Theses

Underground water pipelines are the backbone of our water sup-ply. Due to aging without timely renewal, hidden leaks continu-ally occur, posing serious challenges to water and energy con-servation. Inspired by echolocating animals like bats, emitting calls and using resulting echoes to locate and identify objects, transient (hydroacoustic) waves have been successfully used for localizing leaks in water pipe networks.
Transient wave-based leak localization is achieved by optimizing leak parame-ters within hydroacoustic numerical models to match measured echos. To reduce the computational burden in this optimization, surrogate models have been de-veloped for rapid predictions of wave signals. However, existing surrogate mod-els are typically trained for a specific fixed pipe network and require substantial re-training whenever they are applied to modified or new pipe networks.
Inspired by the composability of LEGO bricks, this project aims to develop a reconfigurable sur-rogate model for water pipe networks. Instead of retraining for each different pipe network from scratch, the surrogate model will be rapidly reconfigured from "surrogate LEGO blocks" to represent any new topology. The "blocks", representing fundamental pipe segments and junc-tions, are pre-trained by advanced graph neural networks (GNN) techniques. This "build once, reuse infinitely" paradigm eliminates the need for repeated physics-based simulations across diverse pipe networks.

This project focuses on applying deep learning tools to simulate watershed processes, which are known to be dynamic, complex, and exhibit high nonlinearity. Recent studies have demonstrated that deep learning models achieved better streamflow predictions than traditional hydrological models such as conceptual or process-based models. Despite these capabilities, these data-driven models struggle to represent intermediate watershed processes (e.g., infiltration and percolation) during streamflow simulation. These limitations arise because deep learning models lack explicit embedded physical principles in their structure.
Our research examines various deep learning structures capable of integrating mass balance equations as governing physical principles. Neural Ordinary Differential Equations (Neural ODE) and Mass-Conservative Long-Short-Term Memory Networks (MCLSTM) are viable choices for this purpose. This project work will explore the application of these model types through practical case studies. Our goal extends beyond making streamflow predictions for different catchments; we also seek to evaluate the model's effectiveness in predicting streamflow in catchments lacking sufficient hydrological data or having none at all.

Groundwater levels can be seen as a large-scale trend, superimposed with local variations around the trend. Knowing the large-scale trend may form a firm basis for refinement with geostatistical approaches. Geostatistical methods often assume so-called stationarity: that the statistics (like mean, variance, and spatial correlation) of groundwater levels are invariant under translation in the space-time domain. Currently, handling trends in geostatistics is only possible with linear, regression-like methods. However, for groundwater applications, the large-scale trend can be a complex, non-linear function due to spatially varying recharge or pumping management regimes, boundary conditions, geological trends, and the nonlinear dependence of heads on hydraulic conductivities.

In such non-linear settings, existing geostatistical methods fail to produce good maps of groundwater levels. Therefore, we want to extend geostatistical methods. The trend ansatz must become nonlinear and should exploit available satellite data or auxiliary information on land use, recharge, boundary conditions, and so forth. We propose this Master thesis topic to formulate an approach that combines different approaches from deep learning with geostatistical interpolation to estimate groundwater levels under nonstationary and non-linear conditions.

Schedules for degree programs should be optimal for all students and lecturers involved, but what does that mean? As few gaps and overlaps as possible, pleasant breaks, all classes in Vaihingen if possible, not starting too early or too late in the evening, lecture halls of the right size and with the right equipment, and so on.
This is difficult for several reasons: (1) the number and size of available rooms are limited; (2) many students from different degree programs have many options to choose from; (3) lectures are exchanged across degree programs and faculties; (4) lecturers have other commitments besides teaching; (5) Degree programs change in size and thus in their space requirements; (6) the lectures offered change over time; (7) at the beginning of the semester, 800 students come to the main lecture hall, but after a few weeks, a smaller lecture hall would actually suffice, and so on.
Faculty 2 wants to offer its students and lecturers better timetables despite limited space. This can be achieved with global optimization. To do this, an optimization model (what is good, what is bad) must be created, realistic data must be collected and used, and suitable algorithms m ust be selected, programmed, and applied. Depending on qualifications and interests, the work can be designed to be more methodological/algorithmic or more applied.

Can be carried out as SimTech project thesis or research module.

The “prediction intervals from three neural networks” method[1] (PI3NN) is a recently developed and easy-to-use approach for learning prediction intervals of artificial neural networks (ANNs).
The estimated percentiles in PI3NN are optimized globally, without distinguishing between data-rich, data-poor, and no-data regions. However, in areas with lots of datapoints (i.e. high data density) the percentiles should be estimated more confidently, whereas they are more uncertain in areas with less or no data (i.e. low data- density). Our aim is to develop a concept for estimating the uncertainty of the percentile curves based on the local data density.
Possible research questions include:
• How can uncertainty bounds for a learned percentile be computed based on local data density? We plan to leverage knowledge about the sample variance distribution in the local neighborhood to create such uncertainty bounds. For example, for a given sample size, the variance of the empirical median estimate is known. We aim to generalize this for arbitrary percentiles.
• How should the neighborhoods be defined to obtain smooth and reasonably localized uncertainty bounds?
We plan to start with a simple 1D artificial case study and optionally extend the approach to more complex settings, such as higher-dimensional input spaces, and ultimately LSTMs.

Can be carried out as SimTech project thesis or research module.

