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-ε 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.
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BibTeX
@misc{ngarti2026amortized,
title = {{Amortized Localized Posterior Inference for Model Calibration with Application to an Ocean Turbulence Closure}},
author = {Exaucé Luweh Adjim Ngarti and Élise Arnaud and Léo Nicoletti and Victor Trappler and Arthur Vidard},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37731},
eprint = {2610.37731},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05840255v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Amortized Localized Posterior Inference for Model Calibration with Application to an Ocean Turbulence Closure
AU - Exaucé Luweh Adjim Ngarti
AU - Élise Arnaud
AU - Léo Nicoletti
AU - Victor Trappler
AU - Arthur Vidard
PY - 2026
DA - 2026/10/27
PB - HAL
DO - 10.48550/arxiv.2610.37731
UR - https://hal.science/hal-05840255v1
AB - 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-ε 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.
ER -