The candidate will work within the research group Models and Measures financed by the Emergences Program of the Paris City Council. The topic are inverse state estimation problems where the goal is to reconstruct numerically the state of a physical system (given by a function living in a high dimensional space) from a limited amount of measurement observations and the knowledge of a physical PDE model. Due to their ill-posedness, these problems are often addressed with Bayesian approaches that consist in searching for the most plausible solution using sampling strategies of the posterior density. In view of their high numerical cost, especially in a high dimensional framework, novel methodologies involving reduced models have recently been proposed as a vehicle to reduce complexity and achieve near real time in the reconstructions.
Recent works on the topic have been devoted to find optimal linear reconstruction algorithms. The task of the post-doctoral candidate will be to develop fast nonlinear solution strategies to the state estimation problem, with possible time-dependence. The envisaged approach is to combine reduced modeling with statistical learning algorithms such as mixture distributions and clustering algorithms.
As a support for our numerical tests, we will consider an application related to air pollution in the city of Paris which is currently being developed within the project.
* The candidate must hold a PhD in Numerical Analysis, Scientific Computing or Statistics.
* Solid experience in the development of numerical methods or data analysis with Python, Julia or C++.
* Solid working knowledge in at least one of the following topics: reduced modeling of PDEs, uncertainty quantification, Bayesian inverse problems, non-parametric statistics, optimization, machine learning.
Applications should be submitted by September 13th 2019 to firstname.lastname@example.org by email, they should provide:
* list of publications,
* 2 letters of recommendation (sent directly to me by the reference).