Posterior Inference of Hamiltonian Parameters from RIXS Spectroscopy

2026-08-13

AI Summary

This study addresses the challenge of posterior inference for Hamiltonian parameters in Resonant Inelastic X-ray Scattering (RIXS) spectra by proposing the first simulation-based inference framework. Integrating a physics-aware Vision Transformer, truncated marginal neural ratio estimation, and conditional flow matching, this approach enables efficient and accurate full posterior inference for nickel compounds under few-shot conditions. The method not only uncovers critical parameter correlations and yields predicted spectra highly consistent with experimental data but also achieves reliable uncertainty quantification. Consequently, this work establishes a novel paradigm for the spectroscopic analysis of complex quantum materials, overcoming longstanding limitations in extracting precise physical parameters from RIXS measurements through advanced probabilistic modeling and domain-informed deep learning architectures.

Abstract

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.

Problem

• Resonant Inelastic X-ray Scattering
• Hamiltonian Parameters
• Posterior Inference
• Simulation-based Inference
• Uncertainty Quantification

Innovation

• Simulation-Based Inference
• Conditional Flow Matching
• Vision Transformer
• Posterior Inference
• Resonant Inelastic X-ray Scattering