System identification through Lipschitz regularized deep neural networks

[摘要] In this paper we use neural networks to learn governing equations from data. Specifically we reconstruct the right-hand side of a system of ODEs (x)over dot(t) = f(t, x(t)) directly from observed uniformly time-sampled data using a neural network. In contrast with other neural network-based approaches to this problem, we add a Lipschitz regularization term to our loss function. In the synthetic examples we observed empirically that this regularization results in a smoother approximating function and better generalization properties when compared with non-regularized models, both on trajectory and non-trajectory data, especially in presence of noise. In contrast with sparse regression approaches, since neural networks are universal approximators, we do not need any prior knowledge on the ODE system. Since the model is applied component wise, it can handle systems of any dimension, making it usable for real-world data. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-01

[关键词] Machine learning;Deep learning;System identification;Ordinary differential equations;Generalization gap;Regularized network