论文标题
HP-VPINN：具有域分解的变异物理信息的神经网络
hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition
论文作者
论文摘要
我们基于浅层和深神经网络的非线性近似以及通过域分解和投影到高阶多项式的空间的非线性近似，为HP变量物理信息信息网络（HP-VPINN）制定了一般框架。试验空间是神经网络的空间，该空间在整个计算域上在全球范围内定义，而测试空间包含分段多项式。特别是在这项研究中，HP进行的使用与本地学习算法相对应，该算法可以有效地定位网络参数优化。我们证明了HP-VPINNS在函数近似和求解微分方程的几个数值示例的准确性和培训成本方面的优势。
We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto space of high-order polynomials. The trial space is the space of neural network, which is defined globally over the whole computational domain, while the test space contains the piecewise polynomials. Specifically in this study, the hp-refinement corresponds to a global approximation with local learning algorithm that can efficiently localize the network parameter optimization. We demonstrate the advantages of hp-VPINNs in accuracy and training cost for several numerical examples of function approximation and solving differential equations.
