SLiDE: Structured Linear Dynamics for Forecasting with Exogenous Inputs

Accurate time series forecasting with exogenous inputs is critical across domains, including energy and retail, yet modern deep learning models often overfit to correlations that do not generalize under shifts in these inputs. We propose SLiDE, a Koopman-inspired architecture for forecasting with exogenous inputs that imposes structure on latent temporal dynamics. SLiDE approximates nonlinear system evolution using a learned linear operator in a latent space, combining (i) a history encoder that reconstructs the current latent state from past targets and inputs with (ii) a shared linear rollout driven by future exogenous variables. By enforcing a common linear recurrence across encoding and prediction, SLiDE aligns how past information is encoded with how future states evolve, reducing parameterization and preventing reliance on spurious correlations in the input history. Empirically, SLiDE achieves state-of-the-art accuracy on real-world benchmarks, including electricity price forecasting and retail demand, while maintaining a computational footprint comparable to lightweight MLP architectures. SLiDE is especially effective at generalizing to shifted exogenous inputs, reducing MSE by 20% on electricity price samples with out-of-range exogenous values and MAE by 30% in a synthetic transfer setting where the same dynamical system is driven by an unseen exogenous process. Ablations confirm the importance of both the structured history encoder and the linear latent rollout, suggesting that structured latent linear dynamics provide a useful inductive bias for forecasting with exogenous inputs.