School of Engineering Sciences at KTH

Project description

Third-cycle subject: applied and computational mathematics, specialization mathematical statistics

The Department of Mathematics at the Royal Institute of Technoloy seeks applications for a Ph.D student position in Applied and Computational Mathematics for a project in machine learning for cryogenic electron microscopy (cryo-EM).

Cryo-EM is a method for imaging biological macromolecules using transmission electron microscopes. The end result of this process is a 3D reconstruction of the given molecule at high enough resolution to resolve individual atoms. However, the images obtained from the electron microscope are often plagued by high levels of noise which needs to be accounted for during reconstruction. This is typically solved by using a large number of images, often in the hundreds of thousands, which leads to high data collection costs. In addition, for particularly small molecules, present methods fail even for very large dataset sizes.

This project proposes a new approach in which deep neural networks (DNNs) are trained to reduce the effect of the noise by incorporating prior information on the imaged molecules from various sources, including previously published 3D reconstructions and outputs from tools like AlphaFold 2. Due to the structure of the problem, a central component will be that of an equivariant transformer network applied to the noisy images combined with reconstruction methods based on invariants.

For more information, see:

Supervision: Joakim Andén is proposed to supervise the doctoral student. Decisions are made on admission

What we offer

  • The possibility to study in a dynamic and international research environment in collaboration with industries and prominent universities from all over the world.Read more
  • A workplace with many employee benefits and monthly salary according to KTH’s Doctoral student salary agreement.
  • A postgraduate education at an institution that is active and supportive in matters pertaining to working conditions, gender equality and diversity as well as study environment.
  • Work and study in Stockholm, close to nature and the water.
  • Help to relocate and be settled in Sweden and at KTH.
  • The successful doctoral candidate will be part of a larger team of researchers working on different aspects of deep learning and cryo-EM imaging at KTH Department of Mathematics. Beyond this core team, the student will also have the opportunity to work with collaborators elsewhere in Sweden and internationally.

Admission requirements

To be admitted to postgraduate education (Chapter 7, 39 § Swedish Higher Education Ordinance), the applicant must have basic eligibility in accordance with either of the following:

  • passed a second cycle degree (for example a master's degree), or
  • completed course requirements of at least 240 higher education credits, of which at least 60 second-cycle higher education credits, or
  • acquired, in some other way within or outside the country, substantially equivalent knowledge

The special requirements for the doctoral program are studies on the advanced level with specialization in mathematics, applied mathematics, or computational mathematics.

In addition to the above, there is also a mandatory requirement for English equivalent to English B/6, read more here


In order to succeed as a doctoral student at KTH you need to be goal oriented and persevering in your work. During the selection process, candidates will be assessed upon their ability to:

  • independently pursue his or her work
  • collaborate with others,
  • have a professional approach and
  • analyse and work with complex issues.
  • In addition to the traditional academic merits, such as a talent for mathematical studies, a relevant degree project or international experience are regarded as advantageous qualifications.
  • Due to the central nature of DNNs in this project, experience with standard deep learning frameworks such as PyTorch or TensorFlow will also be regarded as particularly advantageous qualifications.

After the qualification requirements, great emphasis will be placed on personal competency. 

Target degree: Doctoral degree

Information regarding admission and employment

Only those admitted to postgraduate education may be employed as a doctoral student. The total length of employment may not be longer than what corresponds to full-time doctoral education in four years ' time. An employed doctoral student can, to a limited extent (maximum 20%), perform certain tasks within their role, e.g. training and administration. A new position as a doctoral student is for a maximum of one year, and then the employment may be renewed for a maximum of two years at a time. In the case of studies that are to be completed with a licentiate degree, the total period of employment may not be longer than what corresponds to full-time doctoral education for two years.

Union representatives

You will find contact information for union representatives on KTH's website.

Doctoral section (Students’ union on KTH Royal Institute of Technology)

You will find contact information for doctoral section on the section's website.

To apply for the position

Apply for the position and admission through KTH's recruitment system. It is the applicant’s responsibility to ensure that the application is complete in accordance with the instructions in the advertisement.

Applications must be received at the last closing date at midnight, CET/CEST (Central European Time/Central European Summer Time).

Applications must include the following elements:

  • CV including your relevant professional experience and knowledge.
  • Application letter with a brief description of why you want to pursue research studies, about what your academic interests are and how they relate to your previous studies and future goals. (Maximum 2 pages long)
  • Copies of diplomas and grades from previous university studies and certificates of fulfilled language requirements (see above). Translations into English or Swedish if the original document is not issued in one of these languages.Copies of originals must be certified.
  • Representative publications or technical reports. For longer documents, please provide a summary (abstract) and a web link to the full text.

Other information

Striving towards gender equality, diversity and equal conditions is both a question of quality for KTH and a given part of our values.

For information about processing of personal data in the recruitment process please read here.

The position may include security-sensitive activities. To become authorized, you therefore need to pass a possible security check.

We firmly decline all contact with staffing and recruitment agencies and job ad salespersons.

Disclaimer: In case of discrepancy between the Swedish original and the English translation of the job announcement, the Swedish version takes precedence.



Type of employment Temporary position
Contract type Full time
First day of employment Enligt överenskommelse
Salary Monthly salary according to KTH's doctoral student salary agreement
Number of positions 1
Full-time equivalent 100%
City Stockholm
County Stockholms län
Country Sweden
Reference number S-2024-0144
  • Joakim Andén,
Published 30.Jan.2024
Last application date 08.Mar.2024 11:59 PM CET

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