Prof. Dr. Daniel Peterseim
| Phone: | +49 821 598-2194 |
| Email: | daniel.peterseim@uni-auni-a.de () |
| Room: | 2302 ( I ) |
| Open hours: | by appointment |
| Address: | Universitätsstraße 12, 86159 Augsburg |
About
Daniel Peterseim is Professor and Chair of Computational Mathematics at the University of Augsburg and founding director of the Centre for Advanced Analytics and Predictive Sciences (CAAPS).
He develops mathematical foundations and efficient algorithms for scientific computing on classical and quantum computers. His research combines the design of new methods with rigorous analysis of their accuracy, convergence and computational complexity. His work addresses problems where multiple scales, nonlinearity, randomness or high dimensionality make direct computation prohibitively expensive.
His research has been supported, among other sources, by the ERC Consolidator Grant Computational Random Multiscale Problems and through the DFG Priority Programmes Reliable Simulation Techniques in Solid Mechanics and Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials.
Research
Quantum Numerical Analysis
We develop the mathematical and algorithmic foundations of scientific computing on quantum computers. We combine numerical approximation and preconditioning with the design of quantum algorithms and their implementation and experimental evaluation on quantum hardware. We analyse accuracy, resource requirements and the impact of hardware constraints, and identify the conditions under which quantum methods offer advantages over classical algorithms.
With Unitaria, we develop an open-source library for constructing and verifying quantum linear algebra algorithms and analysing their resource requirements.
Selected publications:
- Quantum realization of the finite element method. Mathematics of Computation (2025; with M. Deiml)
- Nonlinear quantum computation by amplified encodings. arXiv:2411.16435 (2024; with M. Deiml)
- Quantum sampling and moment estimation for transformed Gaussian random fields. to appear in SIAM/ASA Journal on Uncertainty Quantification (2026; with M. Deiml)
Nonlinear Eigenvalue Problems and Riemannian Optimization
We develop and analyse efficient methods for nonlinear eigenvalue problems and constrained energy minimization. We use the energy of the model and the geometry of the constraints to construct problem-adapted metrics and iterative methods. Our approach combines Riemannian optimization, numerical methods for partial differential equations and convergence theory. Important applications arise in quantum physics and chemistry, including Gross–Pitaevskii and Kohn–Sham models.
Selected publications:
- Sobolev gradient flow for the Gross–Pitaevskii eigenvalue problem: global convergence and computational efficiency. SIAM Journal on Numerical Analysis (2020; with P. Henning)
- Energy-adaptive Riemannian Optimization on the Stiefel manifold. ESAIM: Mathematical Modelling and Numerical Analysis (2022; with R. Altmann and T. Stykel)
- Metric-Driven Numerical Methods. Lecture Notes in Computational Science and Engineering (2026; with P. Henning and L. Huynh)
Multiscale Methods, Randomness and Numerical Homogenization
We study how fine-scale structure and randomness shape the solutions of partial differential equations and what information is needed to compute them reliably. This informs the design of homogenization and multiscale methods that do not require periodicity or a clear separation of scales. Localization serves both as a principle for efficient approximation, as in the localized orthogonal decomposition (LOD), and as a subject of mathematical analysis. This connects the development of numerical methods with questions of wave propagation and Anderson localization in disordered media.
Selected publications:
- Localization of elliptic multiscale problems. Mathematics of Computation (2014; with A. Målqvist)
- Eliminating the pollution effect in Helmholtz problems by local subscale correction. Mathematics of Computation (2017)
- Quantitative Anderson localization of Schrödinger eigenstates under disorder potentials. Mathematical Models and Methods in Applied Sciences (2020; with R. Altmann and P. Henning)
Nonlinear Elasticity, Relaxation and Computational Mechanics
We develop numerical methods for nonlinear material models that capture the interplay between microstructure and macroscopic behaviour. Our central question is how to compute deformation, damage and material instabilities reliably in the presence of nonconvex energies. Variational principles, relaxation and convexification connect the mathematical analysis of these models with their numerical treatment and the description of multiscale phenomena.
Selected publications:
- Hierarchical rank-one sequence convexification for the relaxation of variational problems with microstructures. Computer Methods in Applied Mechanics and Engineering (2024; with D. Balzani, M. Köhler, M.A. Peter and T. Neumeier)
- Computational polyconvexification of isotropic functions. Multiscale Modeling & Simulation (2024; with M.A. Peter, T. Neumeier and D. Wiedemann)
- Multidimensional rank-one convexification of incremental damage models at finite strains. Computational Mechanics (2024; with D. Balzani, M. Köhler, T. Neumeier and M. A. Peter)
Scientific Machine Learning and Data-Driven Modelling
We combine numerical analysis with machine learning to accelerate expensive computations and develop models from limited data. We develop and analyse data-driven approximation methods and their interplay with numerical methods. Our focus is on the relationship between available information, achievable accuracy and computational cost.
Selected publications:
- Neural network approximation of coarse-scale surrogates in numerical homogenization. Multiscale Modeling & Simulation (2023; with F. Kröpfl and R. Maier)
- Neural network acceleration of iterative methods for nonlinear Schrödinger eigenvalue problems. Journal of Computational and Applied Mathematics (2026; with J.-F. Pietschmann, J. Püschel and K. Rueß)
- Reconstructing microstructures from statistical descriptors using neural cellular automata. Integrating Materials and Manufacturing Innovation (2024; with K. Kalina, M. Kästner, P. Seibert, A. Raßloff, P. Reck and Y. Zhang)
Curriculum Vitae
- Since 2021: Founding Director, Centre for Advanced Analytics and Predictive Sciences, University of Augsburg
- Since 2017: Chair of Computational Mathematics, University of Augsburg
- 2020–2025: ERC Consolidator Grant Computational Random Multiscale Problems
- 2016: Habilitation in Mathematics, Humboldt-Universität zu Berlin
- 2013–2017: Professor of Numerical Simulation, University of Bonn
- 2009–2013: Head of Junior Research Group, DFG Research Center MATHEON and Humboldt-Universität zu Berlin
- 2009: Research Associate, Humboldt-Universität zu Berlin
- 2007: Doctorate in Mathematics, University of Zurich
- 2004–2008: Research Associate, University of Zurich
- 2004: Diploma in Mathematics, Technische Universität Ilmenau
Associate Editor of SIAM Journal on Numerical Analysis, Mathematics of Computation, Multiscale Modeling & Simulation and IMA Journal of Numerical Analysis.
Co-founder and co-head of the GAMM Activity Group Numerical Analysis (2017–2025).
Plenary lectures at ENUMATH 2023, the 29th Biennial Numerical Analysis Conference (Glasgow 2023) and the 25th International Conference on Domain Decomposition Methods (2018), among others.
Publications
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A. Målqvist and D. Peterseim. Numerical homogenization by localized orthogonal decomposition. SIAM Spotlights 5, ISBN: 978-1-611976-44-1, 2020. [ SIAM ] |