# A transport-based multifidelity preconditioner for Markov chain Monte Carlo

arXiv: https://arxiv.org/abs/1808.09379 · HTML: https://mlsanity.com/paper/1808.09379/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Aug 2018.

## Built on by (most cited first, 9 of 9)

- [Reliable amortized variational inference with physics-based latent distribution correction](https://mlsanity.com/paper/2207.11640/) (2022)
- [Preconditioned training of normalizing flows for variational inference in inverse problems](https://mlsanity.com/paper/2101.03709/) (2021)
- [Bifidelity Parameter Estimation Using Conditional Diffusion Models](https://mlsanity.com/paper/2504.01894/) (2025)
- [Multilevel Stein variational gradient descent with applications to Bayesian inverse problems](https://mlsanity.com/paper/2104.01945/) (2021)
- [PACER: A Fully Push-forward-based Distributional Reinforcement Learning Algorithm](https://mlsanity.com/paper/2306.06637/) (2023)
- [Transport map unadjusted Langevin algorithms: learning and discretizing perturbed samplers](https://mlsanity.com/paper/2302.07227/) (2023)
- [Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models](https://mlsanity.com/paper/2212.03366/) (2022)
- [Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data](https://mlsanity.com/paper/2603.22050/) (2026)
- [Multifidelity Formulations for Triangular Transport](https://mlsanity.com/paper/2610.00698/) (2026)

## Abstract (arXiv)

Markov chain Monte Carlo (MCMC) sampling of posterior distributions arising in Bayesian inverse problems is challenging when evaluations of the forward model are computationally expensive. Replacing the forward model with a low-cost, low-fidelity model often significantly reduces computational cost; however, employing a low-fidelity model alone means that the stationary distribution of the MCMC chain is the posterior distribution corresponding to the low-fidelity model, rather than the original posterior distribution corresponding to the high-fidelity model. We propose a multifidelity approach that combines, rather than replaces, the high-fidelity model with a low-fidelity model. First, the low-fidelity model is used to construct a transport map that deterministically couples a reference Gaussian distribution with an approximation of the low-fidelity posterior. Then, the high-fidelity posterior distribution is explored using a non-Gaussian proposal distribution derived from the transport map. This multifidelity "preconditioned" MCMC approach seeks efficient sampling via a proposal that is explicitly tailored to the posterior at hand and that is constructed efficiently with the low-fidelity model. By relying on the low-fidelity model only to construct the proposal distribution, our approach guarantees that the stationary distribution of the MCMC chain is the high-fidelity posterior. In our numerical examples, our multifidelity approach achieves significant speedups compared to single-fidelity MCMC sampling methods.