Symmetry-Aware Simulation and Modeling of Noise-Robust Electric Load Forecasting Using Hybrid MMPF-NARX and GA/PSO

Reliable electric load forecasting is an important engineering problem for power-system planning, grid stability, and mission-critical energy management. This paper presents a symmetry-aware simulation and modeling framework for medium-range electric load forecasting under noisy and uncertain operating conditions. The proposed approach combines a Multi-Model Partitioning Filter (MMPF) with Nonlinear Autoregressive Exogenous (NARX) submodels, while two adaptive optimization strategies, genetic algorithm-based resource allocation (GARA) and Particle Swarm Optimization (PSO), are used to optimize the contribution weights of the parallel predictors. The modeling process uses real commercial power-system data and evaluates the forecasting framework over April–September 2025. To simulate realistic engineering disturbances, correlated symmetric Gaussian noise is injected into the testing phase under moderate and heavy noise scenarios. The cyclic symmetry of temporal variables, such as hours and months, is preserved through unit-circle encoding, while the symmetry and asymmetry of residual error symmetric distributions are examined through scatter plot analysis. As for the context of forecasting residuals as diagnostic signals, it is important to transfer symmetry properties that can be used to evaluate the behavior of optimized predictors, along with the cyclic encoding of inputs. This means that by implementing residual-symmetry analysis, the conclusion that GARA and PSO produce concentrated, balanced, and biased errors under moderate noise and heavily correlated noise conditions can be achieved. Finally, our results show that both GARA and PSO improve the robustness of the hybrid MMPF-NARX model, but PSO consistently achieves lower MAPE values, smoother convergence, and lower computational burden. The optimal configuration is obtained with nine NARX submodels, beyond which additional model complexity offers no meaningful performance gain. Overall, the study shows that symmetry-aware modeling, adaptive optimization, and noise-based simulation can support more reliable forecasting in modern power-system engineering applications.