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The authors couple differentiable physics solvers with Fisher information to achieve rapid, sampling-free uncertainty quantification over continuous latent fields in physical inverse problems. By evaluating local Gaussian curvature at the inferred solution, the framework isolates modes informed by experimental data from those governed strictly by the prior without requiring costly MCMC sampling. Validated on nuclear optical potential reconstruction, the approach achieves nearly nominal empirical coverage on held-out cross-section data with significantly tighter predictive intervals than standard Bayesian optical baselines.
Full posterior sampling is no longer a bottleneck for physical inverse problems: coupling Fisher information with differentiable solvers yields calibrated latent field uncertainties and tighter predictive intervals without running MCMC.
Many inverse problems in physics infer an unobserved field from measurements connected to it through a governing equation. We combine Fisher information with a differentiable solver to quantify uncertainty in both the inferred field and its predicted observables, using a local Gaussian approximation without sampling the full parameter posterior. Applied to nuclear optical potentials, the method distinguishes features constrained by scattering measurements from those whose uncertainty remains set by the prior. Our flexible model improves agreement with held-out cross sections and achieves nearly nominal coverage with narrower predictive intervals than an established Bayesian optical model.