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

TL;DR

The paper tackles the computational bottleneck of Bayesian parameter estimation in cardiovascular modeling by comparing five multifidelity surrogate strategies that leverage low-fidelity models, discrepancy learning, NeurAM-based dimensionality reduction, and non-Gaussian error modeling via normalizing flows. It introduces NeurAM for nonlinear dimensionality reduction, various surrogate-likelihood formulations, and an offline modeling-error framework with an optimal scaling to control posterior variance. Through analytical benchmarks and two cardiovascular examples (0D Windkessel and a patient-specific 3D bifurcation), the study shows discrepancy-based and NeurAM approaches often offer favorable accuracy-cost trade-offs, while NF-based likelihoods yield well-calibrated but costlier posteriors and potential variance inflation. The findings guide practitioners on choosing surrogate strategies based on LF fidelity, correlation, and computational constraints, with implications for uncertainty-aware boundary condition inference in cardiovascular applications and future extension to real data.

Abstract

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.

Figures (15)

• Figure 1: Flow chart of Method F, whose key elements include main steps (gray), training data (green), and neural networks for nonlinear dimensionality reduction and density estimation (blue).
• Figure 2: Posterior distributions obtained using Method F varying $\sigma_\text{model}$ and $\sigma_\text{noise}$. Here the low-fidelity model is a spatially uncorrelated perturbed version of the high-fidelity model.
• Figure 3: Normalizing flow estimation of the probability density of the noise $\widetilde{\eta}$ in Method F. Here the low-fidelity model is a spatially uncorrelated perturbed version of the high-fidelity model.
• Figure 4: High- and low-fidelity models for the two-dimensional analytical example. The true combination of parameters is marked with a black star on the left plot. Contour limits shown on right.
• Figure 5: Posterior distributions for the two-dimensional analytical example. The surrogate models for Methods A to F are built using $N=100$ data points and evaluated on $100 \times 100$ grid points.

Theorems & Definitions (1)

• Remark 2.1