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-dimensional Lorenz--96, AugRelNet uses about 4,000 training states, roughly an order of magnitude fewer than representative prior Lorenz--96 forecasting studies. Across five seeds, every true interaction ranks above every nonedge, with a mean absolute-weight contrast of approximately \(146{:}1\). Under the same data budget, eight-step RMSE is about \(23\)--\(59\times\) lower than MNO, DySLIM, DeepSkip, and AL-RNN, \(14\)--\(55\times\) lower than NRI and dense GraphODE, and 37\% lower than PySINDy with a matched quadratic dictionary. The same relational representation extends to grids by treating sites as variables and sharing relations across spatial offsets: in discrete (Game of Life), continuous (FitzHugh--Nagumo), and stochastic (Ising) dynamics, learned weights rank physical neighbours above other candidate offsets while supporting multi-step prediction. AugRelNet learns these relations through prediction losses and regularization, without structural labels or system-specific physical losses.

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