12 papers
When is a System Discoverable from Data? Discovery Requires Chaos
Zakhar Shumaylov, Peter Zaika, Philipp Scholl +3
The deep learning revolution has spurred a rise in advances of using AI in sciences. Within physical sciences the main focus has been on discovery of dynamical systems from observa…
Muon is Not That Special: Random or Inverted Spectra Work Just as Well
Zakhar Shumaylov, Nathaël Da Costa, Peter Zaika +6
The recent empirical success of the Muon optimizer has renewed interest in non-Euclidean optimization, typically justified by similarities with second-order methods, and linear min…
Adaptive Coordinate Transforms for Neural Operators
Chaoyu Liu, Zhonghao Li, Gaohang Chen +5
Neural operators have achieved promising performance on partial differential equations (PDEs), but most existing models are built on fixed Eulerian coordinates. This mismatch betwe…
Symplectic Neural Flows for Modeling and Discovery
Priscilla Canizares, Davide Murari, Carola-Bibiane Schönlieb +2
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulation…
Diffeomorphism-Equivariant Neural Networks
Josephine Elisabeth Oettinger, Zakhar Shumaylov, Johannes Bostelmann +2
Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While…
Learning Regularization Functionals for Inverse Problems: A Comparative Study
Johannes Hertrich, Hok Shing Wong, Alexander Denker +16
In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insig…