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_2NiF_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_2NiF_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.