对比7种模型预测洛伦兹混沌系统,发现双向网络加鲁棒损失表现最佳。
LSTM Variants for Chaotic Dynamical Systems: An Empirical Study on the Lorenz Attractor

- 用双向LSTM配合Huber损失,提升对混沌系统的长期预测能力。
- 添加注意力机制使性能下降超10分,卷积前端反而拖累结果。
- 适合研究混沌系统建模、时间序列预测的工程师与科研人员。
预测如洛伦兹吸引子般的混沌动力系统极其困难:微小数值误差在长时自回归推演中会指数级放大。我们针对AI-DEEDS 2026混沌系统挑战赛,评估了七种循环与卷积架构:基础LSTM、带加性注意力的LSTM、双向LSTM(BiLSTM)、使用Huber损失训练的BiLSTM、时间卷积网络(TCN)、CNN前馈接LSTM,以及CNN前馈接BiLSTM。所有模型采用相同预处理、序列长度和推演流程,以隔离设计差异的影响。挑战评分在0-100分之间,分数越高越好。最终得分介于45.72至58.81之间,其中使用Huber损失训练的BiLSTM表现最优。两个关键发现为:(i) 在单向基线中加入加性注意力导致性能下降超过10分;(ii) 在LSTM或BiLSTM前添加CNN前段不仅未提升效果,反而轻微降低分数。每对样本的均方根误差(RMSE)分析显示,BiLSTM族在更难的第6-7对上泛化能力更强,而LSTM+Attention模型在此处崩溃(第6对RMSE高达8.94)。我们讨论了为何双向上下文和鲁棒损失在混沌环境下有效,而注意力机制与CNN前段在此任务中失效的原因。
原文摘要 · Abstract (English)
Forecasting chaotic dynamical systems such as the Lorenz attractor is notoriously difficult: small numerical errors are amplified exponentially over long autoregressive rollouts. We study seven recurrent and convolutional architectures for the AI-DEEDS 2026 Chaotic Systems Challenge: a vanilla LSTM, an LSTM with additive attention, a Bidirectional LSTM (BiLSTM), a BiLSTM trained with the Huber loss, a Temporal Convolutional Network (TCN), a CNN front-end followed by an LSTM, and a CNN front-end followed by a BiLSTM. All models share the same pre-processing, sequence length, and rollout procedure, isolating the contribution of each design choice. The challenge scores predictions on a 0-100 scale where higher is better. We obtain leaderboard scores between 45.72 and 58.81, with the BiLSTM trained with Huber loss being the strongest configuration. Two findings stand out: (i) adding additive attention to the unidirectional baseline degraded performance by over ten points, and (ii) prepending a CNN front-end to either an LSTM or a BiLSTM did not help and slightly hurt the score. Per-pair RMSE measurements confirm that the BiLSTM family generalizes better in the harder pairs (6-7), while the LSTM + Attention model collapses there (RMSE up to 8.94 on pair 6). We discuss why bidirectional context and a robust loss help in chaotic regimes while attention and CNN front-ends fail in this setting.
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