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Data assimilation is a Bayesian inference process that obtains an enhancedunderstanding of a physical system of interest by fusing information from aninexact physics-based model, and from noisy sparse observations of reality. Themultifidelity ensemble Kalman filter (MFEnKF) recently developed by the authorscombines a full-order physical model and a hierarchy of reduced order surrogatemodels in order to increase the computational efficiency of data assimilation.The standard MFEnKF uses linear couplings between models, and is statisticallyoptimal in case of Gaussian probability densities. This work extends MFEnKF towork with non-linear couplings between the models. Optimal nonlinear projectionand interpolation operators are obtained by appropriately trainedphysics-informed autoencoders, and this approach allows to construct reducedorder surrogate models with less error than conventional linear methods.Numerical experiments with the canonical Lorenz '96 model illustrate thatnonlinear surrogates perform better than linear projection-based ones in thecontext of multifidelity filtering.

Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Physics-Informed Autoencoders