Reduced Order Models for Non-Newtonian Fluids Using Non-Stationary Gaussian Process Regression
Published:
Note that this paper was never published, but made for educational purposes. I do however believe it to be of sufficient quality to present it.
For the Master AI & Engineering Systems, an inter-disciplinairy team internship is required. Over the course of 20 weeks, a team with different nationalities and background worked together on the project. My colaborators for this project were: Sven Bendermacher, Vicky Hufken and Wybe Sesink.
For an easier introduction, the slides for a presentation can be found Here
See the Abstract below :
Abstract
This study developed an uncertainty-driven adap-tive sampling framework for data-efficient reduced-ordermodels (ROMs) of non-Newtonian fluid flows, leveraging non-stationary Gaussian Process Regression (NSGPR). The objective was to enhance ROMs performance in scenarios with scarce or computationally expensive data, like Finite Element Method (FEM) simulations. We applied Proper Orthogonal Decomposition (POD) to reduce high-dimensional FEM solutions to a set of coefficients, which were then predicted by NSGPR, providing both a mean prediction and an uncertainty measure to guide subsequent adaptive sampling.The forward problem demonstrated that NSGPR with adaptive sampling achieved a similar mean absolute error using only one-third of the data compared to linear sampling. For the inverse problem, the framework successfully inferred fluid parameters from limited experimental measurements, yielding accurate posterior distributions which accounted for model and experimental uncertainty. The method is equation-free and non-intrusive, making it compatible with existing simulation workflows. It provides a promising solution for parameter estimation in nonlinear, data-scarce systems across engineering and physical sciences, significantly reducing the computational burden of high-resolution simulations.