论文标题
以分子势能表面拟合为例
The loss of the property of locality of the kernel in high-dimensional Gaussian process regression on the example of the fitting of molecular potential energy surfaces
论文作者
论文摘要
基于内核的方法包括高斯工艺回归（GPR）和总体内核脊回归（KRR）一直在发现在计算化学中的使用越来越多，包括在高维特征空间中拟合势能表面和密度函数。经常使用Matern家族（例如高斯样核（基础函数））的内核，这允许它们赋予它们协方差函数的含义，并将GPR作为高斯分布平均值的估计量。内核的局部性概念对于这种解释至关重要。对于在计算化学中广泛使用的多ZETA类型基础函数的制定，我们显示的是，在拟合增加尺寸的分子势能表面的示例中，这是高维度中高斯样子内核的局部性的实际消失。我们还为内核制定了多Zeta方法，并表明它显着提高了低维度的回归质量，但在高维度中失去了任何优势，这归因于当地属性的丧失。
Kernel based methods including Gaussian process regression (GPR) and generally kernel ridge regression (KRR) have been finding increasing use in computational chemistry, including the fitting of potential energy surfaces and density functionals in high-dimensional feature spaces. Kernels of the Matern family such as Gaussian-like kernels (basis functions) are often used, which allows imparting them the meaning of covariance functions and formulating GPR as an estimator of the mean of a Gaussian distribution. The notion of locality of the kernel is critical for this interpretation. It is also critical to the formulation of multi-zeta type basis functions widely used in computational chemistry We show, on the example of fitting of molecular potential energy surfaces of increasing dimensionality, the practical disappearance of the property of locality of a Gaussian-like kernel in high dimensionality. We also formulate a multi-zeta approach to the kernel and show that it significantly improves the quality of regression in low dimensionality but loses any advantage in high dimensionality, which is attributed to the loss of the property of locality.
