Computer Science, Applied Mathematics – Several PhD Positions with Scholarships in Computational Uncertainty Quantification for Inverse Problems, in the Section for Scientific Computing within the Department of Applied Mathematics and Computer Science, Technical University of Denmark
Deadline to Apply
May 25, 2021 (23: 59 GMT +1)
|No. of Position(s)||Multiple|
|Research Area||– Computer Science|
– Applied Mathematics
|Scholarship||According to standard norms|
|Workplace||Department of Applied Mathematics and Computer Science (DTU Compute)|
Technical University of Denmark
|Contract Period||3 Years|
|Starting date||Fall of 2021|
You must have a two-year master’s degree (120 ECTS points) or a similar degree with an academic level equivalent to a two-year master’s degree.
You must have experience with inverse problems or Bayesian inference.
You will be part of a large team consisting of experts in many areas of inverse problems and scientific computing. Together with the team, you will contribute to the project’s goal by developing theory and computational methods that can handle the challenges we face in developing a versatile platform.
These PhD positions will focus on four important areas:
- Dealing with large-scale inverse problems in the CUQI platform, we face a dimensionality challenge that calls for dimension reduction techniques, surrogate modeling, multi-fidelity sampling algorithms, etc. Along this line, we must also study different types of model errors and techniques for handling errors and uncertainties in the reconstruction models. This project requires knowledge of numerical analysis and numerical optimization methods.
- A different way to handle the dimensionality challenge in the CUQI platform is to utilize recent progress on stochastic optimization methods to construct efficient sampling methods. These techniques allow us to implicitly handle given prior/posterior distributions (e.g., for constrained problems) without the need to tune algorithm parameters. This project requires knowledge of numerical optimization. Familiarity with Bayesian sampling methods is a plus but not a necessity.
- In Bayesian inference, we often face uncertain parameters in the likelihoods and priors. Therefore, we introduce hyper-parameters with associated hyper-priors, which must be compatible with the data and reconstruction model. The hyper-parameters generalize the regularization parameters from classical methods. We need theory behind the hyper-priors as well as diagnostic tools to check these priors within the CUQI platform. This project requires knowledge of numerical linear algebra and numerical computations.
- In many inverse problems, we need to go beyond Gaussian priors in order to handle more advanced spatial correlations. In the CUQI platform we will use Besov priors that are suited for producing piecewise smooth reconstructions and for detection of edges and interfaces. This involves the use of linear combinations of wavelets/frames with random coefficients. This project requires knowledge of numerical PDEs, functional analysis and, preferably, harmonic analysis and/or probability theory.
How to Apply?
To apply, please open the link “Apply online”, fill out the online application form, and attach all your materials in English in one PDF file.
- A letter motivating the application (cover letter). In the cover letter, please indicate one or at most two of the above area(s) you would like to work with, and how your background aligns with this choice.
- Curriculum vitae
- Grade transcripts and BSc/MSc diploma
- Excel sheet with translation of grades to the Danish grading system (see guidelines and Excel spreadsheet here – in the right hand column)
In the field “Please indicate which position(s) you would like to apply for”, please indicate which project you are applying for (title from the above list of PhD projectsor individual research projects).
About DTU Compute
DTU Compute is a unique and internationally recognized academic environment spanning the science disciplines mathematics, statistics, computer science, and engineering. We conduct research, teaching and innovation of high international standard—producing new knowledge and technology-based solutions to societal challenges. We have a long-term involvement in applied and interdisciplinary research, big data and data science, artificial intelligence (AI), internet of things (IoT), smart and secure societies, smart manufacturing, and life science.
The Section for Scientific Computing has a strong track record of research within various branches of applied mathematics, including PDEs, inverse problems, numerical linear algebra, and optimization.
- The appointment will be based on the collective agreement with the Danish Confederation of Professional Associations. The allowance will be agreed upon with the relevant union.
- If you are applying from abroad, you may find useful information on working in Denmark and at DTU at DTU – Moving to Denmark.
Professor Per Christian Hansen
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