Physics-guided evaluation of candidate electron density maps for SAXS phase assignment using multimodal machine learning

Small-angle X-ray scattering (SAXS) is a key technique for characterizing mesoscale structures in self-assembled soft materials. Among the structural information derived from SAXS, reconstructed electron density maps (ED maps) provide direct real-space representations of molecular packing, domain connectivity, and morphological organization. However, ED-map reconstruction is intrinsically constrained by the phase problem: different phase assignments can result in distinct real-space density distributions with the same diffraction intensities. Therefore, the central challenge is to identify the most physically plausible candidate. Herein, we develop a physics-guided multimodal machine-learning framework to evaluate the physical plausibility of candidate ED maps for SAXS phase assignment. The framework scores each reconstructed ED map according to its consistency with molecular topology, molecular electronic descriptors, crystallographic symmetry, SAXS reflection features, and real-space density morphology. By converting phase assignment into a quantitative plausibility-ranking task, the model distinguishes physically coherent ED maps from competing mathematically admissible solutions. Representative two- and three-dimensional examples demonstrate reliable selection of ED maps with reasonable density continuity, network connectivity, pore morphology, and interfacial features. Interpretability analyses further show that the model captures meaningful correlations between molecular characteristics, phase-sensitive diffraction features, and ED-map morphology. This work provides a reproducible strategy for physics-guided ED-map selection and artificial-intelligence-assisted SAXS structure determination, with potential applications in complex self-assembled soft-matter systems, giant molecules, and framework materials.