  Ordinary Differential Equations (ODE) based models have become popular as
foundation models for solving many time series problems. Combining neural ODEs
with traditional RNN models has provided the best representation for irregular
time series. However, ODE-based models typically require the trajectory of
hidden states to be defined based on either the initial observed value or the
most recent observation, raising questions about their effectiveness when
dealing with longer sequences and extended time intervals. In this article, we
explore the behaviour of the ODE models in the context of time series data with
varying degrees of sparsity. We introduce SeqLink, an innovative neural
architecture designed to enhance the robustness of sequence representation.
Unlike traditional approaches that solely rely on the hidden state generated
from the last observed value, SeqLink leverages ODE latent representations
derived from multiple data samples, enabling it to generate robust data
representations regardless of sequence length or data sparsity level. The core
concept behind our model is the definition of hidden states for the unobserved
values based on the relationships between samples (links between sequences).
Through extensive experiments on partially observed synthetic and real-world
datasets, we demonstrate that SeqLink improves the modelling of intermittent
time series, consistently outperforming state-of-the-art approaches.
