Learning Deep Dissipative Dynamics

• URL: http://arxiv.org/abs/2408.11479v1
• Date: Wed, 21 Aug 2024 09:44:43 GMT
• Title: Learning Deep Dissipative Dynamics
• Authors: Yuji Okamoto, Ryosuke Kojima,
• Abstract summary: Dissipativity is a crucial indicator for dynamical systems that generalizes stability and input-output stability. We propose a differentiable projection that transforms any dynamics represented by neural networks into dissipative ones. Our method strictly guarantees stability, input-output stability, and energy conservation of trained dynamical systems.
• Score: 5.862431328401459
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 here https://github.com/kojima-r/DeepDissipativeModel

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