Long-term multivariate time series forecasting is crucial for real-world applications, including energy consumption, traffic flow, healthcare, and finance. Usually, some statistical approaches are used for predicting future observations based on historical temporal data. Recently, transformer-based models with patch mechanisms have demonstrated significant potential in enhancing computational efficiency. However, their inability to fully capture intra-patch temporal dependencies often limits the accuracy of predictions. To address this issue, we propose the Frequency Compensation Patch-wise transFormer (FCP-Former), which integrates a frequency compensation layer into the patching mechanism. This layer extracts frequency-domain features via Fast Fourier Transform (FFT) and incorporates them into patched data, thereby enriching patch representations and mitigating intra-patch information loss. To verify the feasibility of this model, FCP-Former was conducted on eight benchmark datasets via PyTorch 2.4.0 and trained on an NVIDIA RTX 4090 GPU (Santa Clara, CA, USA). Results demonstrate that FCP-Former 48 optimal experiment results and 17 suboptimal experiment results across all datasets. Especially on the ETTh1 dataset, it achieves an average MSE of 0.437 and an average MAE of 0.430, while on the Electricity dataset, it achieves an average MSE of 0.186 and an average MAE of 0.277. This demonstrates that FCP-Former has better forecasting accuracy and a superior ability to capture periodic and trend patterns.

Time series forecasting can be applied to various aspects of daily life, providing valuable insights to inform decision-making in areas such as stock market, electricity load, traffic flow and health-care, among others. Many previous studies have demonstrated the effectiveness of transformer-based models in long-term time series forecasting tasks, and the introduction of patch mechanisms can further enhance the predictive performance of Transformer-based models. However, most of the previous works have focused on reducing the computational resource overhead of patch-wise models, with little consideration given to the potential decrease in the model's ability to capture information from each time step within the patches. This often limits the further improvement of prediction accuracy in patch-wise models. To Address this issue, we propose a frequency compensation block, which incorporates frequency-domain data features into each patch before performing the time series forecasting task, to improve patch-wise model, called Frequency Compensation Patch-wise transFormer(FCP-Former). Experimental results demonstrate that the proposed method achieve better performance compared with the state-of-the-art methods in multivariate time series forecasting tasks.

The demand for robust safety monitoring in underground coal mines is increasing, yet traditional methods face limitations in long-term stability due to inadequate energy supply and high maintenance requirements. To address the critical challenges of high computational demand and energy constraints in this resource-limited environment, this paper proposes MineVisual, a battery-free visual sensing scheme specifically designed for underground coal mines. The core of MineVisual is an optimized lightweight deep neural network employing depthwise separable convolution modules to enhance computational efficiency and reduce energy consumption. Crucially, we introduce an energy-aware dynamic pruning network (EADP-Net) ensuring a sustained inference accuracy and energy efficiency across fluctuating power conditions. The system integrates supercapacitor buffering and voltage regulation for stable operation under wind intermittency. Experimental validation demonstrates that MineVisual achieves high accuracy (e.g., 91.5% Top-1 on mine-specific tasks under high power) while significantly enhancing the energy efficiency (reducing inference energy to 6.89 mJ under low power) and robustness under varying wind speeds. This work provides an effective technical pathway for intelligent safety monitoring in complex underground environments and conclusively proves the feasibility of battery-free deep learning inference in extreme settings like coal mines.