Small-angle X-ray scattering (SAXS) lets us look inside nanoparticles without taking them apart. It is a key technique for the lipid nanoparticles that deliver nucleic-acid drugs, where the internal structure controls how well the particle works. But a scattering curve does not hand you a structure. Recovering the internal arrangement and the spread of particle sizes is an inverse problem, and different structures can produce almost the same curve. Realistic forward models are also slow, which makes systematic exploration impractical.
We built a differentiable, machine-learning-accelerated framework for SAXS analysis of heterogeneous, polydisperse nanoparticles (Bånkestad et al., 2026). Two ideas do the heavy lifting. First, a neural surrogate replaces the expensive per-particle scattering computation, cutting its cost by four orders of magnitude. Second, a differentiable integration layer sums over the distribution of particle sizes, so the whole pipeline, from structural parameters to predicted curve, is differentiable end to end.
Differentiability is what makes the analysis honest. We can run large-scale multi-start fitting to escape local optima, and, just as importantly, analyze which structural parameters are actually identifiable from the data and which are traded off against each other. On real MC3 lipid-nanoparticle data, the framework shows that near-identical fits can come from genuinely different structures, a caution that matters whenever SAXS is used to draw structural conclusions.
The framework: simulate scattering per particle, learn a neural surrogate, integrate over polydispersity, and use automatic differentiation to fit experimental data.
The neural surrogate reproduces the physics-based SAXS curves closely across the relevant range, which is what makes the fast, differentiable fitting reliable.
Lipid nanoparticles (LNPs) are efficient delivery systems for negatively charged nucleic acids. Their multi-component architecture yields a core-shell structure. Small-angle X-ray scattering (SAXS) is an important characterization technique for LNPs, but recovering internal structure and size distribution from SAXS is an inverse problem with non-unique solutions. Realistic models are often too expensive for systematic exploration. We introduce a machine-learning-accelerated, differentiable framework for SAXS analysis of heterogeneous, polydisperse LNPs. The forward model combines a core-shell particle with a Gaussian random-field interior, a neural surrogate for the monodisperse SAXS map, and a differentiable layer integrating over particle-size distributions. The surrogate reduces prediction cost by four orders of magnitude, while differentiability enables large-scale multi-start fitting and ensemble identifiability analysis. Applied to synthetic and experimental MC3 LNP data, the framework shows that near-identical SAXS fits can arise from distinct parameter modes, with the experimental fits dominated by a trade-off between size-distribution and interior-structure parameters.
@article{bankestad2026saxs,title={A differentiable machine learning small-angle X-ray scattering analysis framework for structure elucidation of lipid nanoparticles},author={B{\aa}nkestad, Maria and Barman, Sandra and R{\"o}ding, Magnus and Kaunisto, Erik and Meklesh, Viktoriia and Gallud, Audrey and Mendez, Marco and Yanez Arteta, Marianna and Norberg, Stefan and Terry, Ann and Chakraborty, Smita and Yu, Shun and R{\"o}nnols, Jerk and Pashami, Sepideh},journal={arXiv preprint arXiv:2606.05200},year={2026},}
