Semester projects

Kolmogorov–Arnold Networks (KANs) for forward UQ

Supervisor: Dr. N. Lüthen

Surrogate models are crucial for enabling uncertainty propagation and sensitivity analysis for computationally expensive computer simulations. Neural networks can serve as powerful surrogates when large amounts of data are available, whereas traditional UQ methods like Polynomial Chaos Expansion (PCE) and Gaussian Process Regression (GPR) perform well when sample sizes are small. Recently, Kolmogorov–Arnold Networks (KANs) were introduced as an alternative to Multi-Layer Perceptrons (MLPs), placing learnable univariate functions on network edges rather than fixed activations on nodes (Liu et al., 2024). While KANs show strong low-dimensional function approximation and interpretability, recent studies suggest they face higher computational overhead compared to MLPs. The goal of this project is to understand and implement KANs, and to evaluate their accuracy, interpretability, and computational efficiency as UQ surrogates relative to standard methods (PCE, GPR) and traditional MLPs.

Prerequisites:

· Course "Uncertainty Quantification in Engineering"/"Uncertainty Quantification and Surrogate Modeling"

· Proficiency in Matlab or Python programming

· Interest in mathematical topics

Additional information:

· Group work: No

UQ for Computational Aerodynamics

Supervisor: Dr. N. Lüthen

Uncertainty quantification plays a crucial role in assessing the safety and performance of systems under uncertainties. In this thesis, you will work with aerodynamics benchmark datasets provided by the American Institute of Aeronautics and Astronautics. Using the UQLab software framework, you will perform various analyses, such as uncertainty propagation and sensitivity analysis, on realistic aircraft wing simulation data. The goal of this project is to evaluate the capabilities and limitations of existing UQ methods on real-world aerodynamic data, and potentially extend them using techniques such as multi-fidelity modeling.

Prerequisites:

· Course "Uncertainty Quantification in Engineering"/"Uncertainty Quantification and Surrogate Modeling"

· Proficiency in Matlab or Python programming

Additional information:

· Group work: No

Exploring the hybrid PCE-GPR method

Supervisor: N. Lüthen

Polynomial Chaos expansion (PCE) and Gaussian process modelling, also known as Kriging, are two well-established methods in uncertainty quantification in engineering. Recently, a novel hybrid approach has been proposed, which develops Gaussian process models with specific kernels related to orthonormal polynomials (Manfredi, 2025). The method reportedly outperforms sparse PCE, and is able to provide confidence information on post-processed PCE quantities such as moments and Sobol' indices. The goal of this thesis is to understand and implement this innovative method and explore its advantages and drawbacks. 

Prerequisites:

• Uncertainty Quantification in Engineering / Uncertainty Quantification and Surrogate Modeling
• Interest in mathematical topics
• Proficiency  in MATLAB programming

Additional information:

• Group work: No