PhD Project in Computational Uncertainty Quantification for Inverse Problems – Prior Modeling

DTU Compute’s Section for Scientific Computing invites applications for a 3-year PhD position starting Sept. 1, 2019 (or as soon as possible after that). The position is part of the research project CUQI financed by the Villum Foundation. The PhD project deals with mathematical and statistical modelling of priors for reconstruction models and solutions

DTU Compute, the Department of Applied Mathematics and Computer Science at the Technical University of Denmark, provides a unique academic environment spanning the science disciplines mathematics, statistics and computer science. DTU Compute plays a central role in education at all levels of the engineering programmes at DTU – both in terms of scientific disciplines and didactic innovation.

DTU Compute strives to achieve research excellence in its basic science disciplines, and to achieve technological leadership in research and innovation. DTU Compute is an engineering department covering informatics and communication technologies in their broadest sense and plays a major role in addressing societal challenges of the digital society.

Project Description
Uncertainty Quantification (UQ) allows us to characterize and study the sensitivity of a solution taking into account errors and inaccuracies in the data, models, algorithms, etc. We develop the mathematical, statistical and computational framework for applying UQ to inverse problems (e.g., image deblurring, tomographic imaging, source reconstruction, and fault inspection. The goal is to create a computational platform, suited for non-experts, which can be used by many different academic and industrial end users.

A core problem in UQ for inverse problems is to formulate suitable models of the priors for the desired solution and the reconstruction model, and to use these priors in large-scale numerical computations. For example, we must be able to handle solution priors related to local edges in an image (e.g., enforced by total variation regularization) and we must incorporate hyperpriors in a reconstruction model that can handle uncertain aspects of the physics and the acquisition model.

The present PhD project will focus on either one or both aspects of UQ, depending on the candidate. The PhD project involves development of theory as well as computational algorithms, plus evaluation of the results on selected inverse problems, e.g., CT for materials science, electrical impedance tomography, or image analysis. The applicant must therefore have experience with mathematical modelling and analysis, as well as computational algorithms.

Candidates must have a master’s degree in scientific computing, computational science and engineering, applied mathematics, or equivalent academic qualifications. Preference will be given to candidates who can document training in numerical analysis or scientific computing. Experience with inverse problems and/or uncertainty quantification is also desired. Furthermore, good command of the English language is essential.

Approval and Enrolment
The scholarship for the PhD degree is subject to academic approval, and the candidate will be enrolled in DTU Compute’s PhD School Programme. For information about the general requirements for enrolment and the general planning of the scholarship studies, please see the DTU PhD Guide.

The assessment of the applicants will be made by the PI, professor Per Christian Hansen, and members of the CUQI project team.

We offer
DTU is a leading technical university globally recognized for the excellence of its research, education, innovation and scientific advice. We offer a rewarding and challenging job in an international environment. We strive for academic excellence in an environment characterized by collegial respect and academic freedom tempered by responsibility.

Salary and appointment terms
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. The period of employment is 3 years.

You can read more about career paths at DTU here.

Further Information
Further information concerning the project can be obtained at the project’s home page CUQI and from the PI, professor Per Christian Hansen, mail, tel +45 2365 2798.

Further information concerning the application is available at the DTU Compute PhD homepage or by contacting PhD coordinator Lene Matthisson +45 4525 3377.

Applications must be submitted in English as one PDF file, and we must have your online application by 9 June 2019 (local time). Please open the link in the red bar at the top of the page: "apply online" (“ansøg online”).

  • Applications must include:
  • Application (letter of motivation)
  • CV
  • Documentation of a relevant completed MSc or MEng degree
  • Course and grade list of bachelor’s and master’s degrees
  • Excel sheet with translation of grades to the Danish grading system (see guidelines and excel spreadsheet here)

Candidates may apply prior to ob­tai­ning their master's degree, but cannot begin before having received it.

All interested candidates irrespective of age, gender, race, disability, religion or ethnic background are encouraged to apply.


DTU Compute has a total staff of 400 including 100 faculty members and 130 PhD students. We offer introductory courses in mathematics, statistics, and computer science to all engineering programmes at DTU and specialised courses to the mathematics, computer science, and other programmes. We offer continuing education courses and scientific advice within our research disciplines, and provide a portfolio of innovation activities for students and employees.

DTU is a technical university providing internationally leading research, education, innovation and scientific advice. Our staff of 6,000 advance science and technology to create innovative solutions that meet the demands of society, and our 11,200 students are being educated to address the technological challenges of the future. DTU is an independent academic university collaborating globally with business, industry, government and public agencies. 

Job location: 
Contact and application information
Sunday, June 9, 2019