Master theses

Data-driven regression at the boundary between machine learning and uncertainty quantification

Supervisor: S. Marelli

Most uncertainty quantification (UQ) tools specialize in extracting as much information as possible from very small datasets, minimizing the computational burden of complex engineering models. In contrast, machine learning (ML) methods try to extract sensible structures from a large amount of unstructured available data. Albeit apparently at the opposite ends of the spectrum, the two research fields share many similarities, resulting in significant cross-fertilizations throughout recent years.

This master thesis aims at reviewing the state of the art on data-driven regression from both the UQ and ML literature, to then implement and cross-test their efficiency on standard benchmarks from both fields. In particular, focus will be given to artificial neural networks (ANNs) and model selection strategies from ML, and surrogate models from UQ. If time allows, hybrid extensions to the most promising approaches will be also proposed.

Prerequisistes: 

• Good working knowledge of either MATLAB or Python
• Uncertainty quantification in engineering

Additional information

• Group work: No

Benchmark of recent active learning reliability methods

Supervisor: M. Moustapha

Active learning has become a powerful strategy in reliability analysis to efficiently estimate failure probabilities while minimizing computational cost. By adaptively selecting the most informative training points, these methods significantly improve the performance of reliability estimation algorithms, making them well-suited for applications involving computationally expensive limit-state functions. As a result, we have previously conducted a benchmark of active learning strategies and implemented the best approaches in the uncertainty quantification software UQLab using a generalized framework.

This master thesis aims at extending this benchmark by investigating new methods recently proposed in the literature. In particular, the student(s) will explore Bayesian active learning, which provides a principled way to incorporate epistemic uncertainty in the failure probability estimate, leading to new learning functions and stopping criteria. Additionally, they will investigate learning functions based on look-ahead strategies, such as the stepwise uncertainty reduction (SUR), and examine their associated stopping criteria. The most promising methods will be implemented and their performance compared against the approaches currently available in UQLab.

Prerequisites

• Good working knowledge of Matlab
• Structural Reliability and Risk Analysis

Additional information

• Group work: No