We propose a novel type of neural networks known as "attention-based sequence-to-sequence architecture" for a model-free prediction of spatiotemporal systems. This architecture is composed of an encoder and a decoder in which the encoder acts upon a given input sequence and then the decoder yields another output sequence to make a multistep prediction at a time. In order to demonstrate the potential of this approach, we train the neural network using data numerically sampled from the Korteweg-de Vries equation-which describes the interaction between solitary waves-and then predict its future evolution. Furthermore, we validate the applicability of the approach on datasets sampled from the chaotic Lorenz system and three other partial differential equations. The results show that the proposed method can achieve good performance in predicting the evolutionary behavior of studied spatiotemporal dynamics. To the best of our knowledge, this work is the first attempt at applying attention-based sequence-to-sequence architecture to the prediction task of solitary waves.

中文翻译：

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时空系统的序列到序列预测。

我们提出了一种新型的神经网络，称为“基于注意力的序列到序列体系结构”，用于时空系统的无模型预测。此体系结构由编码器和解码器组成，其中编码器作用于给定的输入序列，然后解码器产生另一个输出序列，以一次进行多步预测。为了证明这种方法的潜力，我们使用从Korteweg-de Vries方程中数值采样的数据（描述了孤立波之间的相互作用）训练神经网络，然后预测其未来的发展。此外，我们验证了该方法对从混沌Lorenz系统和其他三个偏微分方程采样的数据集的适用性。结果表明，该方法在预测时空动力学演化行为方面具有良好的性能。据我们所知，这项工作是将基于注意力的序列到序列体系结构应用于孤立波的预测任务的首次尝试。