# On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiological boundary conditions

arXiv: https://arxiv.org/abs/2506.11683 · HTML: https://mlsanity.com/paper/2506.11683/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 68 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 17 of 17)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)
- [Inferring solutions of differential equations using noisy multi-fidelity data](https://mlsanity.com/paper/1607.04805/) (2016)
- [Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities](https://mlsanity.com/paper/2102.13403/) (2021)
- [Deep Multi-fidelity Gaussian Processes](https://mlsanity.com/paper/1604.07484/) (2016)
- [Automated generation of 0D and 1D reduced-order models of patient-specific blood flow](https://mlsanity.com/paper/2111.04878/) (2021)
- [Iterative Updating of Model Error for Bayesian Inversion](https://mlsanity.com/paper/1707.04246/) (2017)
- [Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques](https://mlsanity.com/paper/2312.12361/) (2023)
- [Geometric Uncertainty in Patient-Specific Cardiovascular Modeling with Convolutional Dropout Networks](https://mlsanity.com/paper/2009.07395/) (2020)
- [Personalized and uncertainty-aware coronary hemodynamics simulations: From Bayesian estimation to improved multi-fidelity uncertainty quantification](https://mlsanity.com/paper/2409.02247/) (2024)
- [Bayesian Windkessel calibration using optimized 0D surrogate models](https://mlsanity.com/paper/2404.14187/) (2024)
- [A survey on multi-fidelity surrogates for simulators with functional outputs: unified framework and benchmark](https://mlsanity.com/paper/2408.17075/) (2024)
- [Neural active manifolds: nonlinear dimensionality reduction for uncertainty quantification](https://mlsanity.com/paper/2408.03534/) (2024)
- [Enabling stratified sampling in high dimensions via nonlinear dimensionality reduction](https://mlsanity.com/paper/2506.08921/) (2025)

## Built on by (most cited first, 1 of 1)

- [Uncertainty quantification in mechanics: A unified Bayesian perspective](https://mlsanity.com/paper/2607.18734/) (2026)

## Abstract (arXiv)

Solving inverse problems in cardiovascular modeling is particularly challenging due to the high computational cost of running high-fidelity simulations. In this work, we focus on Bayesian parameter estimation and explore different methods to reduce the computational cost of sampling from the posterior distribution by leveraging low-fidelity approximations. A common approach is to construct a surrogate model for the high-fidelity simulation itself. Another is to build a surrogate for the discrepancy between high- and low-fidelity models. This discrepancy, which is often easier to approximate, is modeled with either a fully connected neural network or a nonlinear dimensionality reduction technique that enables surrogate construction in a lower-dimensional space. A third possible approach is to treat the discrepancy between the high-fidelity and surrogate models as random noise and estimate its distribution using normalizing flows. This allows us to incorporate the approximation error into the Bayesian inverse problem by modifying the likelihood function. We validate five different methods which are variations of the above on analytical test cases by comparing them to posterior distributions derived solely from high-fidelity models, assessing both accuracy and computational cost. Finally, we demonstrate our approaches on two cardiovascular examples of increasing complexity: a lumped-parameter Windkessel model and a patient-specific three-dimensional anatomy.