Exaucè Luweh Adjim Ngarti, Élise Arnaud, Léo Nicoletti, Victor Trappler, Arthur Vidard
原文摘要
Variational inference with normalizing flows provides a flexible posterior approximation for Bayesian model calibration, but struggles when the posterior has several modes separated by regions of low probability mass. We study this behavior in a two-parameter twin experiment and regularize the variational objective. Under Gaussian observation errors and a Gaussian prior, the corresponding minimization objective is the expected Tikhonov calibration objective minus the differential entropy of the approximating distribution. However, the expected Tikhonov term favors concentration near one of the modes, while entropy maximization does not guarantee multimodality. We introduce a regularization term based on Rényi divergence that encourages the approximate posterior to cover the prior support. In the connected bimodal case, a flow approximation represents both modes; in the case with well-separated modes, the flow and Gaussian mixture frequently miss one mode. The introduced regularization reduces the near-collapse fraction from 50% to 25%. While the regularization improves mode coverage in this experiment, it changes the Bayesian variational objective, introduces a trade-off in approximation accuracy, and does not provide a general solution to mode collapse.
Exaucé Luweh Adjim Ngarti, Élise Arnaud, Léo Nicoletti, Victor Trappler, Arthur Vidard
原文摘要
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.