of bulk modulus.
  • This represents the first application of MFGP to fuse DFT and classical interatomic potential predictions in atomistic materials simulations.

Conclusions:

  • The presented multi-fidelity machine learning framework effectively bridges scale and fidelity gaps in atomistic simulations.
  • The method provides accurate property predictions with inherent uncertainty quantification, accelerating materials design.
  • This approach offers a computationally efficient pathway for exploring complex materials composition spaces.