论文标题
使用重球神经odes学习复杂动力学的豆荚
Learning POD of Complex Dynamics Using Heavy-ball Neural ODEs
论文作者
论文摘要
正确的正交分解（POD）允许在很大的水平上减少复杂动力系统的降级建模，同时保持高度准确性在建模基础动力学系统时。机器学习算法的进步使从数据中学习POD的动力学并对动态系统进行准确而快速的预测。在本文中，我们利用最近提出的重球神经odes（hbnodes）[Xia等。 Neurips，2021]用于在POD上下文中学习数据驱动的还原模型（ROM），尤其是用于通过求解完整订单模型生成的训练快照产生的时间变化系数的学习动力学。 HBNODE具有一些具有理论保证的基于POD的ROM的实用优势，包括1）HbNode可以从顺序观察中有效地学习长期依赖性，而2）HbNode在培训和测试中都在计算上有效。我们将HBNODE与其他流行的ROM进行了比较，在几个复杂的动力系统上，包括VonKármán街道流，Kurganov-Petrova-Popov方程以及用于流体建模的一维欧拉方程。
Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning algorithms enable learning POD-based dynamics from data and making accurate and fast predictions of dynamical systems. In this paper, we leverage the recently proposed heavy-ball neural ODEs (HBNODEs) [Xia et al. NeurIPS, 2021] for learning data-driven reduced-order models (ROMs) in the POD context, in particular, for learning dynamics of time-varying coefficients generated by the POD analysis on training snapshots generated from solving full order models. HBNODE enjoys several practical advantages for learning POD-based ROMs with theoretical guarantees, including 1) HBNODE can learn long-term dependencies effectively from sequential observations and 2) HBNODE is computationally efficient in both training and testing. We compare HBNODE with other popular ROMs on several complex dynamical systems, including the von Kármán Street flow, the Kurganov-Petrova-Popov equation, and the one-dimensional Euler equations for fluids modeling.
