The vector field of a controlled differential equation (CDE) describes the
relationship between a control path and the evolution of a solution path.
Neural CDEs (NCDEs) treat time series data as observations from a control path,
parameterise a CDE's vector field using a neural network, and use the solution
path as a continuously evolving hidden state. As their formulation makes them
robust to irregular sampling rates, NCDEs are a powerful approach for modelling
real-world data. Building on neural rough differential equations (NRDEs), we
introduce Log-NCDEs, a novel and effective method for training NCDEs. The core
component of Log-NCDEs is the Log-ODE method, a tool from the study of rough
paths for approximating a CDE's solution. On a range of multivariate time
series classification benchmarks, Log-NCDEs are shown to achieve a higher
average test set accuracy than NCDEs, NRDEs, and two state-of-the-art models,
S5 and the linear recurrent unit.

控制微分方程的向量场描述了控制路径与解路径的演变之间的关系。神经 CDE（NCDEs）将时间序列数据视为来自控制路径的观测值，使用神经网络对 CDE 的向量场进行参数化，并将解路径用作持续演化的隐藏状态。通过引入 Log-NCDEs 方法，利用粗糙路径研究中的 Log-ODE 方法来近似 CDE 的解，Log-NCDEs 在多元时间序列分类基准测试中展现出比 NCDEs、NRDEs 和两种最先进模型 S5 和线性递归单元更高的平均测试集准确率。