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Entropy

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

Entropy

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Global Sensitivity Analysis Based on Entropy: From Differential Entropy to Alternative Measures.

¹Department of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology, 602 00 Brno, Czech Republic.

Entropy (Basel, Switzerland)

|July 2, 2021

Summary

Negative differential entropy is a flaw in global sensitivity analysis. This study proposes a new non-negative entropy-based sensitivity measure, improving sensitivity index structures and reducing higher-order indices.

Keywords:

entropy measures importance measure sensitivity analysis uncertainty quantification

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Area of Science:

* Mathematical and Computational Sciences
* Statistics and Probability

Background:

* Differential entropy can yield negative values, posing a significant flaw when employed as a sensitivity measure in global sensitivity analysis.
* Existing global sensitivity analysis methods based on differential entropy lack the non-negativity property inherent in measures like variance, unlike Sobol sensitivity analysis.

Purpose of the Study:

* To identify and address the flaw of negative entropy in differential entropy-based global sensitivity analysis.
* To propose a novel, non-negative sensitivity measure as an alternative to differential entropy.
* To evaluate the performance of the proposed measure in terms of sensitivity index structure.

Main Methods:

* Development of an alternative sensitivity measure approximating differential entropy using dome-shaped functionals with non-negative values.
* Application and comparison of the new measure against existing distributional sensitivity analysis methods through case studies.

Main Results:

* The proposed sensitivity measure consistently yields non-negative values, resolving the flaw of negative entropy.
* Case studies demonstrate that the new measure results in a more rational structure of sensitivity indices.
* A significantly lower proportion of higher-order sensitivity indices were observed compared to other distributional sensitivity analysis techniques.

Conclusions:

* The proposed non-negative sensitivity measure offers a theoretically sound and practically advantageous alternative for global sensitivity analysis.
* The findings suggest that the transition from differential to discrete entropy, as variance approaches zero, warrants further interdisciplinary investigation.
* The ongoing search for improved functionals for distributional sensitivity analysis may yield further advancements in the field.