Posterior Inference of Hamiltonian Parameters from RIXS Spectroscopy

We present the first application of simulation-based inference to resonant inelastic X-ray scattering spectroscopy. Using truncated marginal neural ratio estimation to efficiently restrict the prior and conditional flow matching as the joint density estimator, we infer full posteriors with a modest simulation budget for two Ni$^{2+}$ compounds---NiPS$_3$ as a representative covalent case and K$_2$NiF$_4$ as a more atomic one. We demonstrate that a vision transformer encoder whose tokenization matches the physical layout of the RIXS map yields better-covered and sharper posteriors than generic image encoders. Applying the validated method to experimental NiPS$_3$ and K$_2$NiF$_4$ data, we recover a joint posterior that reveals parameter correlations invisible to point estimators, and a posterior predictive distribution that closely matches the observed spectrum. The amortized posterior unlocks a class of analyses not previously available to the field such as nuisance-marginalized uncertainty quantification, multi-measurement posterior fusion and active experimental design.