PhD candidate in Structure-preserving Generative Modeling

Ntnu; Trondheim; Hybrid; NOK 522,000 - 638,000; Full time

Benefits offered by this job

Free Norwegian language training (A2)

Open and inclusive working environment

International research environment

Job summary

NTNU invites applications for a PhD candidate position in the Department of Mathematical Sciences. The project integrates structure-preserving generative modeling with AI for decision, in collaboration with SINTEF and aiD, under Professor Elena Celledoni and Sølve Eidnes.

The successful candidate will complete doctoral studies within three years (with potential extension) and contribute to theoretical and algorithmic developments, software work, and industrial case studies.

Qualifications

• Master's degree in mathematical sciences or equivalent with 120 credits at master level (five-year Norwegian course).
• Strong background in mathematics, probabilities and optimization.
• Good oral and written English.
• Strong programming skills considered an asset.

Responsibilities

• Complete the doctoral education until obtaining a doctorate.
• Carry out high-quality research within the described framework.
• Publish academic papers and disseminate popular science.
• Participate in the aiD center and NTNU Energy initiative.
• Present at conferences and through international research stays.

Skills

Mathematics

Probabilities

Optimization

Programming

English

Education

Master's degree in mathematical sciences

Five-year Norwegian course (120 credits)

Job description

PhD candidate in Structure-preserving Generative Modeling

NTNU is a broad-based university with atechnical-scientific profile and a focusin professional education. The university is located in three cities with headquarters in Trondheim.

At NTNU, 9,000 employees and 43,000 students work to create knowledge for a better world.

You will find more information about working at NTNU and the application process here.

About the position

This PhD position will be hosted at the Department of Mathematical Sciences (IMF), holding broad competences in both pure and applied mathematics. The position will be part of the research centre the Norwegian Center on AI for Decision (aiD) cooperating with over 60 companies.

The research will integrate techniques of numerical analysis and structure-preserving algorithms to generative modeling in AI. It will build upon the work done at IMF and SINTEF in this field. We will consider techniques like flow matching, and use ideas from optimal transport and neural (stochastic) differential equations, invariant Kalman filtering and geometric numerical integration. The application areas will be chosen among the use cases of the aiD canter. The direction of research will be adapted to the strengths of the recruited candidate.

Are you motivated to take a step towards a doctorate and open exciting career opportunities? As a PhD Candidate with us, you will work to achieve your doctorate, and at the same time gain valuable experience that qualifies you for a further career in higher education and research, in and outside academia.

Your supervisors will be Professor Elena Celledoni (IMF) and Senior Researcher Sølve Eidnes (SINTEF).

Your immediate leader will be the Head of Department.

About the project

This position is funded by NTNU and will be integrated within the Norwegian Center on AI for Decision (aiD), benefiting from broad and divers expertise, and strong industrial connections. The project will have theoretical and algorithmic developments, software developments, and industrial case studies.

Duties of the position

• Complete the doctoral education until obtaining a doctorate.
• Carry out research of good quality within the framework described above.
• Academic publications and popular science dissemination.
• Participate actively in the aiD center, and in the NTNU strategic area Energy.
• Participate in international activities such as conferences and/or research stays at foreign educational institutions.
• Validate the research on industrial use-cases.

Be prepared for changes to your work duties after employment.

Required selection criteria

• You must have a relevant Master's degree in mathematical sciences or equivalent, in particular computational mathematics, numerical analysis and experience with AI tools. Your course of study must correspond to a five-year Norwegian course, where 120 credits have been obtained at master's level. Master students can apply, but the master's degree must be obtained and documented before starting the position.
• You must have a strong academic background from your previous studies and have an average grade from your Master's degree study, or equivalent education, which is equal to B or better compared to NTNU's grading scale . If you do not have letter grades from previous studies, you must have an equally good academic foundation. If you have a weaker grade background, you maybe considered if you can document that you are particularly suitable for a PhD education.
• Good oral and written presentation skills in English.
• You need strong skills in mathematics, probabilities, optimization and programming.

PLEASE NOTE: For detailed information about what the application must contain, see paragraph “About the application”.

• Experience in one or more of the following research areas is desirable: geometric numerical integration, structure preserving deep learning, stochastic differential equations, generative AI, numerical optimization.
• Experience with numerical optimization is also desirable.

Personal characteristics

To complete a doctoral degree (PhD), it is important that you are able to:

• Be interested in both theoretical understanding and practical application to real world problems.
• Work independently, but seeking feedback and reporting regularly.
• Work in a structured way, set goals and make plans to achieve them.
• Present and discuss your research with other professionals.
• Get involved and contribute constructively with feedback.
• Work constructively under pressure or in the face of adversity.
• Show curiosity and a strong motivation for the subject.
• Analyze data, assess different perspectives and draw well-founded conclusions.
• Be flexible and open to adjusting the plan for the project as needed.
• Enjoy collaborating, working with others.

