Delayed deep learning for continuous-time dynamical systems
OPEN ACCESS
Author / Producer
Date
2021-01-29
Publication Type
Master Thesis
ETH Bibliography
yes
Citations
Altmetric
OPEN ACCESS
Data
Rights / License
Abstract
Bridging the gap between deep learning and dynamical systems, neural
ODEs are a promising approach to model continuous-time dynamical
systems. Motivated by state augmentation in discrete-time models, we
propose to extend the neural ODE framework to neural delay di erential
equations in order to naturally capture non-Markovian e ects such
as time delays or hysteresis, which are often encountered in real world
applications. We demonstrate the superior performance of neural delay
di erential equations on the task of modelling a partially observed
oscillator in comparison with augmented neural ODEs. Moreover, we
showcase robustness to observation noise, generalization over time and
initial conditions, and the expressive power on more complex dynamical
systems. Furthermore, a result on universal approximation is provided
and the connection to delay embeddings is discussed. In an exploratory
part, we discuss deep learning approaches for stability analysis
of time delay systems and propose to jointly learn a dynamics model and
a Lyapunov-Razumikhin function via discretization of the Razumikhin
condition. The applicability of this approach is demonstrated for the
task of stabilizing an inverted pendulum with delayed feedback control.
Permanent link
Publication status
published
External links
Editor
Contributors
Examiner : Dörfler, Florian
Examiner : Krause, A.
Examiner : Wenk, Philippe
Book title
Journal / series
Volume
Pages / Article No.
Publisher
ETH Zurich
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Organisational unit
09478 - Dörfler, Florian / Dörfler, Florian