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Uncertainty: Overview00:59

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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 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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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 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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Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value. 
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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Spatially Resolved Uncertainties for Machine Learning Potentials.

Esther Heid1, Johannes Schörghuber1, Ralf Wanzenböck1

  • 1Institute of Materials Chemistry, TU Wien, A-1060 Vienna, Austria.

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This summary is machine-generated.

This study introduces a novel method to accurately estimate errors in machine learning potentials by aggregating epistemic uncertainty. This enables efficient active learning for atomistic simulations, improving data set composition.

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Machine Learning

Background:

  • Machine learning potentials (MLPs) are crucial for atomistic simulations, offering near ab initio accuracy at lower computational cost.
  • Improving the accuracy of MLPs necessitates careful data set composition, with reliable identification of prediction errors being a key challenge.
  • Current uncertainty estimation techniques for MLPs have shown limited success in correlating uncertainty with actual model error.

Purpose of the Study:

  • To develop a versatile method for correlating uncertainty estimates with model errors in machine learning potentials.
  • To enable reliable identification of erroneously predicted configurations for data set extension.
  • To design an active learning framework that leverages accurate uncertainty quantification for efficient simulation data generation.

Main Methods:

  • Investigated the correlation between epistemic uncertainty and model error in machine learning potentials.
  • Developed a method to aggregate epistemic uncertainty over groups of atoms to improve correlation with model error.
  • Implemented an active learning framework utilizing local uncertainty estimates to guide the selection of configurations for ab initio calculations.

Main Results:

  • Demonstrated that while epistemic uncertainty alone does not correlate with model error, its aggregation over atomic groups yields a strong correlation.
  • Showcased that the proposed method accurately estimates prediction errors both globally (per structure) and locally (per atom).
  • Successfully applied the active learning framework to efficiently generate data for simulations of liquid water in a low-data regime.

Conclusions:

  • The developed method provides a reliable way to estimate prediction errors in machine learning potentials by leveraging aggregated epistemic uncertainty.
  • This approach facilitates the design of effective active learning strategies, significantly improving the efficiency of generating high-quality simulation data.
  • The findings pave the way for more accurate and computationally efficient atomistic simulations across various scientific domains.