  Irregular sampling intervals and missing values in real-world time series
data present challenges for conventional methods that assume consistent
intervals and complete data. Neural Ordinary Differential Equations (Neural
ODEs) offer an alternative approach, utilizing neural networks combined with
ODE solvers to learn continuous latent representations through parameterized
vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend
Neural ODEs by incorporating a diffusion term, although this addition is not
trivial, particularly when addressing irregular intervals and missing values.
Consequently, careful design of drift and diffusion functions is crucial for
maintaining stability and enhancing performance, while incautious choices can
result in adverse properties such as the absence of strong solutions,
stochastic destabilization, or unstable Euler discretizations, significantly
affecting Neural SDEs' performance. In this study, we propose three stable
classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE.
Then, we rigorously demonstrate their robustness in maintaining excellent
performance under distribution shift, while effectively preventing overfitting.
To assess the effectiveness of our approach, we conduct extensive experiments
on four benchmark datasets for interpolation, forecasting, and classification
tasks, and analyze the robustness of our methods with 30 public datasets under
different missing rates. Our results demonstrate the efficacy of the proposed
method in handling real-world irregular time series data.
