Post-Doctoral Associate in Mathematics (Inverse Problems)

About the role

New York University Abu Dhabi's Mathematics Program in the Division of Science is recruiting a Post-Doctoral Associate to work with Professor Elena Beretta on inverse problems for nonlinear partial differential equations arising in the life sciences and medical imaging. The project sits at the intersection of inverse problems, nonlinear PDEs, numerical analysis, mathematical biology, medical imaging and scientific machine learning, focusing on recovering unknown initial states, parameters, coefficients, sources and geometric structures from indirect, partial and noisy measurements, with emphasis on tumor growth, cardiac electrophysiology and medical imaging.

Key responsibilities

• Investigate the mathematical foundations of inverse problems: well-posedness of the forward problem, identifiability and uniqueness, conditional stability estimates, shape sensitivity and regularization of nonlinear inverse problems.
• Design and implement efficient reconstruction algorithms, including iterative regularization, PDE-constrained optimization, shape and topological derivative methods, and neural-network-based approaches.
• Develop scientific machine-learning techniques that preserve the structure of the underlying mathematical models, such as physics-informed or physics-constrained neural networks, neural operators, learned iterative methods, reduced-order models and interpretable architectures.
• Work in a multidisciplinary environment with faculty, postdoctoral researchers, graduate and undergraduate students, and take part in seminars, workshops and collaborative research activities.

Required profile

• PhD in Mathematics, Applied Mathematics, Computational Science, Scientific Computing, Mathematical Biology, Biomedical Engineering or a closely related field, with no more than 5 years since receiving the PhD.
• Strong background in partial differential equations, inverse and ill-posed problems, numerical analysis, scientific computing or mathematical modeling.
• Excellent written and oral communication skills, able to work independently and collaboratively.

Required skills

• Strong programming skills.
• Experience with Python, Julia, MATLAB or C++ and machine-learning frameworks such as PyTorch, JAX or TensorFlow is desirable.
• Previous experience with finite-element, finite-difference, spectral or iso-geometric methods, and with physics-informed neural networks, neural operators or interpretable machine-learning methods is an advantage.

Applications are accepted immediately and considered until the position is filled; the anticipated start date is 1 February 2027 for a one-year appointment. Applicants submit a cover letter, CV with full publication list, research statement, representative publications or preprints and three letters of reference in PDF format.