Scattering-based structural inversion of soft materials via Kolmogorov-Arnold networks

Area of Science:

• Soft Matter Physics
• Materials Science
• Computational Science

Background:

• Small-angle scattering (SAS) is crucial for soft material structure analysis.
• Traditional models struggle with complex systems due to the lack of closed-form scattering functions.
• Accurate structural inversion is vital for understanding soft matter behavior.

Purpose of the Study:

• To develop a machine learning framework for direct real-space structural analysis from reciprocal-space scattering data.
• To overcome limitations of traditional analytical models in complex soft matter systems.
• To demonstrate a model-independent, data-driven approach for structural inversion.

Main Methods:

• Implementation of a machine learning framework utilizing the Kolmogorov-Arnold Network (KAN).
• Direct extraction of real-space structural information from scattering spectra.
• Application and validation of the KAN framework on lyotropic lamellar phases and colloidal suspensions.

Main Results:

• The KAN framework successfully extracts real-space structural information directly from scattering spectra.
• Accurate and efficient resolution of structural collectivity and complexity in tested soft matter systems.
• Demonstrated model-independence and data-driven capabilities for structural analysis.

Conclusions:

• Machine learning, specifically KAN, offers a transformative approach to quantitative analysis of soft materials.
• The developed framework provides a versatile solution for intricate structural configurations.
• This method paves the way for robust structural inversion across a wide range of soft matter systems.