In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of recently introduced Recurrent Equilibrium Networks (RENs). We show how to endow our proposed NodeRENs with contractivity and dissipativity -- crucial properties for robust learning and control. Most importantly, as for RENs, we derive parametrizations of contractive and dissipative NodeRENs which are unconstrained, hence enabling their learning for a large number of parameters. We validate the properties of NodeRENs, including the possibility of handling irregularly sampled data, in a case study in nonlinear system identification.

翻译：本文介绍并研究了一类连续时间深度神经网络（DNNs）。所提出的架构融合了神经常微分方程（Neural ODEs）与近期提出的递归均衡网络（RENs）的模型结构。我们展示了如何赋予所提出的NodeRENs收缩性和耗散性——这些性质对于鲁棒学习与控制至关重要。最重要的是，类似于RENs，我们推导了收缩型与耗散型NodeRENs的无约束参数化形式，从而使得其能够在大参数规模下进行学习。我们通过非线性系统辨识的案例研究，验证了NodeRENs的特性，包括处理不规则采样数据的可行性。