Fast calculation of scattering patterns using hypergeometric function algorithms.

Area of Science:

• Materials Science
• Computational Physics
• Data Science

Background:

• Scattering techniques (light, X-rays, electrons, neutrons) are crucial for structural characterization across various length scales.
• Advances in beam sources and detectors allow high-speed acquisition of large scattering datasets, creating an analysis bottleneck.

Purpose of the Study:

• To develop a computationally efficient algorithm for analyzing scattering patterns.
• To overcome the limitations of current numerical integration methods in scattering data analysis.

Main Methods:

• Introduction of a novel algorithm based on hypergeometric functions.
• Leveraging analytical descriptions of geometrical shapes and rapid computation via series and asymptotic expansions.
• Implementation on Graphics Processing Units (GPUs) for enhanced performance.

Main Results:

• Achieved computational speed gains of up to 10⁵ compared to existing numerical integration algorithms.
• Demonstrated the capability to calculate scattering patterns on timescales suitable for real-time applications.
• Enabled efficient analysis of large-volume scattering data and generation of machine learning training sets.

Conclusions:

• The hypergeometric function-based algorithm significantly accelerates scattering data analysis.
• This advancement facilitates real-time experimental feedback and large-scale data processing.
• The algorithm supports the development of machine learning models for structural characterization.