With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical model trained from the observation data. While neural networks are often seen as uninterpretable black-box architectures, they can still benefit from physical priors on the data and from mathematical knowledge. In this paper, we use a neural network architecture which leverages the long-known Koopman operator theory to embed dynamical systems in latent spaces where their dynamics can be described linearly, enabling a number of appealing features. We introduce methods that enable to train such a model for long-term continuous reconstruction, even in difficult contexts where the data comes in irregularly-sampled time series. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques, with applications to e.g. time series interpolation and forecasting.

使用大规模数据集、计算能力和神经网络架构，基于Koopman算子理论的神经网络架构在动力学系统的潜在空间中对数据进行线性描述，从而实现了长期连续重现，包括在时间序列不规则采样情况下。并展示了训练过的动力学模型作为新型数据同化技术的先验的潜力，应用于时间序列插值和预测。

数据同化的神经Koopman先验