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Overcoming the curse of dimensionality for approximating Lyapunov functions with deep neural networks under a small-gain condition

Title data

Grüne, Lars:
Overcoming the curse of dimensionality for approximating Lyapunov functions with deep neural networks under a small-gain condition.
Bayreuth , 2020 . - 6 p.

Official URL: Volltext

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Project information

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

We propose a deep neural network architecture for storing approximate Lyapunov functions of systems of ordinary differential equations. Under a small-gain condition on the system, the number of neurons needed for an approximation of a Lyapunov function with fixed accuracy grows only polynomially in the state dimension, i.e., the proposed approach is able to overcome the curse of dimensionality.

Further data

Item Type: Preprint, postprint
Keywords: deep neural network; Lyapunov function; stability; small-gain condition; curse of dimensionality
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 27 Jan 2020 14:16
Last Modified: 27 Jan 2020 14:16
URI: https://eref.uni-bayreuth.de/id/eprint/54216