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# Input-to-State Stable Neural Ordinary Differential Equations with Applications to Transient Modeling of Circuits

*Proceedings of The 4th Annual Learning for Dynamics and Control Conference*, PMLR 168:663-675, 2022.

#### Abstract

This paper proposes a class of neural ordinary differential equations parametrized by provably input-to-state stable continuous-time recurrent neural networks. The model dynamics are defined by construction to be input-to-state stable (ISS) with respect to an ISS-Lyapunov function that is learned jointly with the dynamics. We use the proposed method to learn cheap-to-simulate behavioral models for electronic circuits that can accurately reproduce the behavior of various digital and analog circuits when simulated by a commercial circuit simulator, even when interconnected with circuit components not encountered during training. We also demonstrate the feasibility of learning ISS-preserving perturbations to the dynamics for modeling degradation effects due to circuit aging.