Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physically-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. In this work, we propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis that unravels the interplay between consistent dynamics and their associated Koopman operators. Our network is interpretable from a physical viewpoint and its computational requirements are comparable to other baselines. We evaluate our method on a wide range of high-dimensional and short-term dependent problems. The datasets include nonlinear oscillators, sea surface temperature data, and fluid flows on a curved domain. The results show that our model yields accurate estimates for significant prediction horizons, while being robust to noise.

提出了一种新颖的一致性Koopman自编码器模型，结合前向和后向动态，通过探索一致性动态与其关联的Koopman算子之间的相互作用来处理非线性动态系统，取得了在预测中的准确估计，同时对噪声具有鲁棒性。

使用一致的 Koopman 自编码器预测连续数据