Pairwise-to-All: Relational Equilibrium for Simultaneous Forecasting

We introduce Relational Equilibrium State Estimation (RESE), a forecasting framework for multiple interacting systems that models how their relative relations evolve over time. RESE estimates these relations directly from observed trajectories, and the pairwise relations are weighted by reliability and reconciled into a consistent system-level equilibrium state. Individual forecasts are then recovered by combining this state with a separately estimated aggregate. Experiments on synthetic, exchange-rate, COVID-19, and multivariate datasets show that RESE is competitive on its own and can improve existing forecasting models. Standalone RESE achieves the lowest RMSE on the synthetic dataset, while most forecasting baselines improve when combined with RESE on exchange rates. RESE also remains stable under moderate noise, missing observations, and local shocks, and benefits from stronger cross-system dependence. Its computational cost remains low for small and moderate system sizes. Source and data are available at https://anonymous.4open.science/r/RESE-6024