Neural Lad: A Neural Latent Dynamics Framework for Times Series Modeling

Neural ordinary differential equation (Neural ODE) is an elegant yet powerful framework to learn the temporal dynamics for time series modeling. However, we observe that existing Neural ODE forecasting models suffer from two disadvantages: i) controlling the latent states only through the linear transformation over the local change of the observed signals may be inadequate; ii) lacking the ability to capture the inherent periodical property in time series forecasting tasks; To overcome the two issues, we introduce a new neural ODE framework called Neural Lad , a Neural La tent d ynamics model, in which the latent representations evolve with an ODE enhanced by the change of observed signal and seasonality-trend characterization. We incorporate the local change of input signal into the latent dynamics in an attention-based manner and design a residual architecture over basis expansion to depict the periodicity in the underlying dynamics. To accommodate the multivariate time series forecasting, we extend the Neural Lad by learning an adaptive relationship between multiple time series. Experiments demonstrate that our model can achieve better or comparable performance against existing neural ODE families and transformer variants in various datasets. Remarkably, the empirical superiority of Neural Lad is consistent across short and long-horizon forecasting for both univariate and multivariate irregularly sampled time series.