  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 MFEnKF to
work with non-linear couplings between the models. Optimal nonlinear projection
and interpolation operators are obtained by appropriately trained
physics-informed autoencoders, and this approach allows to construct reduced
order surrogate models with less error than 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 filtering.
