PhD student in numerical analysis
Lund University, LTH, Mathematics Center, Mathematics LTH
Sweden

Lund University, LTH, Mathematics Center, Mathematics LTH

 

Lund University was founded in 1666 and is repeatedly ranked among the world’s top 100 universities. The University has 40 000 students and 7 600 staff based in Lund, Helsingborg and Malmö. We are united in our efforts to understand, explain and improve our world and the human condition.

 

LTH forms the Faculty of Engineering at Lund University, with approximately 9 000 students. The research carried out at LTH is of a high international standard and we are continuously developing our teaching methods and adapting our courses to current needs.

The position will be placed at the Division of Mathematics LTH and Numerical Analysis at the Centre for Mathematical Sciences. The Centre currently has strong research environments in numerics for partial differential equations (PDEs) and machine learning, and will now start a new research group at the intersection of these areas. This group is expected to contribute to the grand challenges within mathematics for artificial intelligence (AI) and is funded by the Wallenberg AI, Autonomous Systems and Software Program. The successful candidate will thus be part of a highly stimulating and rewarding work environment, with the possibility of contributing to important modern-day problems. 

Work duties
A doctoral student position is mainly devoted to postgraduate studies, but include 20% department service, usually teaching. The research area for the current call is numerical analysis and machine learning.

Research project
Machine learning is today a rapidly growing field with applications in most areas of science and engineering. In applications arising in supervised learning, the main task is typically to solve large optimization problems. There exist many methods for this purpose, with most of them being variants of the stochastic gradient method or the proximal point algorithm. These are essentially steepest descent-type methods, but where the descent direction is not computed exactly due to high computational costs. By reformulating the problems as gradient flows, one sees that these methods correspond to stochastic perturbations of very basic numerical time integration methods. This suggests that large gains might be achieved by applying more advanced time integration methods. The aim of the project is therefore to investigate this new viewpoint. We will construct new methods, analyse their convergence behaviour, implement them on high-performance systems and apply them to large-scale applications. The analysis will constitute a major part of the project, wherein we will perform rigorous error analyses, utilizing the nonlinear semigroup framework that arises naturally in the context of the gradient flow formulation.

Admission requirements
A person meets the general admission requirements for third-cycle courses and study programmes if he or she

  • has been awarded a second-cycle qualification, or
  • has satisfied the requirements for courses comprising at least 240 credits of which at least 60 credits were awarded in the second cycle, or
  • has acquired substantially equivalent knowledge in some other way in Sweden or abroad.

A person meets the specific admission requirements for third cycle studies in mathematics if he or she has

  • at least 90 credits of relevance to the subject area, of which at least 60 credits from the second cycle and a specialised project of at least 30 second-cycle credits in the field, or
  • a second second-cycle degree in a relevant subject.

In practice this means that the student should have achieved a level of knowledge in mathematics that corresponds to that of a Master of Science programs in Engineering Mathematics or Engineering Physics or a Masters degree in mathematics or applied mathematics.

Additional requirements:

  • Very good oral and written proficiency in English.
  • A project-relevant master's thesis.
  • The candidate is expected to have programming skills.

Assessment criteria
Selection for third-cycle studies is based on the student's potential to profit from such studies. The assessment of potential is made primarily on the basis of academic results from the first and second cycle. Special attention is paid to the following

  • Knowledge and skills relevant to the thesis project and the subject of study.
  • An assessment of ability to work independently and to formulate and tackle research problems.
  • Written and oral communication skills.
  • Other experience relevant to the third-cycle studies, e.g. professional experience.

Consideration will also be given to good collaborative skills, drive and independence, and how the applicant, through his or her experience and skills, is deemed to have the abilities necessary for successfully completing the third cycle programme.

Additional merits:

  • Programming experience (Python, MATLAB, C++).

Terms of employment
Only those admitted to third cycle studies may be appointed to a doctoral studentship. Third cycle studies at LTH consist of full-time studies for 4 years. A doctoral studentship is a fixed-term employment of a maximum of 5 years (including 20% departmental duties). Doctoral studentships are regulated in the Higher Education Ordinance (1993:100), chapter 5, 1-7 §§.

Instructions on how to apply
Applications shall be written in English and include a cover letter stating the reasons why you are interested in the position and in what way the research project corresponds to your interests and educational background. The application must also contain a CV, degree certificate or equivalent, the applicant's master thesis, and other documents you wish to be considered (grade transcripts, contact information for your references, letters of recommendation, etc.).


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