Research

My research interests lie at the intersection of machine learning and applied mathematics. In particular this includes the following topics:

• Geometry of Markov decision processes
• Representational capacity of neural networks
• Connections between neural networks and differential equations

Publications

• Johannes Müller, Guido Montúfar: The Geometry of Memoryless Stochastic Policy Optimization in Infinite-Horizon POMDPs, to appear at the Tenth International Conference on Learning Representations (ICLR 2022), fulltext available

Preprints

• Patrick Dondl, Johannes Müller, Marius Zeinhofer (2021): Uniform Convergence Guarantees for the Deep Ritz Method for Nonlinear Problems, fulltext available

• Johannes Müller, Marius Zeinhofer (2021): Notes on Exact Boundary Values in Residual Minimisation, fulltext available

• Johannes Müller, Marius Zeinhofer (2021): Error Estimates for the variational training of neural newtorks with boundary penalty, fulltext available

Poster presentations

• Johannes Müller joint work with Marius Zeinhofer (2021): A Posteriori Estimates and Convergence Guarantees for Neural Network Based PDE solvers, Workshop on Deep learning and partial differential equations at the Sir Isaac Newton Institute, Cambridge, UK, poster not available

• Johannes Müller joint work with Guido Montúfar (2021): The Geometry of Memoryless Stochastic Policy Optimization in Infinite-Horizon Partially Observable Markov Decision Processes, Geometry & Learning from Data, BIRS workshop hosted by Casa Matem ́atica Oaxaca (CMO), held online, poster available

• Johannes Müller joint work with Guido Montúfar (2021): The geometry of discounted stationary distributions of Markov decision processes, Workshop on Workshop on Mathematics of deep learning at the Sir Isaac Newton Institute, Cambridge, UK, poster available

• Johannes Müller joint work with Guido Montúfar (2021): The geometry of discounted stationary distributions of Markov decision processes, Conference on Mathematics of Machine Learning at the Zentrum für interdisziplinäre Forschung, Bielefeld, Germany, poster available

• Johannes Müller, Marius Zeinhofer (2020): Deep Ritz revisited, ICLR workshop on Integration of Deep Neural Models and Differential Equations, held virtually, fulltext available

• Johannes Müller (2020): On the space-time expressivity of residual networks, ICLR workshop on Integration of Deep Neural Models and Differential Equations, held virtually, fulltext available | ICLR workshop DeepDiffEq

Meetings and conferences

• November 2021: Deep learning and partial differential equations, Workshop at the Sir Isaac Newton Institute, held online
• October 2021: Geometry & Learning from Data, BIRS workshop hosted by Casa Matem ́atica Oaxaca (CMO), held online
• August 2021: Theory of deep learning, Workshop at the Sir Isaac Newton Institute, held online
• August 2021: Conference on Mathematics of Machine Learning, Center for Interdisciplinary Research (ZiF), Bielefeld University, Germany
• January 2021: Developments in the Mathematical Sciences 2020/2021, MPI MiS, Germany
• April 2020: International Conference on Learning Representations (ICLR), held virtually
• November 2019: Oberwolfach Graduate Seminar: Mathematics of Deep Learning, Banach Center, Będlewo, Poland
• October 2019 Computational and Mathematical Methods in Data Science, Zuse Instutite Berlin, Germany
• March 2019: Deep Learning Theory Kickoff Meeting, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
• September 2018: Renormalisation in QFT and SPDEs: A gentle introduction and some recent developments, Sir Isaac Newton Institute, Cambridge, UK
• February 2018: German Probability and Statistics Days, Freiburg im Breisgau, Germany
• November 2017: Systems out of equilibrium: Maths meets Physics, University of Warwick, UK
• November 2017: Graduate student meeting and annual meeting of the London Mathematical Society, London, UK

Talks

• Invited talk at the Minisyposium “Algebraic Geometry and Machine Learning” at the SIAM Conference on Mathematics of Data Science (MDS22), Town and Country Resort, San Diego, California, USA
• July 2022: 5th Multi-disciplinary Conference on Reinforcement Learning and Decision Making (RLDM), Brown University, Providence, Rhode Island, USA
• May 2022: Algebraic Statistics 2022, University of Hawai’i at Manoa, Honolulu, HI, USA
• April 2020: Deep Ritz revisited at Math Machine Learning seminar MPI MIS + UCLA

Thesis

• During my MSc studies at the University of Warwick I was supervised by Nikos Zygouras and Theo Damoulas and completed my thesis on the parameter estimation of determinantal point processes. You can find the PDF here.

• At the University of Freiburg, I studied the approximation capabilities of deep residual networks under the supervision of Philipp Harms and the thesis is available here.