Researcher in Computational Uncertainty Quantification for Inverse Problems – Modeling Platform and Software System

The Section for Scientific Computing at DTU Compute performs interdisciplinary research in mathematical modeling, numerical analysis and computational algorithms aimed at complex and large-scale problems in science, engineering and society. The section's expertise includes many aspects of computational science, from the modeling of physical phenomena to developing, analyzing, and implementing methodologies for the solution of real-life problems. Our research focuses on mathematical modeling, analysis, and simulation; inverse problems; optimization and control; and computational mathematics – with applications in, e.g., inverse problems, energy systems, and engineering design.

We seek a candidate to develop a modeling platform and a flexible software system that performs Uncertainty Quantification (UQ) for inverse problems. The position is associated with the project CUQI funded by the Villum Foundation. The position as a researcher is a permanent entry-level position.

UQ characterizes the sensitivity of a solution taking into account errors and inaccuracies in the data, models, algorithms, etc. In CUQI 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 framework that is suited for non-experts, and which can be used by many different industrial and academic end users.

Responsibilities and tasks
The applicant will be responsible for the development of a framework that turns UQ for inverse problems into an operational tool, consisting of:

  • A modeling platform to formulate and utilize a range of prior models.
  • A software system that can incorporate the user’s specific solution codes.

This task involves a combination of theory development, algorithm design and software implementation, as well as test and validation on use-cases.

The applicant will work in a team of PhD students, Postdocs and faculty members and must contribute with research towards the end goal of the CUQI project. A limited amount of teaching and student supervision is expected.

Background. To solve inverse problems we use regularization to incorporate prior information about the problem and the desired solution. For example, priors can be formulated as smoothness requirements to the solution, or they can take the form of learned dictionaries. The challenge in computational UQ is to formulate mathematical models for the priors such that they are practical and computationally useful.  Moreover, it is desirable to have a general modelling approach that works for a range of different types of prior models.

A potentially promising approach for UQ is to develop a methodology that allows a user to construct priors on their own by allowing for the incorporation of prior knowledge in the reconstruction algorithm. Examples of such priors are non-negativity constraints, location of edges in an image, regions or directions of high/low correlation, etc. We demonstrated the feasibility of this approach in a pilot project on image deblurring with non-negativity constraints. The main challenge is to design and build a general system; additional challenges are how to store and represent the underlying UQ information, and how to visualize it in an intuitive way.

The development of this framework combines elements of inverse problems theory, Bayesian modeling, numerical analysis, optimization, software development, and validation. The end result is a user-friendly abstraction level that lets users focus on modeling and data analysis, instead of mathematical details and low-level algorithm aspects.

Qualifications
Candidates must 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 numerical analysis or scientific computing, and preferably also experience with inverse problems and/or computational uncertainty quantification. Furthermore, good command of the English language is essential.

Assessment
In the assessment of the candidates, consideration will be given to

  • Research experience
  • Research vision and potential
  • Experience and quality of teaching
  • International experience
  • Internal and external collaboration
  • Communication skills

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 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 position as a researcher is a permanent entry-level position. After a maximum of 4 years, a researcher can be promoted to a senior researcher position after assessment. More information can be found here: Career paths at DTU.

Further information
Further information may be obtained at the project’s home page CUQI and from PI, professor Per Christian Hansen, mail pcha@dtu.dk, tel +45 23.65.27.98.

You can read more about DTU Compute at compute.dtu.dk/english.

Application procedure
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)
  • CV
  • Research statement that specifically addresses the CUQI-related research mentioned above
  • Documentation of previous research, as related to the “Assessment” above
  • List of publications
  • H-index, and ORCID (see e.g. http://orcid.org/)
  • Diploma (PhD)
  • 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 university collaborating globally with business, industry, government and public agencies.

Organisation: 
Job location: 
Richard Petersens Plads
Building 324
2800 Copenhagen
Denmark
Contact and application information
Deadline: 
Sunday, June 30, 2019
Contact name: 
Per Christian Hansen
Contact email: 
Categorisation