# Ensemble Transport Filter via Optimized Maximum Mean Discrepancy

arXiv: https://arxiv.org/abs/2407.11518 · HTML: https://mlsanity.com/paper/2407.11518/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 42 references that are in the map.
- First posted on arXiv 16 Jul 2024.

## Builds on (most cited first, 9 of 9)

- [Coupling techniques for nonlinear ensemble filtering](https://mlsanity.com/paper/1907.00389/) (2019)
- [Using machine learning to correct model error in data assimilation and forecast applications](https://mlsanity.com/paper/2010.12605/) (2020)
- [Combining data assimilation and machine learning to infer unresolved scale parametrisation](https://mlsanity.com/paper/2009.04318/) (2020)
- [Data Assimilation: A Mathematical Introduction](https://mlsanity.com/paper/1506.07825/) (2015)
- [Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference](https://mlsanity.com/paper/2310.16975/) (2023)
- [Physics Informed Deep Kernel Learning](https://mlsanity.com/paper/2006.04976/) (2020)
- [Deep learning-enhanced ensemble-based data assimilation for high-dimensional nonlinear dynamical systems](https://mlsanity.com/paper/2206.04811/) (2022)
- [Nonlinear Filtering with Brenier Optimal Transport Maps](https://mlsanity.com/paper/2310.13886/) (2023)
- [Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilation](https://mlsanity.com/paper/2106.07908/) (2021)

## Built on by (most cited first, 2 of 2)

- [Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps](https://mlsanity.com/paper/2503.12633/) (2025)
- [Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2605.13174/) (2026)

## Abstract (arXiv)

In this paper, we present a new ensemble-based filter method by reconstructing the analysis step of the particle filter through a transport map, which directly transports prior particles to posterior particles. The transport map is constructed through an optimization problem described by the Maximum Mean Discrepancy loss function, which matches the expectation information of the approximated posterior and reference posterior. The proposed method inherits the accurate estimation of the posterior distribution from particle filtering while gives an extension to high dimensional assimilation problems. To improve the robustness of Maximum Mean Discrepancy, a variance penalty term is used to guide the optimization. It prioritizes minimizing the discrepancy between the expectations of highly informative statistics for the reference posteriors. The penalty term significantly enhances the robustness of the proposed method and leads to a better approximation of the posterior. A few numerical examples are presented to illustrate the advantage of the proposed method over ensemble Kalman filter.