# Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps

arXiv: https://arxiv.org/abs/2503.12633 · HTML: https://mlsanity.com/paper/2503.12633/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 45 references that are in the map.
- First posted on arXiv 16 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [Conditional Simulation Using Diffusion Schr"odinger Bridges](https://mlsanity.com/paper/2202.13460/) (2022)
- [Coupling techniques for nonlinear ensemble filtering](https://mlsanity.com/paper/1907.00389/) (2019)
- [Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matching](https://mlsanity.com/paper/2403.18705/) (2024)
- [Faithful Inversion of Generative Models for Effective Amortized Inference](https://mlsanity.com/paper/1712.00287/) (2017)
- [Conditional Optimal Transport on Function Spaces](https://mlsanity.com/paper/2311.05672/) (2023)
- [Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference](https://mlsanity.com/paper/2310.16975/) (2023)
- [An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithms](https://mlsanity.com/paper/2203.11869/) (2022)
- [Nonlinear Filtering with Brenier Optimal Transport Maps](https://mlsanity.com/paper/2310.13886/) (2023)
- [Bayesian Posterior Perturbation Analysis with Integral Probability Metrics](https://mlsanity.com/paper/2303.01512/) (2023)
- [Optimal Transport Particle Filters](https://mlsanity.com/paper/2304.00392/) (2023)
- [A Survey of Feedback Particle Filter and related Controlled Interacting Particle Systems (CIPS)](https://mlsanity.com/paper/2301.00935/) (2023)
- [Computational Optimal Transport and Filtering on Riemannian manifolds](https://mlsanity.com/paper/2309.08847/) (2023)
- [Data-Driven Approximation of Stationary Nonlinear Filters with Optimal Transport Maps](https://mlsanity.com/paper/2403.15630/) (2024)
- [Ensemble Transport Filter via Optimized Maximum Mean Discrepancy](https://mlsanity.com/paper/2407.11518/) (2024)

## Built on by (most cited first, 4 of 4)

- [One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators](https://mlsanity.com/paper/2605.06873/) (2026)
- [Closed-form conditional diffusion models for data assimilation](https://mlsanity.com/paper/2603.21291/) (2026)
- [Conditional Sampling via Wasserstein Autoencoders and Triangular Transport](https://mlsanity.com/paper/2604.02644/) (2026)
- [Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimation](https://mlsanity.com/paper/2601.07013/) (2026)

## Abstract (arXiv)

In this paper, we present the amortized optimal transport filter (A-OTF) designed to mitigate the computational burden associated with the real-time training of optimal transport filters (OTFs). OTFs can perform accurate non-Gaussian Bayesian updates in the filtering procedure, but they require training at every time step, which makes them expensive. The proposed A-OTF framework exploits the similarity between OTF maps during an initial/offline training stage in order to reduce the cost of inference during online calculations. More precisely, we use clustering algorithms to select relevant subsets of pre-trained maps whose weighted average is used to compute the A-OTF model akin to a mixture of experts. A series of numerical experiments validate that A-OTF achieves substantial computational savings during online inference while preserving the inherent flexibility and accuracy of OTF.