论文标题
使用HP-Greedy改进的引力波替代物的自动参数域分解方法
An automated parameter domain decomposition approach for gravitational wave surrogates using hp-greedy refinement
论文作者
论文摘要
我们介绍了HP-Greedy，这是一种建立重力波替代的改进方法，作为标准减少基框架的扩展。我们的建议是数据驱动的，具有参数空间的域分解，局部减少的基础和二进制树作为所得结构，这些结构以自动化方式获得。与标准的全球降低基础方法相比，我们的提案的数值模拟显示了三个显着特征：i）较低维度的表示，而不会损失准确性，ii）在某些情况下，基于固定的最大维度的准确性明显更高，在某些情况下，依赖于较大的结果，以及III的结果，这些结果取决于细化的基础种子选择所使用的降低基础种子选择。我们首先使用玩具模型说明了方法的关键部分，然后提出了一个更现实的用例，即通过两个旋转的，不必要的黑洞的碰撞发出的重力波。我们讨论了HP绿色的性能方面，例如对树结构的深度过度拟合以及其他超参数依赖性。作为所提出的HP绿色改进的两个直接应用，我们设想：i）进一步加速统计推断，这可能与聚焦减少的四倍体相辅相成，ii）通过聚类和最近的邻居搜索引力波。
We introduce hp-greedy, a refinement approach for building gravitational wave surrogates as an extension of the standard reduced basis framework. Our proposal is data-driven, with a domain decomposition of the parameter space, local reduced basis, and a binary tree as the resulting structure, which are obtained in an automated way. When compared to the standard global reduced basis approach, the numerical simulations of our proposal show three salient features: i) representations of lower dimension with no loss of accuracy, ii) a significantly higher accuracy for a fixed maximum dimensionality of the basis, in some cases by orders of magnitude, and iii) results that depend on the reduced basis seed choice used by the refinement algorithm. We first illustrate the key parts of our approach with a toy model and then present a more realistic use case of gravitational waves emitted by the collision of two spinning, non-precessing black holes. We discuss performance aspects of hp-greedy, such as overfitting with respect to the depth of the tree structure, and other hyperparameter dependences. As two direct applications of the proposed hp-greedy refinement, we envision: i) a further acceleration of statistical inference, which might be complementary to focused reduced-order quadratures, and ii) the search of gravitational waves through clustering and nearest neighbors.
