PhD: Using numerical linear algebra to exploit structure in data assimilation

Have you ever wondered how weather forecasts are produced? Are you an applied mathematician who wants to work on practical problems with wide-ranging impact? Are you interested in using linear algebra to improve the robustness and efficiency of algorithms that are used daily in weather centres?

Irène Curie Fellowship

No

Department(s)

Mathematics and Computer Science

Reference number

V32.7274

Data assimilation (DA) techniques allow users to estimate the state of a dynamical system at a given time by combining information from measurements with numerical models. A key application of DA is within numerical weather prediction, and elsewhere in geosciences, where estimates of the current state of the atmosphere and ocean are used as initial conditions for e.g. weather forecasts. DA also forms an important research field within applied mathematics. One important subproblem within variational DA involves the solution of extremely high-dimensional linear systems within a very limited computational budget/wallclock time, typically using iterative methods. These extreme time constraints also lead to an unusual mathematical setting compared to general iterative methods – as very few iterations are performed, improvement in early iterations is vital.    

This project will focus on a particular DA method (weak-constraint 4D-Var) which can be reformulated in a number of ways to reveal different aspects of the underlying structure of the problem. In this project you will:

• Develop new theory for different problem formulations e.g. bound eigenvalues of linear systems, prove convergence results for novel iterative methods.
• Use this improved theoretical understanding to design novel and more reliable implementations of iterative solvers for problems coming from data assimilation.
• Develop practical methods and adapt existing algorithms, before testing them numerically. The supervisor can provide an existing code testbed, and you could also work on community code or write your own test problems. 

The balance of these subprojects will depend on the interest of the student.

Possible specific research directions include:

• Designing new preconditioners for varied iterative solvers and problem formulations.
•  Extending results from standard Krylov solvers to matrix-oriented solvers
•  Reformulation of the problem in a tensor framework to exploit modern multilinear algebra approaches.

It is not expected that you know much about data assimilation yet, but you should have an interest in learning more. There may be opportunities for you to attend external data assimilation training, and engage with researchers at meteorological agencies (e.g. the Met Office, Cerfacs). You will join the Computational Science group (https://casa.win.tue.nl/home/computational-science/), and be an active member of the Centre for Analysis, Scientific Computing and Applications (https://casa.win.tue.nl/home/).

• A master’s degree (or an equivalent university degree) in Mathematics or a numerate degree.
• A strong background and interest in (numerical) linear algebra. Some knowledge of Krylov methods is advantageous but not required.
• Programming experience in either Matlab or Python.  
• Ability to work in an interdisciplinary team and interested in collaborating with industrial partners.
• Initiative and motivation to work independently.
• Interest in developing your teaching skills and coaching students.
• Fluent in spoken and written English (C1 level).

A meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train station. In addition, we offer you:

• Full-time employment for four years, with an intermediate evaluation (go/no-go) after nine months. You will spend 10% of your employment on teaching tasks.
• Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch Universities, PhD scale (min. €2,770 max. €3,539).
• A year-end bonus of 8.3% and annual vacation pay of 8%.
• High-quality training programs and other support to grow into a self-aware, autonomous scientific researcher. At TU/e we challenge you to take charge of your own learning process .
• An excellent technical infrastructure, on-campus children's day care and sports facilities.
• An allowance for commuting, working from home and internet costs.
• A Staff Immigration Team and a tax compensation scheme (the 30% facility) for international candidates.

About us

Eindhoven University of Technology is an internationally top-ranking university in the Netherlands that combines scientific curiosity with a hands-on attitude. Our spirit of collaboration translates into an open culture and a top-five position in collaborating with advanced industries. Fundamental knowledge enables us to design solutions for the highly complex problems of today and tomorrow. 

Curious to hear more about what it’s like as a PhD candidate at TU/e? Please view the video .

Information

Do you recognize yourself in this profile and would you like to know more?
Please contact the hiring manager Dr Jemima Tabeart at  [email protected] .

Visit our website for more information about the application process or the conditions of employment. You can also contact [email protected] .

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Application

We invite you to submit a complete application by using the apply button. The application should include a:

• Cover letter in which you describe your motivation and qualifications for the position.
• Curriculum vitae, including a list of your publications and the contact information of three references.
  

We look forward to receiving your application and will screen it as soon as possible. The vacancy will remain open until the position is filled.