Journal
IFAC PAPERSONLINE
Volume 54, Issue 19, Pages 210-216Publisher
ELSEVIER
DOI: 10.1016/j.ifacol.2021.11.080
Keywords
dynamical systems; Hamiltonian systems; deep learning; physics-informed neural network; system symmetries
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Funding
- Deutsche Forschungsgemeinschaft (DFG) [281474342]
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This paper introduces Hamiltonian Neural Networks and their symmetric extensions for learning dynamical systems with Hamiltonian structure. By discussing discrete and continuous symmetries, an improved learning algorithm is proposed to enhance the conservation properties of example systems.
Machine learning techniques, especially neural networks, rapidly gain importance in a variety of applications, headed by image analysis and text or speech recognition. Comparably fewer works address the learning of nonlinear dynamical systems - probably because of the challenging task of learning physical laws. To bridge this gap, Hamiltonian Neural Networks have been introduced, which are especially tailored to learning dynamical systems which preserve the Hamiltonian structure. In this contribution, we build on this approach by introducing symmetry-preserving extensions of the Hamiltonian neural networks' architecture. We discuss discrete symmetry, i.e. periodicity, as well as continuous symmetries in terms of translational or rotational invariances. The proposed learning algorithm provides neural network representations of example systems with improved conservation properties. Copyright (C) 2021 The Authors.
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