8 citations · 29 across the 14 of their papers we have counts for
14 papers
The Advective Fisher-Rao Geometry of Deterministic Measure Transport
Benjamin Gess, Johannes Müller
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 optim…
Functional Neural Wavefunction Optimization
Victor Armegioiu, Juan Carrasquilla, Siddhartha Mishra +4
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 spac…
Central Path Proximal Policy Optimization
Nikola Milosevic, Johannes Müller, Nico Scherf
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 i…
Embedding Safety into RL: A New Take on Trust Region Methods
Nikola Milosevic, Johannes Müller, Nico Scherf
Reinforcement Learning (RL) agents can solve diverse tasks but often exhibit unsafe behavior. Constrained Markov Decision Processes (CMDPs) address this by enforcing safety constra…
Dynamical Measure Transport and Neural PDE Solvers for Sampling
Jingtong Sun, Julius Berner, Lorenz Richter +4
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…
Kronecker-Factored Approximate Curvature for Physics-Informed Neural Networks
Felix Dangel, Johannes Müller, Marius Zeinhofer
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 promisin…
Fisher-Rao Gradient Flows of Linear Programs and State-Action Natural Policy Gradients
Johannes Müller, Semih Çaycı, Guido Montúfar
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…
Position: Optimization in SciML Should Employ the Function Space Geometry
Johannes Müller, Marius Zeinhofer
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-documen…
Achieving High Accuracy with PINNs via Energy Natural Gradients
Johannes Müller, Marius Zeinhofer
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 n…
Invariance Properties of the Natural Gradient in Overparametrised Systems
Jesse van Oostrum, Johannes Müller, Nihat Ay
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 stee…
Uniform Convergence Guarantees for the Deep Ritz Method for Nonlinear Problems
Patrick Dondl, Johannes Müller, Marius Zeinhofer
We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover non-linear variational problems such as the -Laplace equation or…
Notes on Exact Boundary Values in Residual Minimisation
Johannes Müller, Marius Zeinhofer
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 co…
Error Estimates for the Deep Ritz Method with Boundary Penalty
Johannes Müller, Marius Zeinhofer
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 t…
Deep Ritz revisited
Johannes Müller, Marius Zeinhofer
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…