Emphasis will be placed on personal qualities.

We offer

• An exciting job with an important mission in society
• Developing tasks in a strong and international professional environment.
• Open and inclusive working environment with committed colleagues.
• Free Norwegian language training at a basic level (A2) .

We strive to attract employees with different skills, life experiences and perspectives to contribute to even better problem solving of our societal mission in research and education.

At NTNU we want to increase the proportion of women in scientific positions. We have a number ofmeasures to promote equality.

Salary and conditions

In the position of PhD Candidate, code 1017, your gross salary will normally be NOK 580 000,- per annum depending on qualifications and seniority. A 2% statutory contribution to the State Pension Fund is deducted from the salary.

The employment period is 3 years, funded by the project. The department might in addition offer up to 12 months extension for career enhancing work, depending on qualifications and motivation.

For employment as a PhD Candidate, it is a prerequisite that you gain admission to the PhD programme in Mathematical Sciences within three months of your employment contract start date, and that you participate in an organized doctoral programme through out the period of employment.

The position is conditional on external funding.

As an employee at NTNU, it is important that you keep yourself up to date with academic and organizational changes and adapt to them.

For the necessary professional and social interaction, it is a prerequisite that you are physically present and available to the institution on a daily basis.

The appointment is carried out in accordance with the principles of the State Employees Act , and Export control (legislation that regulates the export of knowledge, technology and services). Candidates who, after assessment of the application and attachments, are considered to be in conflict with the criteria in the latter act, will not be able to be employed.

About the application

The attachments (including a description of your scientific work) must accompany the application as these documents form the basis of the application assessment. The documents must be in Norwegian/a Scandinavian language or English.

Please note: the application will only be assessed on the basis of the information we have received by the application deadline. Therefore, make sure that your application clearly shows how your skills and experience meet the criteria described above. The application and all attachments must be sent electronically via Jobbnorge.no. If you are invited to an interview, you must bring certified copies of certificates and diplomas upon request.

The application must include:

• Transcripts and diplomas for Bachelor's and Master's degrees.
• CV.
• Copy of Master's thesis. If you have recently submitted your Master's thesis, you can attach a draft of the thesis. Documentation of a completed Master's degree must be presented before taking up the position.
• Project outline containing proposals for an overall description of research questions, theoretical perspectives, methodological design for the project and progress plan (maximum 1500 words/4 pages).
• Possibly publications etc. other relevant research work.
• Possibly certificates.
• Names and contact information of three relevant referees.

If all, or parts, of your education has been taken abroad, we also ask you to attach documentation of the scope and quality of your entire education, both Bachelor's and Master's education, in addition to other higher education. If your institution uses “diploma supplement” (normal for most European institutions), you must attach this. A description of the documentation required can also be found here . If you already have a statement from Norwegian Directorate for Higher Education and Skills (HK-dir) , please attach this as well.

Joint work will be considered. If it is difficult to identify your contribution to joint work, you must attach a brief description of your participation.

When assessing the best qualified, we emphasize necessary qualifications such as education, experience and personal suitability. Motivation for the position, ambitions, and potential for research will also count when assessing the candidates.
NTNU recognizes a wide range of academic contributions and has committed itself to The San Francisco Declaration on Research Assessment and CoARA (responsible assessment of research and recognition of a greater breadth of academic contributions in accordance with NTNU's social mission).

General information

A public list of applicants with name, age, job title and municipality of residence is prepared after the application deadline. If you wish to be exempt from entry on the public applicant list, this must be justified. Assessment will be made in accordance withcurrent legislation . You will be notified if the exemption is not granted.

The city of Trondheim is a modern European city with a rich cultural scene.Trondheim is the tech capital of Norway with a population of 200,000.The Norwegian welfare state, including healthcare, schools, kindergartens and overall equality, is probably the best of its kind in the world. Professional subsidized day-care for children is easily available. Furthermore, Trondheim offers great opportunities for education (including international schools) and possibilities to enjoy nature, culture and family life and has low crime rates and clean air quality.

NTNU - knowledge for a better world

NTNU - knowledge for a better world

The Norwegian University of Science and Technology (NTNU) creates knowledge for a better world and solutions that can change everyday life.

Department of Mathematical Sciences

We are Norway’s largest university environment in mathematical sciences.
The Department has a particular responsibility for all basis education inmathematical sciences for engineering and natural science students at NTNU.We focus on long-term basic research and applied research at a high international level.
Our aim is to meet the society’s needs for mathematical and statistical expertise inbusiness and public administration as well as in the research and education sector.The Department of Mathematical Sciences is one of seven departments in the Faculty of Information Technology and Electrical Engineering .