MSc Theses Presentation Florian Klöppner
Monday, May 26, 14:15-14:45, LSTM Seminar room
Title: Multivariate Multifidelity Regression by Adaptation of Linear
Model of Coregionalization
Author: Florian Klöppner
Supervision: Philipp Schlatter, Saleh Rezaeiravesh (University of Manchester)
Abstract:
This thesis presents a comprehensive multivariate multifidelity regression model utilizing an
adaptation of the Linear Model of Coregionalization (LMC), broadly applicable to a wide range
of scientific and engineering problems where high-fidelity data availability is limited due to significant
computational or experimental costs. The approach integrates Gaussian Process (GP)
regression, combining inexpensive but less accurate low-fidelity data, such as RANS simulations,
with highly accurate yet costly high-fidelity data derived from DNS simulations or experimental
measurements. The proposed multivariate multifidelity Gaussian Process model could potentially
improve predictive accuracy and efficiency by leveraging the correlation between multiple
output variables through a multivariate approach.
The theoretical foundations, including Gaussian processes, kernels such as Radial Basis Function
(RBF) and Matérn, multifidelity modelling concepts, and multivariate coregionalization techniques,
are thoroughly discussed. Detailed attention is given to hyperparameter optimization
through likelihood maximization, examining the efficiency and robustness of various numerical
algorithms, including L-BFGS-B, TNC and Adam. The implementation of the model is verified
using artificially generated test cases, demonstrating improved performance under diverse kernel
selections and varying data sparsity conditions.
The practical applicability of the developed model is demonstrated through the periodic-hill flow
problem, a common benchmark from fluid dynamics, illustrating its effectiveness in accurately
predicting fluid data, even for challenging scenarios such as recirculation zones. In order to keep
the data amount manageable but the test case challenging, velocity components and pressure
were predicted at a vertical profile intersecting the recirculation zone.
Results show that while no significant improvements were noticeable for the velocities compared
to the singlevariate implementation, the multivariate approach showed a significantly improved
pressure prediction. Ultimately, the multivariate multifidelity model proves to be a valuable
extension when output variables are strongly correlated and singlevariate models fall short in
capturing key dynamics. However, this benefit comes at a notable computational cost. Therefore,
the use of this model is recommended in scenarios where inter-variable correlations are expected
to substantially influence predictive performance and justify the increased complexity.
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