论文标题
参数化神经普通微分方程：计算物理问题的应用
Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems
论文作者
论文摘要
这项工作提出了通过向节点引入一组ODE输入参数的神经常规微分方程（节点）的扩展。此扩展使节点可以学习由输入参数实例指定的多个动力学。我们的扩展灵感来自参数化的普通微分方程的概念，该方程在计算科学和工程环境中得到了广泛研究，其中管理方程的特征在输入参数上有所不同。我们将提出的参数化节点（PNODE）应用于计算物理学中出现的复杂动力学过程的潜在动力学，这是为时间临界物理应用启用快速数值模拟的重要组成部分。为此，我们提出了一个编码器型型框架，该框架将潜在动力学模型为pnodes。我们证明了PNODES具有计算物理学重要的基准问题的PNODE的有效性。
This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter instances. Our extension is inspired by the concept of parameterized ordinary differential equations, which are widely investigated in computational science and engineering contexts, where characteristics of the governing equations vary over the input parameters. We apply the proposed parameterized NODEs (PNODEs) for learning latent dynamics of complex dynamical processes that arise in computational physics, which is an essential component for enabling rapid numerical simulations for time-critical physics applications. For this, we propose an encoder-decoder-type framework, which models latent dynamics as PNODEs. We demonstrate the effectiveness of PNODEs with important benchmark problems from computational physics.
