Professor at
Heidelberg University

PhD and Postdoc Positions in "Scientific Machine Learning"

We are seeking highly motivated PhD candidates and Postdoctoral researchers in the areas of scientific machine learning and applied mathematics.

Our research investigates the mathematical foundations of Scientific Machine Learning (SciML), with a focus on rigorous analysis, probability theory, and modern deep learning methodologies. We aim to develop efficient, provably convergent algorithms and architectures for high-dimensional problems in science and engineering. This involves integrating the mathematical analysis and numerics of PDEs with modern learning-based techniques, and combining theoretical investigation (approximation rates, statistical limits) with the development of practical, domain-aware algorithms.

Research Focus

Successful candidates will contribute to our research in areas such as:

  • Operator Learning: Developing and analyzing neural operator architectures for solving PDEs and approximating infinite-dimensional mappings or dynamical systems.
  • Inverse Problems & Uncertainty Quantification: Bayesian inference, posterior consistency, and generative modeling (measure transport, diffusion models, flow matching) for parameter estimation in high dimensions.
  • Structure-Preserving ML: Integrating physical constraints (conservation laws, symmetries) into learning frameworks.
  • Optimization & Sampling: Analysis of particle-based methods (SVGD, consensus-based optimization) and their mean-field limits.

We also welcome applicants with strong theoretical backgrounds who wish to propose their own research directions within the scope of the group’s interests.

Your Profile

  • PhD Candidates: Excellent Master’s degree in Mathematics, Physics, or Computer Science. Strong background in analysis, probability, optimization, or numerical mathematics. Interest in interdisciplinary research at the interface of math and AI.
  • Postdocs: PhD in Mathematics or a related field with a strong publication record in SciML, numerical analysis, optimization, or statistical learning theory.
  • Programming proficiency is desirable (Python/PyTorch/JAX).

We Offer

  • Duration:
    • PhD: 75% initially for 3 years
    • Postdoc: 100% for 2 years
  • Teaching: Moderate teaching duties (4 SWS), such as supervising tutorials and seminars
  • Access to high-performance computing resources

At Heidelberg University, we are committed to fostering a diverse and inclusive community. We encourage applications from women and individuals from underrepresented groups and strive to create a supportive and welcoming environment for all members of our community.

Application Process

Please send your application as a single PDF file to Prof. Jakob Zech (jakob.zech@uni-heidelberg.de).

Important: Please use the subject line “Application [PhD/Postdoc] - [Your Name]”.

The (soft) deadline is December 31, 2025. All applications received by this date will be given full consideration. Afterwards, applications will be reviewed on a rolling basis until the positions are filled. The application should include:

  • A motivation letter outlining your research interests
  • Your CV
  • Contact details of two referees
  • For PhD candidates: Transcripts of records (Bachelor and Master)
  • For Postdoc candidates: A brief research statement and copies of 1-2 representative publications