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Uncertainty: Overview

Uncertainty: Overview

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...

The Uncertainty Principle

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

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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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Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

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Uncertainty estimation for molecular dynamics and sampling.

Giulio Imbalzano¹, Yongbin Zhuang², Venkat Kapil¹

¹Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.

The Journal of Chemical Physics

|February 20, 2021

Summary

This summary is machine-generated.

Quantifying errors in machine-learning potentials improves simulation accuracy. This work introduces methods to estimate uncertainty in thermodynamic averages, enhancing the reliability of simulations for materials science.

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Area of Science:

Computational Materials Science
Machine Learning in Physics
Statistical Mechanics

Background:

Machine-learning potentials (MLPs) accelerate simulations by replacing expensive electronic-structure calculations.
MLP accuracy relies on training data; predictions outside the training space are unreliable.
Uncertainty in individual configurations propagates to thermodynamic averages, limiting simulation accuracy in unexplored regions.

Purpose of the Study:

To develop methods for quantifying uncertainty in machine-learning potential predictions.
To enhance the resilience and accuracy of molecular dynamics simulations using MLPs.
To support active learning strategies for efficient model development.

Main Methods:

Utilized uncertainty quantification (UQ) with baseline energy models or less accurate interatomic potentials.
Introduced an on-the-fly reweighing scheme for estimating uncertainty in thermodynamic averages from long trajectories.
Applied methods to diverse systems (water, liquid gallium) and properties (structural, thermodynamic).

Main Results:

Demonstrated that UQ improves the robustness of simulations, especially in unexplored regions of phase space.
The on-the-fly reweighing scheme effectively estimates uncertainty in thermodynamic averages.
Validated the approach across different material systems and property types.

Conclusions:

Uncertainty quantification is crucial for reliable machine-learning potential-based simulations.
The proposed methods enhance simulation accuracy and support active learning for model improvement.
UQ provides a pathway to more trustworthy and efficient computational materials discovery.