A Lyapunov Condition for Training ODEs
Control theory is widely used in the study of differential equations to obtain desired behavior from underlying dynamics. We propose a novel method for training ordinary differential equations by using a control-theoretic Lyapunov Condition for stability. This method avoids rolling-out ODE's during training and thus saves the cost of back propagating through a solver or using the adjoint method. We validate our approach experimentally and verify that it has similar performance to ODEs trained by backpropagating through rollouts.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
LyaNet: A Lyapunov Framework for Training Neural ODEs
We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages t…
Adversarial RobustnessLyapunov Characterization for ISS of Impulsive Switched Systems
In this study, we investigate the ISS of impulsive switched systems that have modes with both stable and unstable flows. We assume that the switching signal satisfies mode-dependent average dwell and leave time condition…
FxTS-Net: Fixed-Time Stable Learning Framework for Neural ODEs
Neural Ordinary Differential Equations (Neural ODEs), as a novel category of modeling big data methods, cleverly link traditional neural networks and dynamical systems. However, it is challenging to ensure the dynamics s…
On the robust existence of piecewise quadratic Lyapunov functions for hybrid models of gene regulatory networks
In this work we addressed the problem of stability analysis for an uncertain piecewise affine model of a genetic regulatory network. In particular we considered polytopic parameter uncertainties on the proteins productio…
Structural polyhedral stability of a biochemical network is equivalent to finiteness of the associated generalised Petri net
We consider biochemical systems associated with a generalised class of Petri nets with possibly negative token numbers. We show that the existence of a structural polyhedral Lyapunov function for the biochemical system i…