مقایسهٔ روش‌ها

	کوپا: پیش‌بینی‌کننده‌های کوپمن برای سری‌های زمانی ناایستا	مدل خطی تجزیه‌پذیر برای پیش‌بینی سری‌های زمانی (DLinear)	ترانسفورمر ناایستا	مدل فضای حالت (فیلتر کالمن)
حوزه	یادگیری عمیق	یادگیری عمیق	یادگیری عمیق	اقتصادسنجی
خانواده	Machine learning	Machine learning	Machine learning	Regression model
سال پیدایش	2023	2023	2022	1990
پدیدآور	Yong Liu et al.	Ailing Zeng et al.	Yong Liu et al.	Harvey; Durbin & Koopman (state space treatment); Kalman filter
نوع	Koopman operator-based time-series forecasting model	Decomposition-based linear forecasting model	Transformer-based time-series forecasting model	State space time series model
منبع بنیادین	Liu, Y., Li, C., Wang, J., & Long, M. (2023). Koopa: Learning non-stationary time series dynamics with Koopman predictors. NeurIPS.	Zeng, A., Chen, M., Zhang, L., & Xu, Q. (2023). Are transformers effective for time series forecasting? AAAI.	Liu, Y., Wu, H., Wang, J., & Long, M. (2022). Non-stationary transformers: Exploring the stationarity in time series forecasting. NeurIPS.	Harvey, A. C. (1990). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.
نام‌های دیگر	Koopman Predictor, Koopman-based Time-Series Model, Koopa Forecaster, Koopman Tahmincisi	Decomposition Linear, DLinear Forecaster, Linear Decomposition Model, Ayrışım Doğrusal Modeli	NS-Transformer, Non-stationary Transformer Network, Stationarization-based Transformer, Durağan-Olmayan Transformer	state space, Kalman filter, unobserved components model, Durum Uzayı Modeli (State Space / Kalman Filter)
مرتبط	3	3	3	4
خلاصه	Koopa is a deep learning model for time-series forecasting introduced by Yong Liu, Chang Li, Jianmin Wang, and Mingsheng Long at NeurIPS 2023. It addresses the challenge of non-stationarity by disentangling time series into stationary and non-stationary components, then modeling the non-stationary dynamics using a learned approximation of the Koopman operator — a mathematical framework that lifts nonlinear systems into a linear space for tractable long-horizon prediction.	DLinear is a lightweight time series forecasting model introduced by Zeng et al. at AAAI 2023. It challenges the prevailing assumption that Transformer-based architectures are necessary for accurate long-horizon forecasting. The model decomposes an input sequence into trend and seasonal components using a moving average filter, then applies separate single-layer linear transformations to each component before summing their outputs to produce the final forecast.	Non-stationary Transformer is a Transformer-based time-series forecasting architecture introduced by Yong Liu, Haixu Wu, Jianmin Wang, and Mingsheng Long at NeurIPS 2022. It addresses a fundamental tension in applying Transformers to real-world time series: over-stationarization during preprocessing strips out non-stationary signals that carry predictive information, while raw non-stationary inputs cause attention to collapse. The model resolves this through series stationarization paired with a novel de-stationary attention mechanism that restores the original temporal distribution in predictions.	A state space model is a general time series framework that describes a series through unobserved (latent) state variables linked by a measurement equation and a transition equation, with the states estimated in real time by the Kalman filter. Developed in the state space tradition of Harvey (1990) and Durbin & Koopman (2012), it nests ARIMA and exponential smoothing as special cases.