Learning Deep Dissipative Dynamics

Yuji Okamoto, Ryosuke Kojima
8/21/2024
cs.LGeess.SYmath.DS

Official code: kojima-r/DeepDissipativeModel (3 stars, MIT, last commit 2025-06-14).

Abstract

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 is https://github.com/kojima-r/DeepDissipativeModel

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Code Implementations(1)

kojima-r/DeepDissipativeModelOfficial100%
MIT

This project is an implementation of our method in "Learning Deep Dissipative Dynamics", which can strictly guarantee the "dissipativity" of a dynamical system represented by a state-space neural ODE learned from given time series data.

30Shell, PythonAug 21, 20241 years agoMIT

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Cite this paper

@article{okamoto2024learning,
  title  = {Learning Deep Dissipative Dynamics},
  author = {Yuji Okamoto and Ryosuke Kojima},
  year   = {2024},
  eprint = {2408.11479},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2408.11479v2}
}

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