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Grüne, Lars:
Computing Lyapunov functions using deep neural networks.
In: Journal of Computational Dynamics.
(27 November 2020)
.
 22 pages.
ISSN 21582491
DOI: https://doi.org/10.3934/jcd.2021006
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We propose a deep neural network architecture and a training algorithm for computing approximate Lyapunov functions of systems of nonlinear ordinary differential equations. Under the assumption that the system admits a compositional Lyapunov function, we prove that 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. We show that nonlinear systems satisfying a smallgain condition admit compositional Lyapunov functions. Numerical examples in up to ten space dimensions illustrate the performance of the training scheme.
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Computing Lyapunov functions using deep neural networks. (deposited 20 May 2020 08:51)
 Computing Lyapunov functions using deep neural networks. (deposited 07 Jan 2021 13:50) [Currently Displayed]