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Related Experiment Videos

Maximum entropy and the problem of moments: a stable algorithm.

K Bandyopadhyay1, A K Bhattacharya, Parthapratim Biswas

  • 1Department of Physics, University of Burdwan, Burdwan, West Bengal 713104, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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This study introduces an entropy optimization technique to derive probability distributions from moments. The method iteratively constructs solutions in a dual space, showing stability and performance on complex functions and in electronic structure calculations.

Area of Science:

  • Computational Physics
  • Information Theory
  • Materials Science

Background:

  • Calculating probability distributions from moments is crucial in many scientific fields.
  • Existing methods can be computationally intensive or unstable for complex functions.
  • Shannon entropy offers a principled approach to distribution reconstruction.

Purpose of the Study:

  • To develop a novel entropy optimization technique for distribution calculation from moments.
  • To enhance the stability and performance of distribution reconstruction algorithms.
  • To apply the technique to electronic structure problems, specifically amorphous silica.

Main Methods:

  • Maximizing a discretized Shannon entropy functional.
  • Mapping the problem to a dual space for iterative solution construction.

Related Experiment Videos

  • Testing the algorithm on numerically challenging functions and electronic density of states.

    • Main Results:

    • The developed algorithm demonstrates robust performance and stability.
    • Successful application to calculating the electronic density of states for amorphous silica.
    • Analysis of Fermi level convergence with an increasing number of moments.

    Conclusions:

    • Entropy optimization provides an effective method for distribution reconstruction from moments.
    • The technique offers a stable and performant alternative for complex computational problems.
    • The study highlights the potential of this method in materials science and electronic structure theory.