Multifidelity Formulations for Triangular Transport
Abstract
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.
Related
- The discontinuous Galerkin method for solving the two-dimensional transport equation with distributed-order memory kernel on triangular meshes
- Mutual Information Estimation via Triangular Transport Maps: Finite Sample Guarantees and Sample Allocation
- On the Error Analysis of Triangular Transport Maps for Conditional Generation via MMD-based Objectives
- Enabling risk and reliability analysis in next-generation computational tools via multifidelity methods
- Multifidelity Computer Model Emulation Via Diffusion Model Steering and Targeted Maximum Likelihood
BibTeX
@misc{davis2026multifidelity,
title = {{Multifidelity Formulations for Triangular Transport}},
author = {Owen Davis and Daniel Sharp and Youssef Marzouk and Gianluca Geraci},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00698},
eprint = {2610.00698},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00698},
}
RIS
TY - UNPB
TI - Multifidelity Formulations for Triangular Transport
AU - Owen Davis
AU - Daniel Sharp
AU - Youssef Marzouk
AU - Gianluca Geraci
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00698
UR - https://arxiv.org/abs/2610.00698
AB - 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.
ER -