PhD position in multilevel interacting particle methods for Bayesian inversion

• Candidates must hold a master degree in Mathematical Engineering or (Applied) Mathematics (or equivalent).
• Candidates should have a solid background in numerical methods for differential equations, simulation of stochastic processes and/or optimization.
• Candidates should have experience with programming of scientific software.
• Excellent proficiency in English is required, as well as good communication skills, both oral and written.

To reliably use simulation-generated predictions in science and engineering, one needs trustworthy mathematical models that are calibrated to measurement data. We are motivated by applications in engineering in which the system models are partial differential equations (PDEs) with potentially infinite-dimensional (e.g., space-dependent) parameters and state variables. Inferring these parameters and/or states from large amounts of possibly high-resolution data leads to computationally intensive inverse problems. The team aims at developing Bayesian computational methods for such (ill-posed) inverse problems and aims both at increasing their validity and at reducing their computational cost.

In this project, we will focus on increasing the computational efficiency of interacting particle methods for Bayesian inversion when including model error in a multilevel hierarchy. As model problem, we will consider the inference of parameters in applications arising from structural mechanics.

The research will be carried out in an international team of numerical analysts at NUMA. While the envisaged work is generic (not tied to a specific application), the project will benefit from a long-standing and fruitful collaboration with the Structural Mechanics group in the Department of Civil Engineering.NUMA is a research section within the Department of Computer Science of KU Leuven, with 12 permanent staff members and approximately 60 PhD and postdoctoral researchers. NUMA (Numerical Analysis and Applied Mathematics) develops numerical algorithms and software for large-scale problems in science and engineering. Its research ranges from algorithm design and analysis to software implementation and applications in other scientific and engineering domains.

• A high-level and exciting international research environment.
• A supportive and collaborative team in which you can develop know-how and expertise in state-of-the-art simulation methods.
• The opportunity to build up research and innovation skills that are essential for a future career in research and development, both in an industrial and academic context.
• Funding is secured for four years.
• A competitive salary.