Amortized localized posterior inference with conditional normalizing flows for calibrated ocean turbulence closure
The preprint (arXiv:2610.37731v1) proposes constructing a family of localized posteriors by weighting likelihoods according to proximity in context space using Gaussian localization weights (with covariance inflation, boundary reflection, and optional sampling-correction). A conditional normalizing flow is trained via amortized variational inference to approximate the posterior family; marginalizing over a context measure yields a calibrated parameter distribution. Twin experiments on the Branin–Hoo function and an application to a k-ε turbulence closure in a single-column ocean model show that localized posterior calibration reduces aggregate predictive errors compared with global-posterior and deterministic calibration under settings designed to admit local compensation.