MMformer with adaptive attention: Advancing multivariate time series forecasting for environmental applications

Multivariate time series forecasting is critical in numerous scientific and engineering fields. Current deep learning models, however, face fundamental challenges in this domain. They struggle to handle dynamically changing data distributions, achieve model self-adaptation, and quantify prediction uncertainty. These limitations are particularly severe in fields like environmental science, where high-reliability decisions are essential. To address these limitations, we introduce MMformer, an innovative common adaptive multivariate time series forecasting model. MMformer’s core lies in the synergistic integration of three key components: an encoder-only optimized architecture for capturing temporal dependencies; the Adaptive Transferable Multi-Head Attention mechanism, using meta-learning to enhance model adaptability and generalization; and Monte Carlo Dropout for improved robustness and crucial uncertainty quantification. We rigorously evaluate MMformer on real-world environmental datasets (e.g., 1277 days of air quality data across 331 Chinese cities, 1826 days of temperature and rainfall data from 909 stations) and general MTS benchmarks (PEMS). Results demonstrate that MMformer achieves superior performance in accuracy, adaptability, and uncertainty quantification than iTransformer, PatchTST, TimesNet, and Transformer. Specifically, on air quality data, MMformer reduced MSE, MAE, and MAPE by up to 70.195 %, 37.240 %, and 36.542 %, respectively, compared to iTransformer; up to 69.641 %, 37.121 %, and 35.632 % compared to TimesNet; up to 71.578 %, 40.288 %, and 39.383 % compared to PatchTST; and up to 68.182 %, 36.641 %, and 35.343 % compared to Transformer. On climate data, the performance improvements mirror those on the air quality dataset. MMformer also achieved optimal results on PEMS03, PEMS04, and PEMS08, demonstrating strong generalization. Our approach offers key theoretical insights for researchers and significant practical value for policymakers. It marks a significant advance in forecasting and managing dynamic environmental challenges. This capability enables precise interventions to protect public health and promote environmental sustainability.