Postdoc in Computational Uncertainty Quantification for Inverse Problems – Non-Gaussian Errors
The Section for Scientific Computing at DTU Compute performs interdisciplinary research in mathematical modelling, numerical analysis and computational algorithms 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 the modelling of physical phenomena to developing, analysing, and implementing methodologies for the solution of real-life problems. Our research focuses on mathematical modelling, analysis, and simulation; inverse problems; optimization and control; and computational mathematics – with applications in, e.g., inverse problems, energy systems, and engineering design.
This position is part of the research project CUQI funded by the Villum Foundation with a duration of 2 years. 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. In the CUQI project we develop the mathematical, statistical and computational framework for applying UQ to inverse problems such as deconvolution, image deblurring, tomographic imaging, source reconstruction, and fault inspection. The end goal of CUQI is to create a modeling framework and a computational platform, suited for non-experts, which can be used by many different industrial and academic end users.
Responsibilities and tasks
The goal of the postdoc project is develop UQ models, methods and computational algorithms that perform uncertainty quantification with non-Gaussian errors in inverse problems.
One of the central themes in inverse problems is the statistical modelling that is able to describe and handle errors in the data and the forward operators. The case of UQ for Gaussian errors is broadly studied, and a few other types of errors (e.g., Laplace) can be transformed to Gaussian. But Poisson and Cauchy errors, along with detector and acquisition errors, which are common examples of non-Gaussian errors, cannot be handled with methods designed for Gaussian noise. Therefore, the non-Gaussian errors – stochastic and possibly also structured – need to be theoretically modelled and computationally handled in other ways.
The postdoc will be responsible for developing pragmatic UQ models and methods that can handle a broad class of non-Gaussian and systematic errors in inverse problems, and for implementing and testing these methods by efficient and stable numerical algorithm. Instead of tediously developing UQ theory and algorithms for each special case of errors, the aim is to develop a systematic approach – possibly using suitable approximations – that is more user-friendly. The end result is a first attempt at producing an abstraction level that lets users focus on modelling and data analysis, instead of mathematical details and low-level algorithm aspects.
The applicant will work in a team of PhD students, postdocs and faculty members in the section, and must contribute with research towards the overall goals of the CUQI project. The applicant is expected to interact with our collaborators on applications of UQ for inverse problems. The applicant is also expected to give limited contributions to teaching and training activities as well as supervision of students.
Candidates should have a PhD degree or equivalent in scientific computing, computational science and engineering, applied mathematics, or equivalent academic qualifications. Preference will be given to candidates who can document research in inverse problems, numerical algorithms and scientific computing. Experience with uncertainty quantification is also desired. Furthermore, good command of the English language is essential.
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 terms of employment
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 duration of the position is 2 years, and we aim for at starting date of Sept. 1, 2019 or as soon as possible after that.
You can read more about career paths at DTU here.
You can read more about DTU Compute at compute.dtu.dk/english.
Please submit your online application no later than 30 June 2019 (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
- Application (cover letter)
- Diploma (MSc/PhD)
- List of publications
- Links to other material that may be relevant, e.g., software.
Applications and enclosures received after the deadline will not be considered.
All interested candidates irrespective of age, gender, disability, race, 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.