Multifidelity Ensemble Kalman Filtering using surrogate models defined by Physics-Informed Autoencoders

The multifidelity ensemble Kalman filter aims to combine a full-order model and a hierarchy of reduced order surrogate model in an optimal statistical framework for Bayesian inference in sequential data assimilation. In this work we extend the multifidelity ensemble Kalman filter to work with non-linear couplings between the models. Using autoencoders it is possible to train optimal projection and interpolation operators, and to obtain reduced order surrogate models with less error than conventional linear methods. We show on the canonical Lorenz '96 model that such a surrogate does indeed perform better in the context of multifidelity filtering.