Johannes Müller

Portrait of Johannes Müller

Dr. · Postdoctoral Researcher
TU Berlin

Research profile

Johannes Müller works on the mathematical foundations of learning. His research develops geometric and optimization viewpoints on reinforcement learning, scientific machine learning, neural PDE solvers and sampling.

Research areas

Numerics · Machine Learning · Sampling

Five research keywords

information geometry · reinforcement learning · scientific machine learning · neural PDE solvers · measure transport

Contact and links

Public email

johannes.christoph.mueller@tu-berlin.de

Institution

TU Berlin

Academic links

Personal academic website · ORCID 0000-0001-8729-0466 · arXiv publications

Curriculum vitae

DateAppointment / education
2025–presentPostdoctoral researcher with Benjamin Gess, Institute of Mathematics, Technische Universität Berlin.
2023–2024Scientific employee, Junior Professorship for Mathematics of Machine Learning, RWTH Aachen University.
2020–2023PhD researcher, International Max Planck Research School Mathematics in the Sciences, Leipzig; supervisors: Guido Montúfar and Nihat Ay.
2019MSc in Mathematics, University of Freiburg.
2018MSc in Interdisciplinary Mathematics, University of Warwick.
2016BSc in Mathematics, University of Freiburg.

Publications

This catalogue contains all publications by the member, including work from before joining SAiS. Journal versions and preprints are maintained as one record per scientific work.

  • Fisher-Rao Gradient Flows of Linear Programs and State-Action Natural Policy Gradients

    Published · SIAM Journal on Optimization 35(2) (2025). Kakade’s natural policy gradient method has been studied extensively in recent years, showing linear convergence with and without regularization. We study another natural gradient method based on the Fisher information matrix of…

  • Position: Optimization in SciML Should Employ the Function Space Geometry

    Published · Proceedings of the International Conference on Machine Learning (ICML 2024). Scientific machine learning (SciML) is a relatively new field that aims to solve problems from different fields of natural sciences using machine learning tools. It is well-documented that the optimizers commonly used…

  • Achieving High Accuracy with PINNs via Energy Natural Gradient Descent

    Published · Proceedings of the International Conference on Machine Learning (ICML 2023). We propose energy natural gradient descent, a natural gradient method with respect to a Hessian-induced Riemannian metric as an optimization algorithm for physics-informed neural networks (PINNs) and the deep Ritz method. As…

  • Algebraic optimization of sequential decision problems

    Published · Journal of Symbolic Computation 121, 102241 (2024). We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of deterministic observations, also known as…

  • Geometry and convergence of natural policy gradient methods

    Published · Information Geometry (2024). We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular policy parametrizations. For a variety of NPGs and reward functions we show that…

  • Invariance Properties of the Natural Gradient in Overparametrised Systems

    Published · Information Geometry (2023). The natural gradient field is a vector field that lives on a model equipped with a distinguished Riemannian metric, e.g. the Fisher-Rao metric, and represents the direction of steepest ascent of an…

  • Solving infinite-horizon POMDPs with memoryless stochastic policies in state-action space

    Published · Reinforcement Learning and Decision Making (RLDM 2022), extended abstract. Reward optimization in fully observable Markov decision processes is equivalent to a linear program over the polytope of state-action frequencies. Taking a similar perspective in the case of partially observable Markov decision…

  • Uniform Convergence Guarantees for the Deep Ritz Method for Nonlinear Problems

    Published · Advances in Continuous and Discrete Models (2022). We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover non-linear variational problems such as the $p$-Laplace equation or the Modica-Mortola energy with essential or natural…

  • The Geometry of Memoryless Stochastic Policy Optimization in Infinite-Horizon POMDPs

    Published · International Conference on Learning Representations (ICLR 2022). We consider the problem of finding the best memoryless stochastic policy for an infinite-horizon partially observable Markov decision process (POMDP) with finite state and action spaces with respect to either the discounted…

  • Notes on Exact Boundary Values in Residual Minimisation

    Published · Mathematical and Scientific Machine Learning (MSML 2022). We analyse the difference in convergence mode using exact versus penalised boundary values for the residual minimisation of PDEs with neural network type ansatz functions, as is commonly done in the context…

Current SAiS projects

FluCo
Postdoctoral researcher in the ERC-funded team.

