Postdoc position : Structure-preserving reduced order models for conservation laws

Required skills The candidate should hold a PhD in applied mathematics, scientific computing, computer science or equivalent. The ideal candidate has a good knowledge of either reduced order modelling or numerical methods for hyperbolic PDEs and at least one programming language Post-doc description The position will primarily focus on error estimation and uncertainty quantification (UQ) for ROM. The hired post-doc will develop a posteriori error estimators to assess the accuracy of reduced models with respect to high-fidelity simulations, with a focus on hyperbolic conservation laws. Both theoretical and empirical approaches will be considered, depending on the candidate’s profile. In parallel, the post-doc will investigate how uncertainties in input parameters propagate through reduced models. This includes the use of sensitivity analysis to estimate statistical moments of the solution and to derive confidence intervals for quantities of interest. Finally, the post-doc will contribute to a global analysis of the interaction between different sources of error—spatial discretisation, model reduction, and parametric uncertainty—with the aim of identifying optimal computational strategies under resource constraints The work will involve the design and implementation of advanced numerical methods, as well as their validation on a hierarchy of test cases, ranging from academic benchmarks to more realistic configurations, including problems with parametric geometries.