论文标题
深度学习以发现和预测惯性多种多样的动态
Deep learning to discover and predict dynamics on an inertial manifold
论文作者
论文摘要
开发了一个数据驱动的框架来代表惯性歧管（IM）上的混沌动力学，并应用于库拉莫托 - sivashinsky方程的解决方案。一种结合线性和非线性（神经网络）尺寸的混合方法在整个状态空间和IM上的坐标之间变化。其他神经网络可以预测IM上的时间进化。形式主义解释了翻译不变性和节能，并且基本上优于降低线性尺寸，从而再现了吸引子的非常好的关键动态和统计特征。
A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM), and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension reduction transforms between coordinates in the full state space and on the IM. Additional neural networks predict time-evolution on the IM. The formalism accounts for translation invariance and energy conservation, and substantially outperforms linear dimension reduction, reproducing very well key dynamic and statistical features of the attractor.
