用物理先验替代传统嵌入层，显著降低参数量并提升时序模型性能。
Toward Physics-guided Time Series Embedding
- 基于嵌入对偶理论，用物理重建直接生成数据嵌入。
- 参数减少10倍，速度提升3倍，零样本任务性能提升53%。
- 无需调参，可即插即用，适合科学计算与少样本场景。
在众多科学与工程领域中，研究核心围绕基于物理的动力系统建模与数据驱动的时间序列分析。根据嵌入理论，动力系统与时间序列可通过观测函数与物理重构技术相互转化。基于此，我们提出嵌入对偶理论，其中参数化嵌入层本质上对非线性时序动态进行线性估计。该理论使我们可跳过参数化嵌入层，直接采用物理重构技术获取数据嵌入表示。利用物理先验，实现参数量减少10倍、速度提升3倍，且在专家、少样本和零样本任务中分别获得最高18%、22%和53%的性能提升，且无需任何超参数调整。所有方法封装为即插即用模块。
原文摘要 · Abstract (English)
In various scientific and engineering fields, the primary research areas have revolved around physics-based dynamical systems modeling and data-driven time series analysis. According to the embedding theory, dynamical systems and time series can be mutually transformed using observation functions and physical reconstruction techniques. Based on this, we propose Embedding Duality Theory, where the parameterized embedding layer essentially provides a linear estimation of the non-linear time series dynamics. This theory enables us to bypass the parameterized embedding layer and directly employ physical reconstruction techniques to acquire a data embedding representation. Utilizing physical priors results in a 10X reduction in parameters, a 3X increase in speed, and maximum performance boosts of 18% in expert, 22% in few-shot, and 53\% in zero-shot tasks without any hyper-parameter tuning. All methods are encapsulated as a plug-and-play module
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