Reconstruction of turbulence from partial observations

Candidates have a master degree in one of the following or related fields : applied mathematics, computer science, computational mathematics, engineering or physics. They should have a good background or interest in dynamical systems, stochastic processes, optimization, simulation, and programming (Julia, Python, C / C++, Fortran, C / C++, …). Proficiency in English is a requirement. The position adheres to the European policy of balanced ethnicity, age and gender. Persons of all origins and gender are encouraged to apply.Attractors of dissipative ergodic chaotic systems typically lead to a low-dimensional manifold in the full state space of the attractor. Finding a measure on such a manifold is typically achieved by a long-time push-forward operation of a classical Lebesgues measure. This requires a significant amount of computation for chaotic dynamical systems that result from the discretization of PDEs. To date, fast evaluation of measures on such systems remain elusive.The research aims at the development of stochastic methods, such as Gaussian processes or other machine learning techniques that allow for fast evaluation of measures on ergodic chaotic systems arising from PDEs. The research focuses on simple systems such as the Kuramoto–Shivashinsky equations, Kolmogorov flow, or similar chaotic systems. This methodology can then be used for Bayesian inference of the state of chaotic systems, either in the context of data assimulation or in the context of initialization of complex simulations. This PhD position is supervised by Prof. Dirk Nuyens (Computer Science), and co-supervised by Prof. Johan Meyers (Mechanical Engineering). The position is based in the Numerical Analysis and Computational Mathematics (NUMA) section in the department of Computer Science at the University of Leuven (KU Leuven). The research is part of the project “Computational methods for infinite-dimensional Bayesian inversion of physics-based models in engineering applications” led by Prof. Giovanni Samaey, Prof. Geert Lombaert, Prof. Dirk Nuyens and Prof. Johan Meyers. Timeline and remuneration : Immediate start is possible. The PhD position lasts for the duration of four years, and is carried out at the University of Leuven. The candidate also takes up a limited amount (approx. 10% of the time) of teaching activities. The remuneration is generous and is in line with the standard KU Leuven rates. It consists of a net monthly salary of about 2400 Euro (in case of dependent children or spouse, the amount can be somewhat higher). Following Belgian law, the salary is automatically adjusted for inflation based on the smoothed health index.