Long Short-Term Memory (LSTM) networks have demonstrated good performance in streamflow prediction and are fully adopted hydrological research community. A relatively recent publication (see below) combines LSTMs with PI3NN, a NN approach to generate Prediction Intervals.
We would like to test this approach on the CAMELS-DE dataset, a collection of German river watersheds. Essentially, we use time series on precipitation, temperature and possibly others as input, and then water levels at the gauge stations as output.
After this we would like to analyze the correlation structure of the residuals. What are the joint effects for linked gauges that are commonly missed by only producing marginals? To this end, we envision an empirical copula analysis. The extend of this latter part can be varied depending on the type of thesis/project.

https://www.frontiersin.org/journals/water/articles/10.3389/frwa.2023.1150126/full
https://essd.copernicus.org/articles/16/5625/2024/

Can be carried out as SimTech project thesis or research module.

Hydraulic fracturing is an important procedure for a broad variety of geophysical applications. In many such applications, small scale information is neither homogeneous nor easy to obtain in detail. We thus model the material constants stochastically by means of a Gaussian random field resulting in tortuous (i.e. wiggly) fractures.
We have a workflow in place to generate such data pairs (random field – tortuous fracture) and determine relevant characteristics of the fracture via image processing, such as for example the volume, the curvature changes or the fractal dimension.
Taking a step back, this is a probabilistic mapping from
parameters of the random field towards fracture statistics. The aim of this study is to find a surrogate model giving distributional predictions, e.g. for a correlation length of the random field we want to predict the distribution of possible fracture volumes. To achieve this, we employ PI3NN, Conformal Quantile Regression and possibly other (to be determined) ML methods and statistically evaluate their respective performances.

Can be carried out as SimTech project thesis or research module.

No two fractures look alike and in real world applications predicting exact fracture paths proves all but impossible. Nonetheless, it is important to know some characteristics of fractures. One example: In a geothermal energy plants, to exchange a lot of heat, a large surface area of the fractures is beneficial.
In this thesis, we want to use the Mechanical-MNIST Crack Path dataset to predict stochastic characteristics of fractures. In contrast to many others approaches, this does not include a pointwise prediction from one input configuration to one fracture path.
The set-up of the Mechanical-MNIST analogous to the famous MNIST simplifies fast prototyping. Depending on the specific interests of the student and scope of the thesis, different machine learning methods can be tried. Ranging from ordinary CNNs, to more complex VAEs and Normalizing Flows or towards classical ML methods such as Random Forests or GPR, a lot is possible here.
Many of the picture based postprocessing steps (evaluation of curvature, skeletonization, etc) are already implemented from a previous project, but an extension of this library is possible if aligned with the interests of the student.
The project is open for all levels of theses: A first contact with neural networks on a well curated dataset or a deep dive into advanced methods for distributional predictions.

Can be carried out as SimTech project thesis or research module.

Sampling from a distribution is an important step in a Bayesian inference workflow. In many contexts, it is fair to assume that information about the gradient of the non normalized density function is also available, especially since the advent of automatic differentiation (AD). Many sampling algorithms (such as Hamiltonian Monte Carlo) make use of this additional information to increase efficiency. However, with complex models giving rise to the density function, it can happen that there is some (numerical) noise which is then also present in the gradients.

It is the goal of this thesis, to design and execute numerical experiments to evaluate the robustness of a variety of gradient based sampling algorithms against such noise. To this end, a literature review to identify algorithms of interest is performed first. These are then implemented or imported from existing libraries with special attention on comparability. Useful characterizations of “robustness” and “noisiness” need to be developed in order to eventually ascertain desirable and undesirable properties of the algorithms. A successful execution of this thesis is likely to result in participation in a publication.

Can be carried out as SimTech project thesis or research module.

In recent months, Kolmogorov Arnold Networks (KAN) have emerged as a prominent topic of interest. They share some characteristics and fundamental ideas with our own deep-arbitrary polynomial chaos networks (deep-aPC-NN). Understanding both network types and then documenting their similarities, parallels and differences is the first part of the proposed work. In a parallel work package, available implementation should be used to asses their respective performances on sensibly selected benchmark problems. Of particular interest are comparisons of the robustness and adaptability of the two network types regarding various problem types.

If you are interested or have your own ideas on this topic, don’t hesitate to contact us!

Can be carried out as SimTech research module.

The department (LS3) is part of the Institute of Water and Environmental Systems Modeling (IWS). We are an international team from different fields of science. Our research focus is on hydrology (e.g. hydrological modeling, geostatistics, precipitation measurement and simulation), on resources in the natural subsurface (e.g. groundwater, natural gas, gas storage), and on systems in the environment of energy production (e.g. CO2 storage, geothermal energy, energy system planning).

As part of research projects and doctoral theses in the above-mentioned areas, we have a wide range of possible topics for theses. Current topics include precipitation measurement using opportunistic sensors, space-time geostatistics and interpretable machine learning in the field of hydrology.

If you are interested in writing a master's thesis in one of these subject areas at our department, please feel free to contact us to arrange an appointment for a personal consultation.

Drinking water supply is one of the crucial requirements of human society. The drinking water quality in supply pipe networks depends directly on the soil temperature around the pipes, which has increasing influence on the drinking water temperature with increasing residence time. However, since higher drinking water temperatures are more susceptible to bacterial growth, the question of accurate prediction of the temperature in drinking water pipe networks becomes urgent in face of climate change. The typical operational model describing the temperature along water pipes uses a simple exponential function. To address the influence of the meteorological conditions using heat transport from ground surface through the subsurface to the drinking water pipes pilot site was built in VEGAS. numerical model using the numerical simulation framework DuMuX was developed to describe the heat and moisture transport at the pilot site.

The objective of the proposed thesis is to compare both models (exponential function and process-based model). The aim of this analysis is to explore how the knowledge from the complex process-based model can be incorporated into operational temperature forecasts, e.g., used to design new drinking water networks.

For this purpose, the existing DuMuX model of the pilot site will be utilized. Depending on the candidate's preferences and qualifications, the focus of the thesis can be adjusted between real-world operational modelling and numerical implementation of physical models.