DIFFODE: Neural ODE with Differentiable Hidden State for Irregular Time Series Analysis

Irregular time series analysis is increasingly essential in data management due to the proliferation of complex data irregularly sampled by real-world systems. Traditional time series models, including RNN-based models and transformer variants, face significant challenges in generalizing to continuous-time paradigms, which are essential for capturing the ongoing dynamics of irregular time series. Neural Ordinary Differential Equations (NODEs) assume a continuous latent dynamic and provide an elegant framework for irregular time series analysis, yet they suffer from limitations like fragmented latent processes and the inability to fully exploit interdependencies among observations. To address these challenges, we propose a novel Differentiable hidden state enhanced neural ODE framework, termed DIFFODE, designed to effectively model irregular time series. Concretely, we introduce an attention-based differential hidden state that maps irregular observations into a continuous hidden state space, enabling the extraction of latent dynamics while preserving temporal continuity. Leveraging the theory of generalized inverses, DIFFODE innovatively derives ODEs to describe hidden state dynamics. Furthermore, we incorporate the Hoyer metric into our framework to enhance its capacity to capture subtle yet critical temporal shifts, significantly improving the accuracy of time series modeling. Extensive experiments on both synthetic and real-world datasets demonstrate the effectiveness of DIFFODE across three key tasks, including irregular time series classification, interpolation, and extrapolation.