From Single Spins to Ensembles: A Calibrated Symbolic Regression Pipeline for NV Spectroscopy

Inverse problems in scientific sensing are often solved with either hand-designed regularizers or supervised networks trained on simulated labels, yet both can fail when the forward model is nonlinear, spectrally coupled, and physically delicate. We study this issue for noise sensing based on nitrogen-vacancy (NV) centers in diamond, where a quantum sensor measures magnetic-noise spectra generated by sparse spin sources. We show that replacing a common scalar/coherent forward approximation with a tensor power-summed dipolar operator changes the inverse landscape and exposes a center-collapse failure mode in free-density optimization. We propose NeTMY, an amortization-free coordinate neural field coupled to the differentiable NV forward model, with annealed positional encoding, multiscale optimization, sparsity/gating, and spectrum-fidelity losses. Across sparse synthetic reconstructions generated by the corrected operator, NeTMY achieves the best localization and distributional metrics in the tested benchmark. Mechanism experiments show that NeTMY does not directly execute the raw density-space gradient; its parameterization smooths and redistributes updates, mitigating the center-collapse pathology. These results position NV quantum sensing as a useful testbed for physics-faithful neural inverse problems.

Autonomous neutron spectroscopy must solve three distinct tasks: detection (where is the signal?), inference (which Hamiltonian governs it?), and refinement (what are the parameters?). No single controller solves all three equally well. We present TAS-AI, a hybrid agnostic-to-physics-informed framework for autonomous triple-axis spin-wave spectroscopy that separates these tasks explicitly. In blind reconstruction benchmarks, model-agnostic methods such as random sampling, coarse grids, and Gaussian-process mappers reach a global error threshold more reliably and with fewer measurements than physics-informed planning, supporting the claim that discovery and inference are distinct tasks requiring distinct controllers. Once signal structure is localized, the physics-informed stage performs in-loop Hamiltonian discrimination and parameter refinement: in a controlled square-lattice test between nearest-neighbor-only and J1-J2 Hamiltonians, TAS-AI reaches a decisive AIC-derived evidence ratio (>100) in fewer than 10 measurements, while motion-aware scheduling cuts wall-clock time by 32% at a fixed measurement budget. We also identify a failure mode of posterior-weighted design, algorithmic myopia, in which the planner over-refines the current leading model while under-sampling low-intensity falsification probes. A constrained falsification channel sharply reduces time spent committed to the wrong model and accelerates correct model selection without modifying the Bayesian inference engine. In controlled two-model ablations, both a deterministic top-two max-disagreement rule and an LLM-based audit committee achieve this gain under identical constraints. We demonstrate the full workflow in silico using a high-fidelity digital twin and provide an open-source Python implementation.

Vibrational spectral prediction can become inaccurate when localized stereoelectronic environments perturb intermediate response states and high-risk response units dominate characteristic spectral fingerprints, making prediction across external chemical space difficult. SO(3) Equivariant Neural Kalman Networks (SENK) form a response-state cascade that combines an equivariant transformer backbone for Hessian, dipole-derivative and polarizability-derivative learning, an Equivariant Neural Kalman bridge for state-dependent refinement and reliability sensing, and an NBO-informed electronic-prior pathway coupling consistency regularization with bounded, branch-specific guided spectral calibration. SENK outperforms DetaNet on QM9S and QMe14S while preserving full-spectrum IR and Raman fidelity from small molecules to drug-like systems. SENK remains stable and selectively improves spectrally sensitive features in biomolecular systems with complex stereoelectronic effects. It therefore integrates tensor prediction, reliability diagnosis and physics-informed calibration, supporting transferable vibrational spectroscopy from molecular systems to functional molecular materials.