Amortized Localized Posterior Inference for Model Calibration with Application to an Ocean Turbulence Closure

Abstract:Model discrepancy may prevent a single calibration parameter from reproducing a physical response across the context domain. In addition, uncertainties in observations and contexts affect calibration and must be accounted for and quantified. We construct a family of localized posteriors by weighting observation likelihoods according to their proximity to a target context. Gaussian localization weights incorporate context uncertainty through covariance inflation, with reflection at domain boundaries and an optional correction for uneven context sampling. A conditional normalizing flow approximates the family of posteriors through amortized variational inference. Integrating the localized posteriors under a prescribed context measure gives the marginalized parameter distribution. In a twin experiment with the Branin-Hoo model, we compare global and localized inference under uniform and skewed context distributions. Localization reduces the reported aggregate predictive errors relative to the global posterior. An application to the k-$\epsilon$ turbulence closure in a single-column ocean model, with atmospheric surface forcing as context, shows that localized posterior calibration reduces temperature and zonal-velocity errors relative to deterministic and global-posterior calibration. Both twin experiments are constructed to admit local compensation.

Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2610.37731 [cs.AI]

(or arXiv:2610.37731v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.37731 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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