Talks and posters

Talks

DateTalk or event
Oct 2026The Advective Fisher–Rao Geometry of Deterministic Measure Transport, Analysis–Probability seminar, MPI MiS.
Aug 2026The Advective Fisher–Rao Geometry on Deterministic Flows of Measures, Institute for Data Science Foundations, TU Hamburg.
Jun 2026Implicit Bias in Neural Network Optimization, SIAM Conference on Optimization, Edinburgh.
Apr 2026Workshop on Structured Learning: Constraints and Geometry in Reinforcement Learning and Scientific Machine Learning, University of Freiburg.
Jun 2024Geometry and Convergence of Natural Policy Gradient Methods, Learning Theory and Statistical Optimization Seminar, University of Oxford.
Jun 2024Geometry of Optimization in Scientific Machine Learning and Reinforcement Learning, Geometric Deep Learning workshop, University of Cambridge.
Jan 2024Natural Gradients for Scientific Machine Learning, Postgraduate Seminar, RWTH Aachen University.
Apr 2023Theoretical Analysis of Boundary Penalties for Neural-Network-Based PDE Solvers, Machine Learning + X Seminar, Brown University, online.
Feb 2023Geometry of Sequential Decision Problems, Optimization and Data Science Seminar, University of California San Diego, online.
Nov 2022Geometry of Markov Decision Processes, annual meeting of Priority Programme 2298, Tutzing.
Oct 2022Geometry of Natural Policy Gradient Methods, Applied Mathematics Colloquium, UCLA.
Sep 2022Minisymposium on Algebraic Geometry and Machine Learning, SIAM Mathematics of Data Science Conference, San Diego.
Aug 2022Workshop on Algebraic Geometry, Combinatorics, and Machine Learning, MPI MiS.
May 2022Algebraic Statistics 2022, University of Hawaiʻi at Mānoa.
Apr 2020Mathematics of Machine Learning seminar, MPI MiS and UCLA.

Poster presentations

DatePoster or event
Feb 2024Geometry and Convergence of Natural Policy Gradient Methods, Symposium on Sparsity and Singular Structures, RWTH Aachen University.
Jan 2024Fisher–Rao Gradient Flows of Linear Programs and State-Action Natural Policy Gradients, Symposium on Sparsity and Singular Structures, RWTH Aachen University.
Jan 2024Geometry and Convergence of Natural Policy Gradient Methods, Mini-Workshop on Reinforcement Learning, University of Mannheim.
Jun 2022Solving Infinite-Horizon POMDPs with Memoryless Stochastic Policies in State-Action Space, RLDM, Brown University.
Apr 2022Geometry of Memoryless Stochastic Policy Optimization in Infinite-Horizon POMDPs, ICLR, online.
Nov 2021A Posteriori Estimates and Convergence Guarantees for Neural-Network-Based PDE Solvers, Isaac Newton Institute, Cambridge.
Oct 2021Geometry of Memoryless Stochastic Policy Optimization in Infinite-Horizon POMDPs, BIRS workshop, online.
Aug 2021Geometry of Discounted Stationary Distributions of Markov Decision Processes, Isaac Newton Institute, Cambridge.
Aug 2021Geometry of Discounted Stationary Distributions of Markov Decision Processes, Mathematics of Machine Learning Conference, Bielefeld.
Apr 2020Deep Ritz Revisited; Space–Time Expressivity of Residual Networks, ICLR DeepDiffEq workshop, online.

Teaching

TermCourse or supervision
Summer 2025Teaching assistant, Mathematics for Physicists IV, TU Berlin.
Summer 2024Seminar: Approximation Properties of Neural Networks, RWTH Aachen University.
Winter 2024Teaching assistant, Mathematical Foundations of Deep Learning, RWTH Aachen University.
2024Master’s thesis supervision: Reza Zolnouri, “The Role of Geometry in Policy Mirror Descent.”
2024Master’s thesis supervision: Jonas Nießen, “Optimization Guarantees for Physics-Informed Neural Networks.”
2022Research-intern supervision: Friedrich Wicke, “State-Action Geometry of Multi-Agent Problems.”