PhD student of Inverse Problems Wave- Imaging

PhD student on the subject of Inverse Problems for Wave-Based Imaging

Founded in 1946, CWI is the national research institute for mathematics and computer science in the Netherlands and is located at Science Park Amst...

Centrum Wiskunde & Informatica (CWI) has a vacancy in the Computational Imaging research group for a talented PhD student (m/f/x) on the subject of Inverse Problems for Wave-based imaging.

Waves are widely used for imaging in applications ranging from geophysics and medical ultrasound to non-destructive testing. In these applications, the aim is to infer quantitative properties of an object or medium from measurements of waves that have propagated through it. Mathematically, such problems lead to large-scale nonlinear inverse problems governed by partial differential equations (PDEs).

Full-waveform inversion is a powerful approach to such problems, but its practical use is limited by the strong nonlinearity of the inverse problem and by the computational cost of repeatedly solving wave equations.

In the project, we will develop a new mathematical and computational framework that combines PDE-based modelling with ideas from data-driven reduced-order modelling. The aim is to obtain imaging methods that are more robust and computationally efficient, while also providing a natural framework for uncertainty quantification and experimental design. A central question is whether suitable relaxations of the underlying PDE constraints can effectively reduce the nonlinearity of the inverse problem.

Understanding this requires mathematical analysis of the PDEs and the resulting inverse problems, as well as the development of numerical methods that can eventually be applied to large-scale wave-imaging problems.

The PhD project will have a strong mathematical component. You will investigate questions concerning, for example, the analysis of PDE-constrained inverse problems, properties of wave equations and their solution operators, and the conditions under which relaxed formulations lead to better-behaved inverse problems. These mathematical insights will subsequently be translated into computational algorithms for inversion, uncertainty quantification and experimental design. The research will initially focus on relatively simple model problems in which mathematical questions can be studied rigorously, before progressing towards multidimensional acoustic and elastic wave propagation and realistic imaging applications.

The mathematical level and type of research are illustrated, for example, by the paper An Analysis of Constraint-Relaxation in PDE-Based Inverse Problems by Van Leeuwen and Yang (arXiv:).

As a PhD student on this project, you will:

• develop mathematical theory for non-linear inverse problems governed by wave equations;
• design and analyse numerical algorithms for inverse problems, uncertainty quantification and experimental design in the context of wave-based imaging;
• implement prototype numerical methods and test them on increasingly realistic computational wave-based imaging problems;
• collaborate with researchers in applied mathematics, scientific computing and wave-based imaging, as well as with academic and industrial partners;
• present your results at international conferences and publish them in leading scientific journals.

Your day-to-day research will take place in the Computational Imaging group  will be supervised by Prof. Tristan van Leeuwen (CWI) and co-supervised by Dr. Chris Stolk (University of Amsterdam). You will interact with researchers with backgrounds in inverse problems, numerical analysis, scientific computing and imaging, and with project partners working on applications including seismic imaging, medical ultrasound and non-destructive testing. The project offers considerable freedom to pursue fundamental mathematical questions while maintaining a clear connection to challenging real-world imaging problems.

We are looking for a candidate with a strong mathematical background and an interest in developing mathematics that ultimately leads to computational methods for imaging.

You have:

• a Master's degree in mathematics, applied mathematics, computational science, mathematical physics, or a closely related field;
• a strong background in one or more of the follow areas: partial differential equations, inverse problems, numerical methods for PDEs, scientific computing;
• the ability and interest to work with both rigorous mathematical arguments and numerical experiments;
• programming experience in a language such as Python, Julia, MATLAB, C or C++;
• good written and spoken English;
• the ability to work independently while also collaborating in an interdisciplinary research team.

The terms of employment are in accordance with the Dutch Collective Labour Agreement for Research Centres ("CAO-onderzoeksinstellingen"). The initial labour agreement will be for a period of 18 months. After a positive evaluation, the agreement will be extended by 30 months. The gross monthly…