Interpolating between small- and large- g expansions using Bayesian model mixing
Interpolating between small- and large- g expansions using Bayesian model mixing
复制标题
使用贝叶斯模型混合在小 g 展开和大 g 展开之间进行插值
DOI：
10.1103/physrevc.106.044002
复制
发表时间：
2022
影响因子：
3.1
通讯作者：
Phillips, D. R.
中科院分区：
文献类型：
--
作者：
Semposki, A. C.;Furnstahl, R. J.;Phillips, D. R.
贝叶斯模型混合（BMM）是一种统计技术，可用于将在不同输入域中具有预测性的联合收割机模型组合成复合分布，该复合分布在整个输入空间上具有改进的预测能力。我们探讨了BMM的应用混合的两个扩展的一个耦合常数的函数是有效的，分别在小和大的值。这种类型的问题在核物理中非常常见，其中物理性质在强相互作用极限和弱相互作用极限或低密度和高密度或动量转移下可以直接计算，但在两者之间很难计算。这些极限之间的插值通常通过合适的插值函数来实现，例如，Padé近似，但不清楚如何量化插值的不确定性。我们在零维理论的配分函数的简单上下文中解决这个问题，其中小的（渐近）扩展和大的（收敛）扩展都是已知的。我们考虑三种混合方法：线性混合BMM，本地化二元BMM，本地化多元BMM高斯过程。我们发现，在两个预测模型之间的中间区域采用高斯过程导致三种方法的最佳结果。我们在这里提出的方法和验证策略应该推广到其他核物理设置。
Bayesian model mixing (BMM) is a statistical technique that can be used to combine models that are predictive in different input domains into a composite distribution that has improved predictive power over the entire input space. We explore the application of BMM to the mixing of two expansions of a function of a coupling constantthat are valid at small and large values ofrespectively. This type of problem is quite common in nuclear physics, where physical properties are straightforwardly calculable in strong and weak interaction limits or at low and high densities or momentum transfers, but difficult to calculate in between. Interpolation between these limits is often accomplished by a suitable interpolating function, e.g., Padé approximants, but it is then unclear how to quantify the uncertainty of the interpolant. We address this problem in the simple context of the partition function of zero-dimensionaltheory, for which the (asymptotic) expansion at smalland the (convergent) expansion at largeare both known. We consider three mixing methods: linear mixture BMM, localized bivariate BMM, and localized multivariate BMM with Gaussian processes. We find that employing a Gaussian process in the intermediate region between the two predictive models leads to the best results of the three methods. The methods and validation strategies we present here should be generalizable to other nuclear physics settings.