Inverse Uncertainty Quantification of a Cell Model Using a Gaussian Process Metamodel

Abstract

In order to accurately describe the mechanics of red blood cells (RBCs) and resulting fluid dynamics, a cell-resolved blood flow fluid solver is required. The parameters of the material model for the RBC membranes are carefully tuned to reproduce the behavior of real cells under various experimental conditions. In this work, uncertainty in the parameters of the material model for RBCs used in a model for RBC suspensions was estimated with Inverse Uncertainty Quantification (IUQ) using Bayesian Annealed Sequential Importance Sampling (BASIS). Due to the relatively high computational cost of the model, a Gaussian Process regression metamodel was trained in order to feasibly draw the large number of samples required to obtain an accurate posterior distribution estimate. Additionally, the identifiability of the model parameters was estimated using Sobol sensitivity indices. The elongation index of simulated RBCs in a perfect sheared environment was the model prediction used to calibrate model parameters. The results show good identifiability of the parameter defining the tensile properties of the cell membrane and viscosity ratio, and poor identifiability of the parameter defining the response of the cell surface while undergoing bending. This suggests that the latter should be identified using a different quantity of interest. Overall, the model outputs with the optimal values of the parameters obtained using the Gaussian Process metamodel match better or close to the measurements than the results with the parameters' values obtained with the original model. Therefore, we can conclude that it is a valid method to decrease the computational cost of IUQ of the model.

Stable Likelihood Computation for Machine Learning of Linear Differential Operators With Gaussian Processes

“…In the following, the proposed data-driven algorithm presented by Raissi et al [6] for learning general parametric linear equations of the form (1) corresponding to the differential operators is presented. The algorithm starts by ′ assuming that u(x) is GP with mean 0 and covariance function k uu (x, x ; θ), i.e., ′ u(x) ∼ GP(0, k uu (x, x ; θ)), (2) where θ denotes the hyperparameters of the kernel k uu . The key observation to make is that any linear transformation of a GP such as differentiation and integration is still a GP.…”

“…One of the major fields in applied sciences is to model different phenomena in terms of flexible operational equations [1,2]. In other words, the researchers usually attempt to find a coherent form of flexible operational equations corresponding to the observed data to the effect that they best describe and govern them [3,4].…”

Inverse uncertainty quantification of a mechanical model of arterial tissue with surrogate modeling

“…IUQ is usually applied to quantify uncertainties of input parameters inversely, improves consistency between in silico experiments or benchmark data by adjusting selected tunable parameters and estimates the values of unknown parameters [9]. We use Bayesian approach of calibration [10,11],…”