PhD student on the subject of Inverse Problems for Wave-Based Imaging Centrum Wiskunde & Informatica (CWI) in Netherlands

Centrum Wiskunde & Informatica (CWI), the Dutch national research institute for mathematics and computer science, is offering a PhD position in the Computational Imaging group on Inverse Problems for Wave-Based Imaging. The project sits at the intersection of applied mathematics, scientific computing, and imaging science, with applications that include geophysics, medical ultrasound, seismic imaging, and non-destructive testing.

The research addresses large-scale nonlinear inverse problems governed by partial differential equations (PDEs). A key challenge is full-waveform inversion: while it is a powerful imaging strategy, its use is limited by strong nonlinearity and the computational expense of repeatedly solving wave equations. This PhD project aims to develop a new mathematical and computational framework that combines PDE-based modelling with ideas from data-driven reduced-order modelling. The goal is to create imaging methods that are more robust and more efficient, while also supporting uncertainty quantification and experimental design.

A central scientific question is whether relaxed formulations of the underlying PDE constraints can reduce the nonlinearity of the inverse problem and improve computational tractability. The project therefore has a strong theoretical component, involving the analysis of PDE-constrained inverse problems, properties of wave equations and their solution operators, and the conditions under which relaxed models lead to better-behaved inversions. These mathematical insights will then be translated into numerical algorithms for inversion, uncertainty quantification, and experimental design.

The research will begin with simpler model problems to establish rigorous mathematical understanding, and then progress toward multidimensional acoustic and elastic wave propagation and more realistic wave-imaging settings. The work is closely connected to current research in constraint relaxation for PDE-based inverse problems, and it offers the opportunity to contribute both foundational analysis and practical computational methods.

You will be based in the Computational Imaging group at CWI, collaborating with researchers in inverse problems, numerical analysis, scientific computing, and imaging, as well as academic and industrial partners. Supervision will be provided by Prof. Tristan van Leeuwen at CWI, with co-supervision by Dr. Chris Stolk at the University of Amsterdam. The project offers substantial freedom to explore fundamental mathematical questions while maintaining a direct link to challenging real-world imaging applications.

The position is a full-time PhD appointment under the Dutch Collective Labour Agreement for Research Centres (CAO-onderzoeksinstellingen). The initial contract is for 18 months and, after positive evaluation, will be extended by 30 months. The salary starts at €3,115 gross per month in the first year and rises to €3,989 over the four-year period, with an 8% holiday allowance and an 8.33% year-end bonus. CWI also mentions flexible scheduling and help with housing for expat employees.

Applicants should hold a Master's degree in mathematics, applied mathematics, computational science, mathematical physics, or a closely related field, and should have a strong background in partial differential equations, inverse problems, numerical methods for PDEs, or scientific computing. Programming experience in Python, Julia, MATLAB, C, or C++ is expected, along with strong English communication skills and the ability to work independently and in a collaborative interdisciplinary environment. Applications are due by 31 October 2026.