In Chaos, a minor divergence between two initial conditions exhibits exponential amplification over time, leading to far-away outcomes, known as the butterfly effect. Thus, the distant future is full of uncertainty and hard to forecast. We introduce Group Reservoir Transformer to predict long-term events more accurately and robustly by overcoming two challenges in Chaos: (1) the extensive historical sequences and (2) the sensitivity to initial conditions. A reservoir is attached to a Transformer to efficiently handle arbitrarily long historical lengths, with an extension of a group of reservoirs to reduce the uncertainty due to the initialization variations. Our architecture consistently outperforms state-of-the-art DNN models in multivariate time series, including NLinear, Pyformer, Informer, Autoformer, and the baseline Transformer, with an error reduction of up to -89.43\% in various fields such as ETTh, ETTm, and air quality, demonstrating that an ensemble of butterfly learning, the prediction can be improved to a more adequate and certain one, despite of the traveling time to the unknown future.

翻译：在混沌系統中，初始條件的微小差異會隨時間呈指數級放大，導致截然不同的結果，即所謂的蝴蝶效應。因此，遙遠的未來充滿不確定性且難以預測。我們引入群體儲層Transformer（Group Reservoir Transformer），通過克服混沌系統中的兩個挑戰（1）長歷史序列與（2）對初始條件的敏感性，更準確且穩健地預測長期事件。該架構將儲層連接至Transformer以高效處理任意長度的歷史序列，並擴展為儲層群組以降低初始參數變化帶來的不確定性。在多變量時間序列預測任務中，我們的模型持續優於包括NLinear、Pyformer、Informer、Autoformer及基準Transformer在內的頂尖深度神經網絡模型，在ETTh、ETTm及空氣品質等多個領域中誤差降低最高達-89.43%。這表明，通過集成蝴蝶學習（butterfly learning）機制，即使面對通往未知未來的時間旅程，預測仍能提升至更充分且確定的水平。