PhD Project in Goal-Oriented Uncertainty Quantification for Inverse Problems at DTU Compute
DTU Compute’s Section for Scientific Computing invites applications for a 3-year PhD position starting June 1, 2020 or soon thereafter. The project is associated with the research initiative CUQI financed by the Villum Foundation.
The Section for Scientific Computing at DTU Compute performs interdisciplinary research in mathematical modeling, numerical analysis and computational methods aimed at complex and large-scale problems in science, engineering and society. The section's expertise includes many of the aspects of computational science, from modeling of physical phenomena to developing, analyzing, and implementing methodologies for the solution of real-life problems. Our research focuses on functional analysis; partial differential equations; matrix computations; inverse problems and imaging; optimization and control; and computational mathematics – with applications in, e.g., energy systems and engineering design.
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 focus on inverse problems (e.g., image deblurring, tomographic imaging, source reconstruction, and fault inspection), and the overall goal of the CUQI project is to create a computational platform, suited for non-experts in academia and industry.
In many applications, the end-goal is to compute a Quantity of Interest (QoI) defined on the solution to an inverse problem, such as the segmentation of a deblurred image, the dynamics of an object in CT imaging, or the location of details in a CT or EIT reconstruction. Performing UQ on a QoI is often referred to as Goal-Oriented UQ, and some core problems here are 1) how to develop efficient computational algorithms and 2) whether we can compute the QoI directly from the data.
Our activities in Goal-Oriented UQ are performed in a collaboration with the Department of Mathematics, Virginia Tech, Blacksburg, VA, and the PhD student will have co-supervision from there. Therefore, the PhD student must spend some of the time at Virginia Tech.
Responsibilities and Tasks
The present PhD project will focus on computational aspects of Goal-Oriented UQ, and we will study how to incorporate these types of problems in a general computational platform. The PhD project involves development of theory as well as computational algorithms, plus evaluation of the results on selected inverse problems, e.g., sound source reconstruction, electrical impedance tomography, or image analysis. The PhD student must collaborate with fellow students and colleagues in the CUQI project, and be prepared to spend time at Virginia Tech.
Candidates should 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. The master degree should be in applied mathematics, computational science and engineering (CSE) or equivalent academic qualifications.
Preference will be given to candidates who can document training in one or more of these areas: numerical analysis, scientific computing, inverse problems and uncertainty quantification. 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 the DTU Compute PhD School Programme. For information about the general requirements for enrolment and the general planning of the PhD study programme, 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.
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 position is a full-time position. The period of employment is 3 years starting June 1, 2020 (or as soon as possible thereafter).
You can read more about career paths at DTU here.
Further information concerning the application is available at the DTU Compute PhD homepage.
Please submit your online application no later than February 29, 2020 (local time). Apply online at www.career.dtu.dk.
Applications must be submitted as one PDF file containing all materials to be given consideration. 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. The file must include:
- A letter motivating the application (cover letter)
- 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)
Candidates may apply prior to obtaining their master's degree, but cannot begin before having received it.
Applications and enclosures received after the deadline will not be considered.
All interested candidates irrespective of age, gender, race, disability, religion or ethnic background are encouraged to apply.
DTU Compute is an internationally unique academic environment spanning the science disciplines mathematics, statistics and computer science. At the same time, we are an engineering department covering informatics and communication technologies (ICT) in their broadest sense. Finally, we play a major role in addressing the societal challenges of the digital society where ICT is a part of every industry, service, and human endeavor.
DTU Compute has a total staff of 400 including 100 faculty members and 130 Ph.D. students. We offer introductory courses to all engineering programs at DTU and specialized courses to the mathematics, computer science, and other programs. We offer continuing education courses and scientific advice within our research disciplines, and provide a portfolio of innovation activities for students and employees.
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DTU develops technology for people. With our international elite research and study programmes, we are helping to create a better world and to solve the global challenges formulated in the UN’s 17 Sustainable Development Goals. Hans Christian Ørsted founded DTU in 1829 with a clear vision to develop and create value using science and engineering to benefit society. That vision lives on today. DTU has 11,500 students and 6,000 employees. We work in an international atmosphere and have an inclusive, evolving, and informal working environment. Our main campus is in Kgs. Lyngby north of Copenhagen and we have campuses in Roskilde and Ballerup and in Sisimiut in Greenland.