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Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF. 

Abstract. Rejuvenation in particle filters is necessary to prevent the collapse of the weights when the number of particles is insufficient to properly sample the high-probability regions of the state space. Rejuvenation is often implemented in a heuristic manner by the addition of random noise that widens the support of the ensemble. This work aims at improving canonical rejuvenation methodology by the introduction of additional prior information obtained from climatological samples; the dynamical particles used for importance sampling are augmented with samples obtained from stochastic covariance shrinkage. A localized variant of the proposed method is developed.Numerical experiments with the Lorenz '63 model show that modified filters significantly improve the analyses for low dynamical ensemble sizes. Furthermore, localization experiments with the Lorenz '96 model show that the proposed methodology is extendable to larger systems. 

Abstract. Ever since its inception, the ensemble Kalman filter (EnKF) has elicited many heuristic approaches that sought to improve it. One such method is covariance localization, which alleviates spurious correlations due to finite ensemble sizes by using relevant spatial correlation information. Adaptive localization techniques account for how correlations change in time and space, in order to obtain improved covariance estimates. This work develops a Bayesian approach to adaptive Schur-product localization for the deterministic ensemble Kalman filter (DEnKF) and extends it to support multiple radii of influence. We test the proposed adaptive localization using the toy Lorenz'96 problem and a more realistic 1.5-layer quasi-geostrophic model. Results with the toy problem show that the multivariate approach informs us that strongly observed variables can tolerate larger localization radii. The univariate approach leads to markedly improved filter performance for the realistic geophysical model, with a reduction in error by as much as 33 %. 

Abstract Many measurements at the LHC require efficient identification of heavy-flavour jets, i.e. jets originating from bottom (b) or charm (c) quarks. An overview of the algorithms used to identify c jets is described and a novel method to calibrate them is presented. This new method adjusts the entire distributions of the outputs obtained when the algorithms are applied to jets of different flavours. It is based on an iterative approach exploiting three distinct control regions that are enriched with either b jets, c jets, or light-flavour and gluon jets. Results are presented in the form of correction factors evaluated using proton-proton collision data with an integrated luminosity of 41.5 fb -1 at  √s = 13 TeV, collected by the CMS experiment in 2017. The closure of the method is tested by applying the measured correction factors on simulated data sets and checking the agreement between the adjusted simulation and collision data. Furthermore, a validation is performed by testing the method on pseudodata, which emulate various mismodelling conditions. The calibrated results enable the use of the full distributions of heavy-flavour identification algorithm outputs, e.g. as inputs to machine-learning models. Thus, they are expected to increase the sensitivity of future physics analyses.