Publications and highlights associated with Johannes Müller.
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…
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…
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…
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…
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…
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…
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…
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…
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…
Published · Mathematical and Scientific Machine Learning (MSML 2022). We estimate the error of the Deep Ritz Method for linear elliptic equations. For Dirichlet boundary conditions, we estimate the error when the boundary values are imposed through the boundary penalty method…
Published · Workshop on Integration of Deep Neural Models and Differential Equations at ICLR 2020. Recently, progress has been made in the application of neural networks to the numerical analysis of partial differential equations (PDEs). In the latter the variational formulation of the Poisson problem is used…
Published · Workshop on Integration of Deep Neural Models and Differential Equations at ICLR 2020. Residual networks (ResNets) are a deep learning architecture that substantially improved the state of the art performance in certain supervised learning tasks. Since then, they have received continuously growing attention. ResNets have…
