Master theses

Implementing an uncertainty propagation module in UQLab

Supervisor: Dr. Nora Lüthen

Description:
Computer simulations are a powerful tool for understanding and optimizing the behavior of real-world systems. They usually depend on a number of parameters, whose values can be affected by uncertainty. The influence of this uncertainty on the simulation results is studied in the field of uncertainty quantification (UQ).

UQLab is a Matlab-based UQ software developed here at ETH Zürich. Its motto is "Make uncertainty quantification available for anybody, in any field of applied science and engineering", focusing on a straightforward user interface while providing state-of-the-art scientific methods.

In this thesis, you will create a new uncertainty propagation module for UQLab, which performs a Monte Carlo simulation and reports the results. This includes the design of the module, implementation, testing, and documentation.

Prerequisites: Good command of Matlab and interest in statistical methods

Additional information:

- Limited capacity: Yes (1)
- Group work: No
- Language: English

Normalizing field flows for learning random fields from data

Supervisor: Dr. N. Lüthen

Normalizing flows are generative deep learning models that construct invertible transformations between tractable reference probability distributions and complex target distributions. Recently, the Normalizing Field Flow framework has been introduced to extend flow-based generative modeling to continuous random fields (Guo et al., 2022). This framework can learn non-Gaussian random fields from scattered sensor measurements. The goal of this thesis is to understand and implement the method, and compare its performance and computational efficiency with standard uncertainty quantification techniques.

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

Neural operators for civil engineering

Supervisor: S. Marelli

Neural operators are a recently proposed data-driven technique to emulate the behavior of complex, time-dependent models. While the body of literature on their properties is constantly growing, few applications exist to mechanical and civil engineering. The goal of this project is to benchmark their performance in Engineering scenarios.This project will assess the usability and performance of the NeuralOperator pytorch package (https://github.com/neuraloperator/neuraloperator) on a multi-story building subject to seismic excitation.

Prerequisites:

- Uncertainty Quantification in Engineering

- Basic Python proficiency 

Additional information:

- Group work: No

Gaussian process modeling in high dimensions

Supervisor: M. Moustapha

Gaussian process (GP) models are widely used as surro-gate models for complex engineering systems due to their flexibility and built-in uncertainty quantification. However, their application in high-dimensional settings remains chal-lenging because of the curse of dimensionality and the diffi-culty of identifying relevant input variables. The goal of this project is to investigate strategies for constructing efficient GP models in high dimension by exploiting variable im-portance. In a first step, the student will explore sample-based sensitivity analysis techniques to identify the most influential inputs. Based on this information, custom covari-ance functions will be designed that reflect anisotropy and sparsity in the input space. The project will assess how such tailored kernels improve prediction accuracy and computa-tional efficiency compared to standard isotropic kernels. Im-plementation will be carried out in MATLAB, using UQLab as the primary platform.

Prerequisites: 

- Uncertainty Quantification in Engineering / Uncertainty Quantification and Surrogate Modeling 

- Good MATLAB proficiency

Additional information:

- Group work: No