Enhancing engineering time series forecasting: An uncertainty-calibrated feature modulation framework for robust multi-step ahead predictions

Abstract

Accurate multi-step forecasting of engineering time series is challenging because real-world signals often exhibit evolving operating states, non-stationarity, noisy fluctuations, and long-range dependencies. Existing forecasters typically rely on shared deterministic representations, which may overfit dominant regimes and underrepresent transitional or ambiguous patterns. To address this issue, this study proposes UFM-Mamba, an uncertainty-calibrated feature modulation framework for robust and efficient forecasting. Instead of using heavy expert subnetworks, UFM-Mamba reformulates specialization as lightweight feature-wise affine modulation over shared temporal representations. An uncertainty-aware router confines Monte Carlo dropout to the routing branch and uses stochastic routing-score moments to recalibrate logits before sparse Top- 𝑘 selection, reducing overconfident assignments under noisy and non-stationary inputs. The modulated representations are processed by stacked state-space blocks for linear-time long-range modeling. Experiments on electricity, transformer temperature, weather, and economic benchmarks demonstrate improved long-horizon accuracy with favorable parameter counts, FLOPs, and inference latency.