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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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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 interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
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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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Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...
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Uncertainty Prediction for Machine Learning Models of Material Properties.

Francesca Tavazza1, Brian DeCost1, Kamal Choudhary1

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Quantifying uncertainty in artificial intelligence (AI) material property predictions is crucial. This study compares methods for individual prediction intervals, favoring direct modeling for accuracy and ease of use in materials science.

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Area of Science:

  • Materials Science
  • Artificial Intelligence
  • Computational Materials Science

Background:

  • Uncertainty quantification (UQ) is vital for reliable AI in materials science.
  • Confidence intervals are common for ML models, but individual prediction intervals are less frequent.
  • Accurate prediction intervals enhance trust and applicability of AI-driven material discovery.

Purpose of the Study:

  • To compare three distinct methods for calculating individual prediction intervals in AI-based material property predictions.
  • To evaluate the advantages and disadvantages of each UQ approach.
  • To identify the most effective method for reliable uncertainty estimation in materials informatics.

Main Methods:

  • Comparison of three approaches: quantile loss function, direct prediction interval modeling, and Gaussian processes.
  • Testing on 12 machine learning (ML)-physical properties using data from the JARVIS-DFT database.
  • Development and availability of codes within the JARVIS-tools package for prediction interval computation.

Main Results:

  • Each method demonstrated unique strengths and weaknesses for UQ.
  • Direct modeling of prediction intervals proved easiest to implement.
  • Direct modeling generally minimized over- and underestimation of predicted errors across tested properties.

Conclusions:

  • Directly modeling individual prediction intervals is a promising approach for AI in materials science.
  • This method offers a balance of simplicity and accuracy in quantifying prediction uncertainty.
  • The developed tools facilitate the integration of robust UQ into materials informatics workflows.