AugRelNet: Relation-Augmented Dynamics for Structure Discovery and Forecasting from Limited Data

Complex dynamics often arise from persistent interactions whose effects vary with the system state. We introduce AugRelNet for short- and medium-horizon trajectory forecasting from limited data. A shared learnable relation matrix explicitly routes source signals to targets, while evolving local features \(u\) and a persistent response state \(η\) transform them into nonlinear, history-dependent responses. Feeding these responses back into the dynamics separates shared relational organization from its changing realization. The learned relations reflect dense coupling in Lotka--Volterra systems and develop structured, neighbour-preferential organization in locally interacting systems. On 40...

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