KUMA: A Novel Framework with Koopman Separation and Efficient Multilevel Extraction in Time Series Forecasting

Time series forecasting plays a crucial role in a wide range of real-world applications and has become increasingly complex with the growth of multivariate dimensions and extended historical observations, leading to the prosperity of deep forecasting models. Previous models are hindered by three major challenges: high computational complexity, inefficient token utilization caused by redundancy and scarcity, and temporal distribution shifts resulting from non-stationary dynamics. Inspired by Koopman theory and the success of multilevel encoder–decoder architectures with skip connections, we design an input-dependent Koopman module to decompose time series into Koopman dynamics and residual dynamics. Building upon this formulation, we propose a U-shaped Multilevel Attention module (UMA) that integrates element-wise attention filtering and linear attention, giving rise to KUMA. The input-dependent Koopman operator mitigates the issue of operator mixture and alleviates temporal distribution shifts, while UMA achieves a favorable balance between token redundancy and token scarcity with acceptable computational efficiency. Comprehensive evaluations across 12 benchmark datasets demonstrate that KUMA achieves superior performance compared to existing excellent approaches.

Many important decisions depend on predicting the future from past data, such as estimating electricity usage, weather conditions, traffic flow, or financial trends. These prediction tasks are becoming increasingly difficult because modern datasets often contain many related signals observed over long periods of time. Current deep learning models can handle such data, but they often require high computational cost, repeatedly process similar information, and become less reliable when the data pattern changes over time. We introduce KUMA, a new model for time series forecasting. The key idea is to separate the input data into two parts: one part that captures the main evolving pattern, and another part that captures the remaining variations. After this separation, KUMA uses a U-shaped structure to analyze the data at multiple levels, so it can preserve useful information while avoiding unnecessary repetition. We evaluate KUMA on 12 standard forecasting datasets. The results show that KUMA performs better than many strong existing methods, suggesting that separating stable patterns from changing details is an effective way to improve forecasting accuracy and efficiency.