Deep learning forecasting model and visual explanation for large-scale time-series data

Abstract

Large-scale time-series forecasting underpins decision-making in energy systems, traffic operations, industrial monitoring and financial analytics. Recent recurrent, convolutional and Transformer-based models have improved predictive accuracy, yet three limitations remain: inefficient modelling of long input windows, incomplete representation of multi-scale temporal patterns and cross-variable dependencies, and limited interpretability in operational settings. Here we propose MSPI-Former, an interpretable multi-scale patch-inverted Transformer for large-scale multivariate forecasting. The model combines reversible normalization and seasonal-trend decomposition to reduce distribution shift, overlapping temporal patches to encode local dynamics, and inverted cross-variable attention to learn dependencies across high-dimensional variables. A multi-scale temporal convolution branch further captures short-term fluctuations, daily periodicity and long-term trend residuals. For interpretation, we introduce a temporal-variable attribution module that integrates attention rollout, gradient attribution and perturbation consistency to produce horizon-aware heat maps. On ETTm1, Electricity, Traffic and Weather, MSPI-Former achieved the best average performance among eight baselines under a unified evaluation protocol. Under the 96-step setting, it obtained average MSE/MAE values of 0.293/0.331, reducing MSE by 8.4% compared with PatchTST and by 11.2% compared with iTransformer. Ablation analysis further confirmed that patch encoding, inverted attention, multi-scale convolution and attribution-guided regularization contributed complementary benefits. These results indicate that MSPI-Former can improve long-horizon forecasting while exposing physically meaningful variables and lag intervals.