Generative Kolmogorov-Arnold Network Architecture for Enhanced Quantative Small Angle Neutron Scattering Data Analysis

Small-angle neutron scattering (SANS) is a powerful tool for probing molecular interactions, offering essential insights into the statistical mechanics of soft matter systems. However, deriving analytical connections between microscopic interactions and scattering functions becomes particularly challenging in dense systems, where many-body correlations are complex and not easily truncated. To address these challenges, we developed a generative model based on an asymmetrical Kolmogorov-Arnold Network (KAN) architecture, grounded in the Kolmogorov-Arnold representation theorem. This flexible, efficient model serves as a numerical bridge between SANS data and the physical properties of the system, particularly adept at handling highly nonlinear responses to interaction parameters. The model generates smooth, continuous outputs as a function of the scattering vector and integrates with least-square fitting algorithms to enable robust parameter inversion. This approach addresses the fixed-point output limitations inherent in traditional neural networks. We validated the accuracy and reliability of our model by applying it to two important soft matter systems: charged repulsive colloids and lyotropic lamellar phases, both of which are of significant interest in chemical physics.