Hybrid evolutionary-gradient training improves long-term time series forecasting

Long-Term Time Series Forecasting requires robust learning under nonstationarity, noisy gradients, and delayed adaptation caused by distribution shifts. Evolutionary-Guided Module Fusion with Gradient Refinement (EGMF-GR) is an architecture-agnostic training framework that combines population-based global exploration with gradient-based local refinement, rather than introducing a new forecasting architecture. During training, aligned modules between the current individual and the global best individual are monitored, and their discrepancies are evaluated using multiple complementary criteria. An interquartile range based hybrid threshold determines whether each module state is fused or retained. Fusion is performed at the module state level by merging learnable parameters and synchronizing non-learnable buffers, which reduces state inconsistency after merging and improves optimization stability. Experiments on eight public benchmarks demonstrate that EGMF-GR improves forecasting accuracy and training stability under a controlled optimization budget.