From regularization to physics: Uncertainty quantification and the essential role of specific priors in fast-ion distribution function inference

Inferring physical quantities from indirect measurements is an ill-posed inverse problem where data alone are insufficient. Extending our Bayesian inference framework for fast-ion distribution inference[1], this work presents three advances: 1) improved inference fidelity using numerical simulations for the prior, 2) uncertainty quantification (UQ) including all known sources of uncertainty, and 3) demonstration that specific priors improve, not compromise, inference credibility. Unlike previous work where UQ was dismissed or based on statistically biased methods, our framework provides robust uncertainty analysis by using high-fidelity numerical priors, applying approximation error modeling that accounts for uncertainties in plasma parameters and detector geometries, and implementing posterior sampling via the Randomize-then-Optimize method for non-negativity constrained linear inverse problems. Using DIII-D FIDA data, we show priors with varying physical specificity yield distinct fast-ion distributions whose forward models are statistically indistinguishable ($\chi_\nu^2 \approx 0.6$). This ambiguity is resolved by physics-informed priors. We thus challenge the long-standing view that detailed priors are a ``concession,'' establishing instead that credible inference requires incorporating all available knowledge through maximally specific, physically justified priors.



Work supported by US DOE under DE-SC0020337, DE-FG02-06ER54867 and DE-FC02-04ER54698.