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Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

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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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Propagation of Uncertainty from Random Error00:59

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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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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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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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Uncertainty-aware mixed-variable machine learning for materials design.

Hengrui Zhang1, Wei Wayne Chen1, Akshay Iyer1

  • 1Department of Mechanical Engineering, Northwestern University, Evanston, IL, 60208, USA.

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Summary
This summary is machine-generated.

Bayesian optimization (BO) accelerates materials discovery by reducing search costs. This study compares frequentist and Bayesian models for BO with mixed variables, offering guidance for materials design applications.

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Area of Science:

  • Materials Science
  • Computational Chemistry
  • Machine Learning

Background:

  • Data-driven design accelerates materials discovery but faces challenges in navigating vast chemical and structural spaces.
  • Bayesian optimization (BO) reduces discovery costs by using uncertainty-aware machine learning to select promising candidates.
  • BO with mixed numerical and categorical variables is crucial for materials design but remains underexplored.

Purpose of the Study:

  • To survey frequentist and Bayesian uncertainty quantification methods for machine learning with mixed variables.
  • To systematically compare the performance of representative frequentist (Lolo) and Bayesian (latent variable Gaussian process) models in BO.
  • To provide practical guidance for selecting appropriate models for mixed-variable BO in materials design.

Main Methods:

  • Survey of frequentist and Bayesian approaches for uncertainty quantification in machine learning with mixed variables.
  • Comparative performance study of Lolo (random forest-based, frequentist) and latent variable Gaussian process (Bayesian) models within a Bayesian optimization framework.
  • Evaluation across mathematical functions and material property optimization problems (structural and functional materials).

Main Results:

  • Observed performance differences between frequentist and Bayesian models, influenced by problem dimensionality and complexity.
  • Analysis of machine learning models' predictive accuracy and uncertainty estimation capabilities provided interpretations for performance variations.
  • Demonstrated efficacy of both approaches in optimizing material properties, with distinct strengths depending on the problem characteristics.

Conclusions:

  • The study offers practical insights into selecting between frequentist and Bayesian uncertainty-aware machine learning models for mixed-variable Bayesian optimization in materials design.
  • Understanding model performance variations based on problem characteristics is key to successful application.
  • This research contributes to more efficient and cost-effective materials discovery through informed model selection.