AI 中文总结
针对非平稳时间序列，提出基于演化谱理论的TimeES框架，通过可参数化演化谱和复杂度降低，实现高效且可解释的概率与确定性预测，并达到最优性能。
AI 中文摘要
真实世界的时间序列本质上是非平稳的，其趋势、周期模式和不确定性随时间演化。虽然傅里叶域为时间序列建模提供了自然的视角，但当前的深度学习方法并未显式建模傅里叶谱中的演化和随机性，这限制了它们在非平稳时间序列中准确预测期望轨迹及其不确定性的能力。受演化谱（Evolutionary Spectra, ES）理论的启发，我们提出了TimeES，一个通过演化谱理论实现概率与确定性预测的通用框架。具体而言，我们推导了一种可参数化的演化谱公式，将非平稳随机过程建模重新表述为学习由随机变量调制的演化表示。此外，我们利用厄米对称性和谱能量稀疏性进行频率选择，将估计谱的复杂度从O(NM)降低到O(NK)，其中K << M/2。基于简单的线性主干网络，我们提出的TimeES在确定性和概率预测任务中均取得了持续的最优性能，同时具有高效率和可解释性。代码可在以下网址获取：this https URL。
英文摘要
Real-world time series are inherently non-stationary, with trends, periodic patterns, and uncertainty evolving over time. While the Fourier domain offers a natural lens to model time series, current deep learning approaches do not explicitly model evolution and randomness in the Fourier spectra, which limits their ability to accurately predict both the expected trajectory and its uncertainty in non-stationary time series. Motivated by Evolutionary Spectra (ES) theory, we propose TimeES, a general framework that enables probabilistic and deterministic forecasting via the evolutionary spectra theory. Specifically, we derive a parameterizable evolutionary spectra formulation, recasting non-stationary random process modeling as learning an evolving representation modulated by random variables. Furthermore, we reduce the complexity of the estimated spectra from O(NM) to O(NK), where K << M/2, by exploiting Hermitian symmetry and spectral energy sparsity for frequency selection. Based on a simple linear backbone, our proposed TimeES achieves consistent state-of-the-art performance across both deterministic and probabilistic forecasting tasks, with high efficiency and interpretability. Code is available at: https://github.com/wwy155/TimeES.
CommentsAccepted as NeurIPS 2026 Poster
