21 citations · 62 across the 7 of their papers we have counts for
9 papers
Learning Lie Group Symmetry Transformations with Neural Networks
Alex Gabel, Victoria Klein, Riccardo Valperga +4
The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existin…
Rewiring Networks for Graph Neural Network Training Using Discrete Geometry
Jakub Bober, Anthea Monod, Emil Saucan +1
Information over-squashing is a phenomenon of inefficient information propagation between distant nodes on networks. It is an important problem that is known to significantly impac…
Learning reversible symplectic dynamics
Riccardo Valperga, Kevin Webster, Victoria Klein +2
Time-reversal symmetry arises naturally as a structural property in many dynamical systems of interest. While the importance of hard-wiring symmetry is increasingly recognized in m…
Bounding the first exit from the basin: Independence Times and Finite-Time Basin Stability
Paul Schultz, Frank Hellmann, Kevin N. Webster +1
We study the stability of deterministic systems given sequences of large, jump-like perturbations. Our main result is to dervie a lower bound for the probability of the system to r…
Timing of Transients: Quantifying Reaching Times and Transient Behavior in Complex Systems
Tim Kittel, Jobst Heitzig, Kevin Webster +1
When quantifying the time spent in the transient of a complex dynamical system, the fundamental problem is that for a large class of systems the actual time for reaching an attract…
Approximation of Lyapunov Functions from Noisy Data
Peter Giesl, Boumediene Hamzi, Martin Rasmussen +1
Methods have previously been developed for the approximation of Lyapunov functions using radial basis functions. However these methods assume that the evolution equations are known…
A reinterpretation of set differential equations as differential equations in a Banach space
Martin Rasmussen, Janosch Rieger, Kevin Webster
Set differential equations are usually formulated in terms of the Hukuhara differential, which implies heavy restrictions for the nature of a solution. We propose to reformulate se…
Approximation of reachable sets using optimal control and support vector machines
Martin Rasmussen, Janosch Rieger, Kevin Webster
We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorit…
Ancient Dynamics in Bianchi Models: Approach to Periodic Cycles
Stefan Liebscher, Jörg Härterich, Kevin Webster +1
We consider cosmological models of Bianchi type. In particular, we are interested in the alpha-limit dynamics near the Kasner circle of equilibria for Bianchi classes VIII and IX.…