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

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.

@article{al-jarrah2025_2503.12633,
  title={ Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps },
  author={ Mohammad Al-Jarrah and Bamdad Hosseini and Amirhossein Taghvaei },
  journal={arXiv preprint arXiv:2503.12633},
  year={ 2025 }
}