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.

  • The Advective Fisher-Rao Geometry of Deterministic Measure Transport

    A novel advective Fisher-Rao metric is introduced for optimization tasks on paths of probability measures governed by the continuity equation. This metric is shown to lead to optimal descent directions. It is then shown that this metric arises naturally from three different…

  • Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States

    Deep learning offers a powerful approach to quantum many-body problems via neural network wavefunctions, but their optimization remains a severe bottleneck. Existing optimization methods, including natural gradient descent and stochastic reconfiguration, suffer from spectral gap-dependent convergence that limits their effectiveness on systems…

  • Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks

    Published · Computer Methods in Applied Mechanics and Engineering 462, 119289 (2026). Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy — faithfully capturing complex physical behavior governed by differential equations. In…

  • Functional Neural Wavefunction Optimization

    We propose a framework for the design and analysis of optimization algorithms in variational quantum Monte Carlo, drawing on geometric insights into the corresponding function space. The framework translates infinite-dimensional optimization dynamics into tractable parameter-space algorithms through a Galerkin projection onto the…

  • Central Path Proximal Policy Optimization

    Published · Exploration in AI Today Workshop at ICML 2025. In constrained Markov decision processes, enforcing constraints during training is often thought of as decreasing the final return. Recently, it was shown that constraints can be incorporated directly into the policy geometry,…

  • Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks

    Published · Scientific Machine Learning: Emerging Topics, SEMA SIMAI Springer Series (2026). In this work, we provide a non-asymptotic convergence analysis of projected gradient descent for physics-informed neural networks for the Poisson equation. Under suitable assumptions, we show that the optimization error can be…

  • Embedding Safety into RL: A New Take on Trust Region Methods

    Published · Proceedings of the 42nd International Conference on Machine Learning, PMLR 267 (2025). Reinforcement Learning (RL) agents can solve diverse tasks but often exhibit unsafe behavior. Constrained Markov Decision Processes (CMDPs) address this by enforcing safety constraints, yet existing methods either sacrifice reward maximization or…

  • Dynamical Measure Transport and Neural PDE Solvers for Sampling

    The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using deterministic or stochastic…

  • Optimal Rates of Convergence for Entropy Regularization in Discounted Markov Decision Processes

    Published · Information and Inference 15(1), iaaf034 (2026). We study the error introduced by entropy regularization in infinite-horizon discrete discounted Markov decision processes. We show that this error decreases exponentially in the inverse regularization strength, both in a weighted KL-divergence…

  • Kronecker-Factored Approximate Curvature for Physics-Informed Neural Networks

    Published · Advances in Neural Information Processing Systems (NeurIPS 2024). Physics-informed neural networks (PINNs) are infamous for being hard to train. Recently, second-order methods based on natural gradient and Gauss-Newton methods have shown promising performance, improving the accuracy achieved by first-order methods…

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.”