Multifidelity Formulations for Triangular Transport

The paper introduces multifidelity techniques for building triangular transport maps when high‑fidelity data are limited but low‑fidelity data are plentiful. Two strategies are proposed: a hierarchical approach that composes maps across fidelity levels, and a non‑hierarchical method that uses monotonicity‑preserving corrections to incorporate low‑fidelity information. Numerical tests show these methods outperform single‑fidelity transport and, when applied to amortized simulation‑based inference, improve conditional sampling and uncertainty quantification in data‑scarce regimes.

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