Post-doctor in numerical analysis - Hiring in process/Finished, not possible to apply

Description of the workplace

In your closest surroundings at the Centre for Mathematical Sciences will be the research group for Numerical Analysis, who successfully do research with a focus on numerical methods for time integration. We are about 15 persons who do both pure theoretical analysis at a high level of abstraction as well as more practical software development.

We offer

Lund University is a public authority which means that employees get particular benefits, generous annual leave and an advantageous occupational pension scheme. Read more on the University website about being a Lund University employee Work at Lund University. These various projects include travel grants.

Description of the projects

The Division of Mathematics LTH and Numerical analysis is seeking candidates for the postdoctoral projects below. Please state in the application which project(s) you are interested in. If you are interested in more than one project please rank them according to your preferences. 

Project 1: Locally Adaptive Methods for Free Discontinuity Problem

In many modern applications, like medical image reconstruction, the solution of interest is described by a discontinuous function. Unfortunately, it is a priori unknown where the discontinuities are located and their location has to be determined numerically. In fact, computing discontinuities wrongly or inaccurately could be either fatal (as in obstacle and tumour detection) or scientifically costly.

In this project, we solve image reconstruction problems by constructing methods that automatically adjust to the discontinuities of the underlying (observed) data. This adjustment leads to methods, which adaptively (in an iterative manner) reduce the reconstruction error, allowing to obtain the discontinuities more accurately and hence yield qualitatively better reconstructions than state-of-the-art methods, while keeping the computational complexity of the underlying problem on a manageable size.

This project is funded by the Crafoord Foundation. Read more:

https://www.crafoord.se

(contact: Andreas Langer, andreas.langer@math.lth.se)

Project 2: Randomized time stepping schemes

In this project, we focus on the temporal approximation of evolution equations. We aim to construct and analyze randomized time-stepping methods. In the past, randomized methods have been a popular tool for machine learning applications and also quadrature rules in the form of stochastic optimization schemes and Monte Carlo methods. Compared to deterministic methods, they can lead to an increased convergence order or lower computational costs depending on the type of randomization. We plan to apply these successful randomization tools in the field of temporal discretization of differential equations. In particular, we will concentrate on including splitting methods in this context.

This project is funded by the Crafoord Foundation. Read more:

https://www.crafoord.se

 (contact: Monika Eisenmann, monika.eisenmann@math.lth.se)

Project 3: Convergence analysis of neural/universal differential equations

Here, we will study and develop numerical methods for so-called neural differential equations and more generally, universal differential equations. These are differential equations with embedded universal approximators such as neural networks. Such equations have recently proven to be very useful e.g. for data-driven model discovery and for solving high-dimensional partial differential equations. To use them effectively, they require accurate, stable and fast methods for both forward- and backward-integration of the underlying differential equation, corresponding to evaluation and training of the neural network. Most of the focus in the literature so far has been on implementation issues and on maximising speed, while less effort has been made on quantifying errors. You will help us remedy this situation by performing rigorous convergence analyses in appropriate functional analytic frameworks for both existing methods and for novel methods to be developed within the project.

This project is funded by Wallenberg AI, Autonomous Systems and Software Program (WASP). WASP is Sweden’s largest individual research program ever, a major national initiative for strategically motivated basic research, education and faculty recruitment. The program addresses research on artificial intelligence and autonomous systems acting in collaboration with humans, adapting to their environment through sensors, information and knowledge, and forming intelligent systems-of-systems.

The vision of WASP is excellent research and competence in artificial intelligence,

autonomous systems and software for the benefit of Swedish industry. Read more: https://wasp-sweden.org

(contact: Tony Stillfjord, tony.stillfjord@math.lth.se)

Work duties

The main duties involved in a post-doctoral position is to conduct research. Teaching may also be included, but up to no more than 20% of working hours. The position includes the opportunity for three weeks of training in higher education teaching and learning. The purpose of the position is to develop the independence as a researcher and to create the opportunity of further development.

Detailed description of the work duties, such as:

• Research within one of the projects
• Teaching in the first, second and third cycles of studies
• Supervision of degree projects and doctoral students
• Administration related to the work duties listed above

Qualification requirements

Appointment to a post-doctoral position requires that the applicant has a PhD, or an international degree deemed equivalent to a PhD, within the subject of the position. The certificate proving the qualification requirement is met, must be received before the employment decision is made. Priority will be given to candidates who have graduated no more than three years ago before the last day for application. Under special circumstances, the doctoral degree can have been completed earlier.

Additional requirements:

• Very good oral and written proficiency in English.
• Research experience related to the project(s) you express interest in.

 Assessment criteria

This is a career development position primarily focused on research. The position is intended as an initial step in a career, and the assessment of the applicants will primarily be based on their research qualifications and potential as researchers. Particular emphasis will be placed on research skills within the subject.

For appointments to a post-doctoral position, the following shall form the assessment criteria:

• A good ability to develop and conduct high quality research.
• Teaching skills.

Other merits for all projects:

• Programming experience.
• Documented independence and leadership within research projects.
• Publications in subject-relevant journals or conferences.

Other merits for the individual projects:

Project 1:

• Experience with (adaptive) discretisation schemes and numerical analysis.
• Knowledge of optimisation and inverse problems, in particular image reconstruction and analysis.

 Project 2:

• Experience with temporal approximation methods for partial differential equations and stochastic analysis.
• Knowledge of convergence analysis in abstract frameworks, for example by variational arguments or semigroup theory.
  
  

Project 3:

• A strong theoretical background in numerical methods for time integration, or in optimization for scientific machine learning.
• Knowledge of convergence analysis in abstract frameworks, for example by variational arguments or semigroup theory.

Consideration will also be given to how the applicant’s experience and skills complement and strengthen ongoing research within the department, and how they stand to contribute to its future development.

Further information

This is a full-time, fixed-term employment of two years. The period of employment is determined in accordance with the agreement “Avtal om tidsbegränsad anställning som postdoktor” (“Agreement on fixed-term employment as a post-doctoral fellow”).

How to apply

Applications shall be written in English. Please draw up the application in accordance with LTH’s Academic qualifications portfolio – see link below – together with a list of references, one of which is your PhD supervisor. Upload the application as PDF-files in the recruitment system. Read more: http://www.lth.se/english/working-at-lth/to-apply-for-academic-positions-at-lth/

Welcome with your application!