@unpublished{55159,
  abstract     = {{We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design. We provide a rigorous convergence statement of the method. The proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus.
Moreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory. This is illustrated on the example of the discrete wave equation and Schrödinger equation.
The article constitutes an extension of our previous article  arXiv:2404.19626 for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.}},
  author       = {{Offen, Christian}},
  keywords     = {{System identification, inverse problem of variational calculus, Gaussian process, Lagrangian learning, physics informed machine learning, geometry aware learning}},
  pages        = {{28}},
  title        = {{{Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification}}},
  year         = {{2024}},
}

@inproceedings{42163,
  abstract     = {{The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE.}},
  author       = {{Offen, Christian and Ober-Blöbaum, Sina}},
  booktitle    = {{Geometric Science of Information}},
  editor       = {{Nielsen, F and Barbaresco, F}},
  keywords     = {{System identification, discrete Lagrangians, travelling waves}},
  location     = {{Saint-Malo, Palais du Grand Large, France}},
  pages        = {{569--579}},
  publisher    = {{Springer, Cham.}},
  title        = {{{Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}}},
  doi          = {{10.1007/978-3-031-38271-0_57}},
  volume       = {{14071}},
  year         = {{2023}},
}

@inproceedings{26539,
  abstract     = {{In control design most control strategies are model-based and require accurate models to be applied successfully. Due to simplifications and the model-reality-gap physics-derived models frequently exhibit deviations from real-world-systems. Likewise, purely data-driven methods often do not generalise well enough and may violate physical laws. Recently Physics-Guided Neural Networks (PGNN) and physics-inspired loss functions separately have shown promising results to conquer these drawbacks. In this contribution we extend existing methods towards the identification of non-autonomous systems and propose a combined approach PGNN-L, which uses a PGNN and a physics-inspired loss term (-L) to successfully identify the system's dynamics, while maintaining the consistency with physical laws. The proposed method is demonstrated on two real-world nonlinear systems and outperforms existing techniques regarding complexity and reliability.}},
  author       = {{Götte, Ricarda-Samantha and Timmermann, Julia}},
  booktitle    = {{2022 3rd International Conference on Artificial Intelligence, Robotics and Control (AIRC)}},
  keywords     = {{data-driven, physics-based, physics-informed, neural networks, system identification, hybrid modelling}},
  location     = {{Cairo, Egypt}},
  pages        = {{67--76}},
  title        = {{{Composed Physics- and Data-driven System Identification for Non-autonomous Systems in Control Engineering}}},
  doi          = {{10.1109/AIRC56195.2022.9836982}},
  year         = {{2022}},
}

@inproceedings{31066,
  abstract     = {{While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose a physics-guided hybrid approach for modeling non-autonomous systems under control. Starting from a traditional physics-based model, this is extended by a recurrent neural network and trained using a sophisticated multi-objective strategy yielding physically plausible models. While purely data-driven methods fail to produce satisfying results, experiments conducted on real data reveal substantial accuracy improvements by our approach compared to a physics-based model. }},
  author       = {{Schön, Oliver and Götte, Ricarda-Samantha and Timmermann, Julia}},
  booktitle    = {{14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022)}},
  keywords     = {{neural networks, physics-guided, data-driven, multi-objective optimization, system identification, machine learning, dynamical systems}},
  location     = {{Casablanca, Morocco}},
  number       = {{12}},
  pages        = {{19--24}},
  title        = {{{Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems}}},
  doi          = {{https://doi.org/10.1016/j.ifacol.2022.07.282}},
  volume       = {{55}},
  year         = {{2022}},
}