Low-Dimensional Discovery of Port-Hamiltonian Systems by Combining Model Order Reduction and Machine Learning

  • Rettberg, Johannes (University of Stuttgart (ITM))
  • Kneifl, Jonas (University of Stuttgart (ITM))
  • Fehr, Jörg (University of Stuttgart (ITM))
  • Haasdonk, Bernard (University of Stuttgart (IANS))

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Complex technical systems are frequently modelled by coupled multiphysics equations and are subsequently subject to virtual multiobjective optimization. The energy-based port-Hamiltonian framework in combination with structure-preserving model order reduction is an ideal approach for modelling such systems in a hierarchical manner [1, 2]. Unfortunately, the derivation of pH systems is not trivial and often a system description to be transformed is not available at all. A possible approach to circumvent this problem is data-based system identification. Existing approaches identify pH systems in the frequency-domain [3] and time-domain [4] by optimization. In contrast we aim to discover a low-dimensional pH-system using a deep learning based framework. Deep neural networks have drawn a lot of attention through their flexibility and performance in many areas. For example, in [5] autoencoders were used to find low-dimensional system coordinates in which a system can be described with ODEs based on a library of ansatz functions. In this work, we propose a new approach to discover pH systems from data obtained from multiphysics systems to usefully complement existing classical linear pH modeling approaches and identification by optimization. In detail, we combine a (variational) autoencoder with a multi-layer perceptron (MLP) to identify the dynamics in the latent space. Consequently, the autoencoder not only reduces the dimensionality of the underlying system, but also nonlinearly transforms the system states to a low-dimensional manifold in which the system is describable in the pH formulation. The MLP is constrained to learn a dynamical system which follows the description of the pH framework based on the reduced coordinates as well as their time derivatives. A high-fidelity model of a thermoelastic disc brake serves as a demonstrative example.