PhD Scholarship in Numerical Analysis at Lund University

Lund University is pleased to invite applicants to apply for a new opening PhD position in artificial intelligence. The funds for this position are available for 5 years. Applications are welcome before September 19, 2019.

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

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

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.

Assessment criteria

Selection for third-cycle studies is based on the student’s potential to profit from such studies. Theassessment of potential is made primarily on the basis of academic results from the first and secondcycle. Special attention is paid to the following

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

Only those admitted to third cycle studies may be appointed to a doctoral studentship. Third cyclestudies 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 areinterested in the position and in what way the research project corresponds to your interests andeducational 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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