Jointly Corrected Parallel Responses in Forecasting Models for Nonlinear Dynamical Systems

How should added nonlinear computation be organized for forecasting nonlinear dynamical systems? We introduce the Jointly Corrected Parallel Forecaster (JCPF), which combines explicit aggregation of learned parallel increments with response-conditioned vector correction. The Compact Shared Forecaster (CSF) provides a common encoder/head reference and remains competitive on several generic forecasting tasks. With known future driving inputs, JCPF substantially improves on CSF across three measured-system benchmarks. On Silverbox and Wiener–Hammerstein, it reduces mean MSE relative to near-budget additive branches by 18.99% and 32.54%, with every seed agreeing, and improves on a wider residual MLP. Retrained ablations support retaining both direct aggregation and response-conditioned correction. Branch-conditioned and aggregate-conditioned corrections attain comparable final accuracy but different add-only-to-full error reductions: a larger correction gain can reflect greater reliance on that path rather than a better predictor. Complete increments can also be composed as parallel macro modules, with $K$ denoting their number. From $K=1$ to $K=2$, WH improves under both fixed total budgets and fixed module widths, while F16 retains comparable accuracy. These findings support joint correction of parallel responses for nonlinear-system forecasting and distinguish final predictive value from the division of work learned by internal paths.