arXiv subjects

Aricia Rinkens

Publications and source records attributed to Aricia Rinkens.

3 recordsLinked to original sources

arXiv2026

A comparison of Markov Chain Monte Carlo algorithms for Bayesian inference of constitutive models

Employing Bayesian inference to calibrate constitutive model parameters has grown substantially in recent years. Among the available techniques, Markov Chain Monte Carlo (MCMC) sampling remains one of the most widely used approaches for estimating the posterior distribution. Nevertheless, the selection of a specific MCMC algorithm is often driven by practical considerations, such as software availability or prior user experience. To support sampler selection, we present a comparison of three prominent samplers in the context of two distinct physical systems: a thermal conduction system and a viscous flow system. Calibration data are obtained through tailor-made experimental setups. We use the Kullback-Leibler (KL) divergence, which quantifies the statistical distance between the sampled posterior and the reference ('true') posterior, as a measure of convergence to compare the performance of the following MCMC sampling methods: the Metropolis-Hastings (MH) sampler, the Affine Invariant Stretch Move (AISM) sampler, and the No-U-Turn Sampler (NUTS). We study how this metric correlates to heuristic indicators such as the Gelman-Rubin diagnostic and the effective sample size. In addition, we assess the samplers' computational effort in terms of required number of model evaluations. Based on the results, we find that the heuristic convergence and performance indicators provide a good qualitative measure for KL-divergence for both systems. Regarding computational effort, the NUTS is net beneficial for the viscous flow system, as the high effective sample size outweighs the additional effort required for gradient-based proposal generation. For the thermal conduction system, which involves more expensive model evaluations, the NUTS is not advantageous. Thus, the computational efficiency of gradient evaluations is an important argument in sampler selection.

cs.CE↗

arXiv2026

Bayesian Model Selection for Complex Flows of Yield Stress Fluids

Modeling yield stress fluids in complex flow scenarios presents significant challenges, particularly because conventional rheological characterization methods often yield material parameters that are not fully representative of the intricate constitutive behavior observed in complex conditions. We propose a Bayesian uncertainty quantification framework for the calibration and selection of constitutive models for yield stress fluids, explicitly accounting for uncertainties in both modeling accuracy and experimental observations. The framework addresses the challenge of complex flow modeling by making discrepancies that emanate from rheological measurements explicit and quantifiable. We apply the Bayesian framework to rheological measurements and squeeze flow experiments on Carbopol 980. Our analysis demonstrates that Bayesian model selection yields robust probabilistic predictions and provides an objective assessment of model suitability through evaluated plausibilities. The framework naturally penalizes unnecessary complexity and shows that the optimal model choice depends on the incorporated physics, the prior information, and the availability of data. In rheological settings, the Herschel-Bulkley and biviscous power law models perform well. However, when these rheological outcomes are used as prior information for a rheo-informed squeeze flow analysis, a significant mismatch with the experimental data is observed. This is due to the yield stress inferred from rheological measurements not being representative of the complex squeeze flow case. In contrast, an expert-informed squeeze flow analysis, based on broader priors, yields accurate predictions. These findings highlight the limitations of translating rheological measurements to complex flows and underscore the value of Bayesian approaches in quantifying model bias and guiding model selection under uncertainty.

physics.flu-dyn↗

arXiv2023

Uncertainty quantification for the squeeze flow of generalized Newtonian fluids

The calibration of rheological parameters in the modeling of complex flows of non-Newtonian fluids can be a daunting task. In this paper we demonstrate how the framework of Uncertainty Quantification (UQ) can be used to improve the predictive capabilities of rheological models in such flow scenarios. For this demonstration, we consider the squeeze flow of generalized Newtonian fluids. To systematically study uncertainties, we have developed a tailored squeeze flow setup, which we have used to perform experiments with glycerol and PVP solution. To mimic these experiments, we have developed a three-region truncated power law model, which can be evaluated semi-analytically. This fast-to-evaluate model enables us to consider uncertainty propagation and Bayesian inference using (Markov chain) Monte Carlo techniques. We demonstrate that with prior information obtained from dedicated experiments - most importantly rheological measurements - the truncated power law model can adequately predict the experimental results. We observe that when the squeeze flow experiments are incorporated in the analysis in the case of Bayesian inference, this leads to an update of the prior information on the rheological parameters, giving evidence of the need for recalibration in the considered complex flow scenario. In the process of Bayesian inference we also obtain information on quantities of interest that are not directly observable in the experimental data, such as the spatial distribution of the three flow regimes. In this way, besides improving the predictive capabilities of the model, the uncertainty quantification framework enhances the insight into complex flow scenarios.

physics.flu-dyn↗