6 citations · 6 across the 5 of their papers we have counts for
6 papers
Stochastic Flows with Strong Shear - Part I: Strong Completeness and Set Attractors
Dennis Chemnitz, Maximilian Engel, Michael Scheutzow
We study strong completeness and the existence of a set attractor for the stochastic flows induced by a class of two-dimensional stochastic differential equations resembling a plan…
Mixing at the Batchelor Scale for White-In-Time Flows
Robin Chemnitz, Dennis Chemnitz
We consider the mixing properties of solutions to the advection-diffusion equation of a white-in-time velocity field on the 2-dimensional torus with four forced modes. As the diffu…
A Dynamical Systems Perspective on the Analysis of Neural Networks
Dennis Chemnitz, Maximilian Engel, Christian Kuehn +1
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide var…
Characterizing Dynamical Stability of Stochastic Gradient Descent in Overparameterized Learning
Dennis Chemnitz, Maximilian Engel
For overparameterized optimization tasks, such as those found in modern machine learning, global minima are generally not unique. In order to understand generalization in these set…
Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise
Dennis Chemnitz, Maximilian Engel
We prove the positivity of Lyapunov exponents for the normal form of a Hopf bifurcation, perturbed by additive white noise, under sufficiently strong shear strength. This completes…
The conditioned Lyapunov spectrum for random dynamical systems
Matheus M. Castro, Dennis Chemnitz, Hugo Chu +3
We establish the existence of a full spectrum of Lyapunov exponents for memoryless random dynamical systems with absorption. To this end, we crucially embed the process conditioned…