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

Authors: Exaucé Luweh Adjim Ngarti (AIRSEA), Élise Arnaud (AIRSEA), Léo Nicoletti , Victor Trappler (Mines Saint-Étienne MSE, LIMOS, FAYOL-ENSMSE, FAYOL-ENSMSE), Arthur Vidard (AIRSEA)

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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.

Subjects:

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

Cite as:

arXiv:2610.37731 [cs.AI]

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

https://doi.org/10.48550/arXiv.2610.37731

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arXiv-issued DOI via DataCite (pending registration)

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From: Exauce LUWEH ADJIM NGARTI [ view email ] [via CCSD proxy]

[v1]

Tue, 27 Oct 2026 12:50:10 UTC (3,312 KB)

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