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

TL;DR

This paper evaluates multi-fidelity neural emulators and reduced-dimensional techniques to efficiently perform Bayesian inference in cardiovascular modeling, balancing accuracy and computational cost.

Contribution

It introduces and compares five novel methods leveraging low-fidelity models and discrepancy modeling for Bayesian inverse problems in physiology.

Findings

Discrepancy modeling improves posterior approximation accuracy.

Reduced-dimensional approaches decrease computational cost significantly.

Methods are validated on analytical and real cardiovascular models.

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.