A swarm intelligence approach to density function reconstruction from moments using entropy optimization.

Area of Science:

• Computational Physics
• Applied Mathematics
• Data Science

Background:

• Inverse problems are crucial in science and engineering.
• Entropy optimization (EOP) is a key technique for reconstructing distributions from moments.
• Existing methods face challenges with high-dimensional data and accuracy.

Purpose of the Study:

• To present a novel bioinspired optimization approach for entropy optimization problems.
• To reconstruct probability density distributions from a sequence of moments.
• To demonstrate the method's efficacy on diverse datasets.

Main Methods:

• Utilized a bioinspired optimization approach based on swarm intelligence.
• Addressed the Hausdorff moment problem by inverting moment sequences.
• Incorporated information from up to a thousand moments for enhanced accuracy.

Main Results:

• Successfully reconstructed invariant density functions for the logistics map.
• Determined spectral densities for large real-symmetric random matrices.
• Analyzed financial time series, including mutual fund price fluctuations.
• Achieved robust and accurate solutions using collective intelligence.

Conclusions:

• The bioinspired optimization approach offers an efficient and effective solution for entropy optimization inverse problems.
• The method demonstrates broad applicability across physics, mathematics, and finance.
• The technique provides accurate reconstructions of probability densities from moments.