PhD candidate in Structure-preserving Generative Modeling

This is NTNU NTNU is a broad-based university with a technical-scientific profile and a focus in 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. Video: https://youtu.be/Xt-yHCN5QS0 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. - You must meet the requirements for admission to the faculty's Doctoral Programme. - 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”. The appointment is to be made in accordance with NTNUs guidelines for recruitment positions and Regulations for the degrees philosophiae doctor (ph.d.) and philosophiae doctor (ph.d.) in artistic development work at the Norwegian University of Science and Technology (NTNU) for general criteria for the position. Preferred selection criteria - 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. - Strong programming skills (Python, Julia, Jax). - 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. - Career guidance and follow-up during the PhD period . - Open and inclusive working environment with committed colleagues. - Working capital that can be used to implement the project. - Favorable terms as a member of the Norwegian Public Service Pension Fund (SPK) . - Free Norwegian language training at a basic level (A2) . As a PhD Candidate at NTNU, you will have access to employee benefits . Diversity Diversity is a strength, and at NTNU we aim to be an employer th