# Multifidelity Formulations for Triangular Transport

arXiv: https://arxiv.org/abs/2610.00698 · HTML: https://mlsanity.com/paper/2610.00698/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 67 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Optimal experimental design: Formulations and computations](https://mlsanity.com/paper/2407.16212/) (2024)
- [Inference via low-dimensional couplings](https://mlsanity.com/paper/1703.06131/) (2017)
- [On the representation and learning of monotone triangular transport maps](https://mlsanity.com/paper/2009.10303/) (2020)
- [Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference](https://mlsanity.com/paper/2310.16975/) (2023)
- [On minimax density estimation via measure transport](https://mlsanity.com/paper/2207.10231/) (2022)
- [Triangular Flows for Generative Modeling: Statistical Consistency, Smoothness Classes, and Fast Rates](https://mlsanity.com/paper/2112.15595/) (2021)
- [Deep composition of tensor-trains using squared inverse Rosenblatt transports](https://mlsanity.com/paper/2007.06968/) (2020)
- [Bayesian model calibration for block copolymer self-assembly: Likelihood-free inference and expected information gain computation via measure transport](https://mlsanity.com/paper/2206.11343/) (2022)
- [MFNets: Data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources](https://mlsanity.com/paper/2008.02672/) (2020)
- [Scalable Bayesian transport maps for high-dimensional non-Gaussian spatial fields](https://mlsanity.com/paper/2108.04211/) (2021)
- [A transport-based multifidelity preconditioner for Markov chain Monte Carlo](https://mlsanity.com/paper/1808.09379/) (2018)
- [Multifidelity Simulation-based Inference for Computationally Expensive Simulators](https://mlsanity.com/paper/2502.08416/) (2025)
- [Ensemble transport smoothing. Part II: Nonlinear updates](https://mlsanity.com/paper/2210.17435/) (2022)
- [Tractable Optimal Experimental Design using Transport Maps](https://mlsanity.com/paper/2401.07971/) (2024)
- [Ensemble transport smoothing. Part I: Unified framework](https://mlsanity.com/paper/2210.17000/) (2022)
- [Expected information gain estimation via density approximations: Sample allocation and dimension reduction](https://mlsanity.com/paper/2411.08390/) (2024)
- [A friendly introduction to triangular transport](https://mlsanity.com/paper/2503.21673/) (2025)
- [A transport approach to sequential simulation-based inference](https://mlsanity.com/paper/2308.13940/) (2023)
- [Density Estimation via Measure Transport: Outlook for Applications in the Biological Sciences](https://mlsanity.com/paper/2309.15366/) (2023)
- [Distributed Nonlinear Filtering using Triangular Transport Maps](https://mlsanity.com/paper/2310.19000/) (2023)
- [Neural Triangular Transport Maps: A New Approach Towards Sampling in Lattice QCD](https://mlsanity.com/paper/2510.13112/) (2025)
- [Accelerating Bayesian Inference via Multi-Fidelity Transport Map Coupling](https://mlsanity.com/paper/2510.17946/) (2025)
- [Adaptive Nonlinear Data Assimilation through P-Spline Triangular Measure Transport](https://mlsanity.com/paper/2603.19058/) (2026)

## Abstract (arXiv)

We develop multifidelity methods for constructing triangular transport maps from samples, when high-fidelity data are scarce but lower-fidelity data are more abundant. Using this set of multifidelity data, we approximate a triangular transport map that bijectively maps between a tractable reference density and the high-fidelity target distribution. We introduce two strategies to leverage low-fidelity data: a hierarchical approach that composes maps between adjacent fidelity levels, and a non-hierarchical method that incorporates low-fidelity information through monotonicity-preserving corrections to the map parameterization. Numerical experiments compare these strategies with single-fidelity transport and demonstrate how the proposed multifidelity approaches can improve map estimation from limited high-fidelity data. To illustrate the broader utility of the learned maps, we also deploy them in a downstream amortized simulation-based inference task. This example shows that multifidelity improvements in map estimation can translate to improved conditional sampling and uncertainty quantification when high-fidelity data are scarce.