Irregularly measured time series are common in many of the applied settings in which time series modelling is a key statistical tool, including medicine. This provides challenges in model choice, often necessitating imputation or similar strategies. Continuous time autoregressive recurrent neural networks (CTRNNs) are a deep learning model that account for irregular observations through incorporating continuous evolution of the hidden states between observations. This is achieved using a neural ordinary differential equation (ODE) or neural flow layer. In this manuscript, we give an overview of these models, including the varying architectures that have been proposed to account for issues such as ongoing medical interventions. Further, we demonstrate the application of these models to probabilistic forecasting of blood glucose in a critical care setting using electronic medical record and simulated data. The experiments confirm that addition of a neural ODE or neural flow layer generally improves the performance of autoregressive recurrent neural networks in the irregular measurement setting. However, several CTRNN architecture are outperformed by an autoregressive gradient boosted tree model (Catboost), with only a long short-term memory (LSTM) and neural ODE based architecture (ODE-LSTM) achieving comparable performance on probabilistic forecasting metrics such as the continuous ranked probability score (ODE-LSTM: 0.118$\pm$0.001; Catboost: 0.118$\pm$0.001), ignorance score (0.152$\pm$0.008; 0.149$\pm$0.002) and interval score (175$\pm$1; 176$\pm$1).

翻译：不规则采样的时间序列常见于许多将时间序列建模作为关键统计工具的应用场景中，包括医学领域。这给模型选择带来了挑战，通常需要插值或类似策略。连续时间自回归循环神经网络（CTRNN）是一种深度学习模型，通过引入观测之间隐藏状态的连续演化来处理不规则观测。这是利用神经常微分方程（ODE）或神经流层实现的。在本文中，我们概述了这些模型，包括为解决持续性医疗干预等问题而提出的不同架构。此外，我们展示了将这些模型应用于电子病历和模拟数据中重症监护环境下血糖的概率预测。实验证实，在不规则测量场景中，添加神经ODE或神经流层通常能提升自回归循环神经网络的性能。然而，几种CTRNN架构表现不如自回归梯度提升树模型（Catboost），只有基于长短期记忆（LSTM）和神经ODE的架构（ODE-LSTM）在概率预测指标上取得了可比性能，例如连续排序概率评分（ODE-LSTM: 0.118±0.001；Catboost: 0.118±0.001）、无知度评分（0.152±0.008；0.149±0.002）和区间评分（175±1；176±1）。