D${}^2$ARIF: Delay and Density Aware Representation for Irregular Multivariate Time Series Forecasting

In irregular multivariate time series (IMTS), measurements are recorded asynchronously across variables, creating two challenges for forecasting. First, existing methods usually perform information interaction among temporally aligned or nearby observations, which makes cross-variable delayed interactions with long time intervals difficult to model directly. Second, existing methods usually treat irregular sampling as a difficulty in modeling, and lack the utilization of observation density information brought by irregular sampling. To address the above challenges, we propose Delay- and Density-Aware Representation Learning for Irregular Multivariate Time Series Forecasting (D${}^2$ARIF) with two corresponding components: the Delay-Aware Module and Density-Aware Module. The Delay-Aware Module maintains a separate state for each source variable, decays these states according to the elapsed interval between active patches, and uses each target variable's query to weight information from previously observed sources. The Density-Aware Module estimates a continuous observation-time density for each variable and temporal patch using locally adaptive bandwidths, then encodes the resulting distributions for forecasting. Compared with state-of-the-art methods, D${}^2$ARIF achieves improvements of up to 6.8% across four benchmarks.