论文标题
在通用残留网络上，用于深度学习未知动力学系统
On generalized residue network for deep learning of unknown dynamical systems
论文作者
论文摘要
我们提出了一种使用深神经网络（DNN）学习未知动力学系统的一般数值方法。我们的方法建立在最近的研究基础上，该研究将残基网络（RESNET）确定为有效的神经网络结构。在本文中，我们提出了一个广义的重新系统框架，并将残基广泛定义为观察数据和另一个模型的预测之间的差异，该模型可以是现有的粗制模型或还原阶模型。在这种情况下，广义重新NET可作为对现有模型的模型校正，并恢复未解决的动力学。如果没有现有的粗糙模型，我们会提出用于快速创建粗模型的数值策略，该模型与广义重新结合结合使用。这些粗模型是使用相同数据集构建的，因此不需要其他资源。广义的重新系统能够学习基础未知方程式，并以高于标准的重新结构结构的精度产生预测。这是通过几个数值示例来证明的，包括对混乱系统的长期预测。
We present a general numerical approach for learning unknown dynamical systems using deep neural networks (DNNs). Our method is built upon recent studies that identified the residue network (ResNet) as an effective neural network structure. In this paper, we present a generalized ResNet framework and broadly define residue as the discrepancy between observation data and prediction made by another model, which can be an existing coarse model or reduced-order model. In this case, the generalized ResNet serves as a model correction to the existing model and recovers the unresolved dynamics. When an existing coarse model is not available, we present numerical strategies for fast creation of coarse models, to be used in conjunction with the generalized ResNet. These coarse models are constructed using the same data set and thus do not require additional resources. The generalized ResNet is capable of learning the underlying unknown equations and producing predictions with accuracy higher than the standard ResNet structure. This is demonstrated via several numerical examples, including long-term prediction of a chaotic system.
