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math.OC2026
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…
math.OC2024★ 2 cited
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…
math.OC2024
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…