# A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates

arXiv: https://arxiv.org/abs/2007.00793 · HTML: https://mlsanity.com/paper/2007.00793/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 10 of 10)

- [On Fast Simulation of Dynamical System with Neural Vector Enhanced Numerical Solver](https://mlsanity.com/paper/2208.03680/) (2022)
- [Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Physics-Informed Autoencoders](https://mlsanity.com/paper/2102.13025/) (2021)
- [iPINNER: An Iterative Physics-Informed Neural Network with Ensemble Kalman Filter](https://mlsanity.com/paper/2506.00731/) (2025)
- [Investigation of Nonlinear Model Order Reduction of the Quasigeostrophic Equations through a Physics-Informed Convolutional Autoencoder](https://mlsanity.com/paper/2108.12344/) (2021)
- [Adjoint-Matching Neural Network Surrogates for Fast 4D-Var Data Assimilation](https://mlsanity.com/paper/2111.08626/) (2021)
- [Multi-Fidelity Covariance Estimation in the Log-Euclidean Geometry](https://mlsanity.com/paper/2301.13749/) (2023)
- [Neural-POD: A Plug-and-Play Neural Operator Framework for Infinite-Dimensional Functional Nonlinear Proper Orthogonal Decomposition](https://mlsanity.com/paper/2602.15632/) (2026)
- [A Meta-learning Formulation of the Autoencoder Problem for Non-linear Dimensionality Reduction](https://mlsanity.com/paper/2207.06676/) (2022)
- [Balancing Accuracy and Speed: A Multi-Fidelity Ensemble Kalman Filter with a Machine Learning Surrogate Model](https://mlsanity.com/paper/2512.12276/) (2025)
- [Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data](https://mlsanity.com/paper/2603.22050/) (2026)

## Abstract (arXiv)

This work develops a new multifidelity ensemble Kalman filter (MFEnKF) algorithm based on linear control variate framework. The approach allows for rigorous multifidelity extensions of the EnKF, where the uncertainty in coarser fidelities in the hierarchy of models represent control variates for the uncertainty in finer fidelities. Small ensembles of high fidelity model runs are complemented by larger ensembles of cheaper, lower fidelity runs, to obtain much improved analyses at only small additional computational costs. We investigate the use of reduced order models as coarse fidelity control variates in the MFEnKF, and provide analyses to quantify the improvements over the traditional ensemble Kalman filters. We apply these ideas to perform data assimilation with a quasi-geostrophic test problem, using direct numerical simulation and a corresponding POD-Galerkin reduced order model. Numerical results show that the two-fidelity MFEnKF provides better analyses than existing EnKF algorithms at comparable or reduced computational costs.