Learning Dissipative Neural Dynamical Systems

TL;DR

This paper proposes a two-stage method to learn neural dynamical systems that approximate unknown dissipative nonlinear systems while explicitly preserving their dissipativity property.

Contribution

It introduces a novel approach to enforce dissipativity in neural dynamical models through weight and bias perturbations after initial unconstrained learning.

Findings

Successfully guarantees dissipativity in learned models

Achieves close approximation to original system dynamics

Provides a practical method for constrained neural system identification

Abstract

Consider an unknown nonlinear dynamical system that is known to be dissipative. The objective of this paper is to learn a neural dynamical model that approximates this system, while preserving the dissipativity property in the model. In general, imposing dissipativity constraints during neural network training is a hard problem for which no known techniques exist. In this work, we address the problem of learning a dissipative neural dynamical system model in two stages. First, we learn an unconstrained neural dynamical model that closely approximates the system dynamics. Next, we derive sufficient conditions to perturb the weights of the neural dynamical model to ensure dissipativity, followed by perturbation of the biases to retain the fit of the model to the trajectories of the nonlinear system. We show that these two perturbation problems can be solved independently to obtain a neural dynamical model that is guaranteed to be dissipative while closely approximating the nonlinear system.