Scattering-Based Structural Inversion of Soft Materials via Kolmogorov-Arnold Networks

TL;DR

This paper introduces a machine learning framework using Kolmogorov-Arnold Networks to directly invert small-angle scattering data, enabling detailed structural analysis of complex soft materials without relying on traditional analytical models.

Contribution

The paper presents a novel, model-independent machine learning approach that effectively extracts real-space structures from scattering spectra in soft matter systems.

Findings

Accurately resolves structures in lyotropic lamellar phases.

Efficiently analyzes colloidal suspensions.

Demonstrates versatility across diverse soft matter systems.

Abstract

Small-angle scattering (SAS) techniques are indispensable tools for probing the structure of soft materials. However, traditional analytical models often face limitations in structural inversion for complex systems, primarily due to the absence of closed-form expressions of scattering functions. To address these challenges, we present a machine learning framework based on the Kolmogorov-Arnold Network (KAN) for directly extracting real-space structural information from scattering spectra in reciprocal space. This model-independent, data-driven approach provides a versatile solution for analyzing intricate configurations in soft matter. By applying the KAN to lyotropic lamellar phases and colloidal suspensions -- two representative soft matter systems -- we demonstrate its ability to accurately and efficiently resolve structural collectivity and complexity. Our findings highlight the transformative potential of machine learning in enhancing the quantitative analysis of soft materials, paving the way for robust structural inversion across diverse systems.