## 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.

## Related URLs

## Project information

Project financing: |
Deutsche Forschungsgemeinschaft |
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## 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.