Observation geometry for uncertainty-aware Hamiltonian inference and experimental design in quantum magnets
Determining microscopic interactions from spectroscopic and scattering measurements is central to understanding quantum materials, yet it often remains unclear which interactions can be reliably revealed by the available experimental data and how additional experimental modalities should be designed to resolve the remaining ambiguities. Here we present an artificial intelligence-enabled framework for uncertainty-aware Hamiltonian inference and adaptive experimental design. By combining Hamiltonian-conditioned neural surrogates with Bayesian inference and observation geometry, the framework characterizes how measurements constrain Hamiltonian parameter space, quantifies the identifiability of microscopic interactions, and propagates posterior uncertainty directly in the physical Hamiltonian parameter space rather than an abstract learned representation. Using multimodal powder and single-crystal inelastic neutron scattering measurements of the quantum magnet NiPS$_{3}$, we demonstrate physically interpretable Hamiltonian inference, modality-aware uncertainty quantification, and adaptive experimental design. The framework provides a general strategy for uncertainty-aware microscopic characterization and multimodal experimental design across quantum materials.