Physics-informed Discovery of State Variables in Second-Order and Hamiltonian Systems
<|reference_start|>Physics-informed Discovery of State Variables in Second-Order and Hamiltonian Systems: The modeling of dynamical systems is a pervasive concern for not only describing but also predicting and controlling natural phenomena and engineered systems. Current data-driven approaches often assume prior knowledge of the relevant state variables or result in overparameterized state spaces. Boyuan Chen and his co-authors proposed a neural network model that estimates the degrees of freedom and attempts to discover the state variables of a dynamical system. Despite its innovative approach, this baseline model lacks a connection to the physical principles governing the systems it analyzes, leading to unreliable state variables.   This research proposes a method that leverages the physical characteristics of second-order Hamiltonian systems to constrain the baseline model. The proposed model outperforms the baseline model in identifying a minimal set of non-redundant and interpretable state variables.<|reference_end|>
@article{chavelli2024physics-informed,
    title={Physics-informed Discovery of State Variables in Second-Order and
  Hamiltonian Systems},
    author={F'elix Chavelli, Zi-Yu Khoo, Dawen Wu, Jonathan Sze Choong Low,
  St'ephane Bressan},
    journal={arXiv preprint arXiv:2408.11691},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.11691},
    primaryClass={cs.AI}
}