Post-Doctoral Associate In The Division Of Science Mathematics - Dr Elena Beretta

The Mathematics Program in the Division of Science at New York University Abu Dhabi seeks to recruit 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 successful applicant will contribute to a research project at the intersection of inverse problems, nonlinear partial differential equations, numerical analysis, mathematical biology, medical imaging, and scientific machine learning. The project will focus on the recovery of unknown initial states, physical parameters, coefficients, sources, and geometric structures from indirect, partial, and noisy measurements. Particular emphasis will be placed on nonlinear PDE models arising in tumor growth, cardiac electrophysiology, and medical imaging.

The project will build on recent work by Professor Beretta and collaborators on inverse problems for nonlinear phase-field and reaction-diffusion models of tumor evolution, inverse problems in cardiac electrophysiology, nonlinear conductivity equations, and computational reconstruction methods based on regularization and interpretable neural networks. In the context of tumor growth, possible research directions include the reconstruction of earlier tumor configurations from later-time measurements, the identification of biological parameters and nutrient distributions, and the analysis of nonlinear phase-field systems coupling tumor evolution, nutrient transport, chemotaxis, and biomarkers. In cardiac electrophysiology, the project may address the identification of ischemic or electrically inactive regions, the recovery of anisotropic and discontinuous conductivities, and reconstruction from localized or finitely many boundary measurements. Related questions in medical imaging may include electrical impedance tomography, inverse conductivity problems, and shape or interface reconstruction.

The candidate will investigate both the mathematical foundations and the computational aspects of these inverse problems. The analytical component of the project may include the well-posedness of the forward problem, identifiability and uniqueness, conditional stability estimates, shape sensitivity, and regularization of nonlinear inverse problems. The computational component will involve the design and implementation of efficient reconstruction algorithms, including iterative regularization, PDE-constrained optimization, shape and topological derivative methods, and neural-network-based approaches.

A central objective will be to develop scientific machine-learning techniques that preserve the structure of the underlying mathematical models. Possible directions include physics-informed or physics-constrained neural networks, neural operators, learned iterative methods, reduced-order models, and interpretable neural architectures in which trainable parameters are directly related to physical coefficients, initial states, sources, or interfaces. Particular attention will be devoted to the mathematical justification, stability, robustness, interpretability, and computational efficiency of the proposed algorithms.

The candidate will work in a multidisciplinary research environment involving faculty members, postdoctoral researchers, graduate students, and undergraduate students in mathematics, scientific computing, data science, biology, and biomedical applications. The successful applicant will be encouraged to participate actively in seminars, workshops, and collaborative research activities within the Mathematics Program and the Division of Science.

Applicants must have a PhD in Mathematics, Applied Mathematics, Computational Science, Scientific Computing, Mathematical Biology, Biomedical Engineering, or a closely related field, with no more than 5 ears post receipt of PhD. A strong background in partial differential equations, inverse and ill-posed problems, numerical analysis, scientific computing, or mathematical modeling is required. Candidates with experience in nonlinear elliptic or parabolic PDEs, phase-field models, reaction-diffusion systems, regularization methods, PDE-constrained optimization, shape reconstruction, or medical imaging are particularly encouraged to apply.

Strong programming skills are required. Experience with Python, Julia, MATLAB, or C++, and with machine-learning frameworks such as PyTorch, JAX, or TensorFlow, is desirable. Previous experience with finite-element, finite-difference, spectral, or iso-geometric methods, as well as with physics-informed neural networks, neural operators, or interpretable machine-learning methods, would be an advantage. The successful applicant should have excellent written and oral communication skills and the ability to work both independently and collaboratively.

For consideration, applicants need to submit a cover letter, a curriculum vitae including a complete publication list, a statement of research accomplishments and interests, one or two representative publications or preprints, and three letters of reference, all in PDF format. The research statement should explain how the applicant’s previous work and future research interests relate to inverse problems, nonlinear PDEs, numerical analysis, mathematical biology, medical imaging, or scientific machine learning. Questions regarding the research project may be directed to Professor Elena Beretta at eb147@nyu.edu.

The terms of employment are very competitive and include a comprehensive benefits package. Applications will be accepted immediately, and candidates will be considered until the position is filled. The anticipated starting date is 1 February 2027, and the initial appointment will be for one year.

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