Learning Deep Dissipative Dynamics
<|reference_start|>Learning Deep Dissipative Dynamics: This study challenges strictly guaranteeing ``dissipativity'' of a dynamical system represented by neural networks learned from given time-series data. Dissipativity is a crucial indicator for dynamical systems that generalizes stability and input-output stability, known to be valid across various systems including robotics, biological systems, and molecular dynamics. By analytically proving the general solution to the nonlinear Kalman-Yakubovich-Popov (KYP) lemma, which is the necessary and sufficient condition for dissipativity, we propose a differentiable projection that transforms any dynamics represented by neural networks into dissipative ones and a learning method for the transformed dynamics. Utilizing the generality of dissipativity, our method strictly guarantee stability, input-output stability, and energy conservation of trained dynamical systems. Finally, we demonstrate the robustness of our method against out-of-domain input through applications to robotic arms and fluid dynamics. Code here https://github.com/kojima-r/DeepDissipativeModel<|reference_end|>
@article{okamoto2024learning,
    title={Learning Deep Dissipative Dynamics},
    author={Yuji Okamoto and Ryosuke Kojima},
    journal={arXiv preprint arXiv:2408.11479},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.11479},
    primaryClass={cs.LG cs.SY eess.SY math.DS}
}