We are looking for a postdoctoral candidate who will work within the new research group on Data-Driven Scientic Computing led by Olga Mula, located at CASA, the Center for Analysis, Scientic Computing and Applications of TU Eindhoven.
The goal of the group is to develop algorithms mixing the strengths of physics-based PDE methods with the ones offered by data-driven machine learning approaches. Both strategies have classically been considered separately, despite that they often provide complementary descriptions of the same reality. The group will address the growing need to combine them in an optimal way, using strategies that will depend on the application.
The candidate's research project will consist in developing numerical methods for inverse problems where the goal is to recover the state of a physical system based on a limited set of noisy partial observations. The study will focus on physical phenomena that are modeled with high-dimensional PDEs involving strong advection effects. Examples of such equations can be conservation laws, transport or kinetic equations, Fokker-Planck equations, or Mean Field Game Equations. For this type of advection-dominated problems, it is known that classical linear approximation methods are not well suited. The postdoctoral candidate will address this problem by developing nonlinear methods based on optimal transport, and machine learning. In order to address high dimensionality, and many-query evaluations, nonlinear model order reduction of parametric PDEs may be required.
References [1, 2] could serve as a starting point for the intended research project.

References
[1] V. Ehrlacher, D. Lombardi, O. Mula, and F.-X. Vialard. Nonlinear model reduction on metric
spaces. application to one-dimensional conservative pdes in wasserstein spaces. ESAIM M2AN,
54(6):21592197, 2020.
[2] Albert Cohen, Wolfgang Dahmen, Olga Mula, and James Nichols. Nonlinear reduced models for
state and parameter estimation. SIAM/ASA Journal on Uncertainty Quantication, 10(1):227
267, 2022.

The ideal candidate will have the following skills:

• PhD degree in Applied Mathematics (Numerical Analysis, Applied Analysis, Scientic Computing), Statistics, or Machine Learning.
• Interest and some knowledge in at least one of the following topics: Optimal Transport, Machine Learning, Inverse Problems, Data-Assimilation, Optimization, Numerical Schemes.
• for Conservation Laws or Mean Field Games, Model Order Reduction of parametric PDEs.
• Provable coding experience in Python, Julia, or C++.
• Interest in teaching activities.
• Strong interpersonal, organizational and communication skills. Ability to work both independently and in a team.
• Working and teaching is in English so excellent skills in this language are required.

We are offering:

• A meaningful job in a dynamic and ambitious university with the possibility to present your work at international conferences.
• A full-time employment for one year which will be extended for a second year after positive evaluation.
• You will have free access to high-quality training programs on general skills, didactics and topics related to research and valorization.
• A gross monthly salary and benefits in accordance with the Collective Labor Agreement for Dutch Universities. The gross monthly salary depends on the candidates' experience.
• Additionally, an annual holiday allowance of 8% of the yearly salary, plus a year-end allowance of 8.3% of the annual salary.
• A broad package of fringe benefits (including an excellent technical infrastructure, moving expenses, and savings schemes).
• Should you come from abroad and comply with certain conditions, you can make use of the so-called '30% facility', which permits you not to pay tax on 30% of your salary.
• Family-friendly initiatives are in place, such as an international spouse program, and excellent on-campus children day care and sports facilities.