Data-Efficient System Identification via Lipschitz Neural Networks

TL;DR

This paper introduces a data-efficient method for nonlinear system identification using Lipschitz neural networks, providing error bounds and demonstrating superior performance with limited data.

Contribution

It proposes a novel approach employing Lipschitz neural networks for system identification, including error estimation, under weak assumptions about the system.

Findings

Outperforms classic neural networks in simulation studies

More effective with less training data

Provides bounds on approximation and trajectory errors

Abstract

Extracting dynamic models from data is of enormous importance in understanding the properties of unknown systems. In this work, we employ Lipschitz neural networks, a class of neural networks with a prescribed upper bound on their Lipschitz constant, to address the problem of data-efficient nonlinear system identification. Under the (fairly weak) assumption that the unknown system is Lipschitz continuous, we propose a method to estimate the approximation error bound of the trained network and the bound on the difference between the simulated trajectories by the trained models and the true system. Empirical results show that our method outperforms classic fully connected neural networks and Lipschitz regularized networks through simulation studies on three dynamical systems, and the advantage of our method is more noticeable when less data is used for training.