My research interests are where numerical algorithms enter machine learning models. I am currently working on probabilistic numerics and the simulation of ordinary and partial differential equations. Most of the methods I come up with in my papers end up as publically available code.

I am always keen to discuss questions that align with my research interests. If you would like to chat, please feel invited to get in touch!

Preprints

• Emilia Magnani, Nicholas Krämer, Runa Eschenhagen, Lorenzo Rosasco, Philipp Hennig. Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs arXiv: 2208.01565, 2022 (paper).
• Jonathan Wenger, Nicholas Krämer, Marvin Pförtner, Jonathan Schmidt, Nathanael Bosch, Nina Effenberger, Johannes Zenn, Alexandra Gessner, Toni Karvonen, Francois-Xavier Briol, Maren Mahsereci, Philipp Hennig. ProbNum: Probabilistic numerics in Python arXiv: 2112.02100, 2021 (paper, code).
• Nicholas Krämer, Philipp Hennig. Stable implementation of probabilistic ODE solvers. arXiv:2012.10106, 2020 (paper, code).

Publications

• Jonathan Österle, Nicholas Krämer, Philipp Hennig, Philipp Berens. Probabilistic solvers enable a straight-forward exploration of numerical uncertainty in neuroscience models. Journal of Computational Neuroscience, 2022 (paper, code ).
• Nicholas Krämer, Nathanael Bosch, Jonathan Schmidt, Philipp Hennig. Probabilistic ODE solutions in millions of dimensions. ICML, 2022 (paper, code).
• Nicholas Krämer, Jonathan Schmidt, Philipp Hennig. Probabilistic numerical method of lines for time-dependent partial differential equations. AISTATS, 2022 (paper, code).
• Nicholas Krämer, Philipp Hennig. Linear-time probabilistic solutions of boundary value problems. NeurIPS, 2021 (paper, code).
• Jonathan Schmidt, Nicholas Krämer, Philipp Hennig. A probabilistic state space model for joint inference from differential equations and data. NeurIPS, 2021 (paper, code).
• Hans Kersting, Nicholas Krämer, Martin Schiegg, Christian Daniel, Michael Tiemann, Philipp Hennig. Differentiable likelihoods for fast inversion of 'likelihood-free' dynamical systems. ICML, 2020 (paper, code ).

Dissertations

• Krämer, N. (2019). Gaussian Processes and Uncertainty Quantification. Masterarbeit, Institut für Numerische Simulation, Universität Bonn. (code).
• Krämer, N. (2016). Numerisches Lösen von Eigenwertproblemen [Numerical Solution of Eigenvalue Problems]. Bachelorarbeit, Universität Mannheim.

Code

• tornadox: Probabilistic solvers for high-dimensional ODEs (link).
• probfindiff: Probabilistic numerical finite differences (link).
• TUEplots: Matplotlib configurations for scientific papers (link).
• ProbNum-Evaluation: Evaluate the efficiency of probabilistic numerical algorithms (link).
• ProbNum: Probabilistic numerics in Python (link).