论文标题
基于内核的机器学习方法，用于计算多体绿色功能理论中的准粒子能量
A Kernel-based Machine Learning Approach to Computing Quasiparticle Energies within Many-Body Green's Functions Theory
论文作者
论文摘要
我们提出了基于内核脊回归（KRR）的监督学习方法，并结合了遗传算法（气），以计算多体绿色功能理论中的准粒子能量。这些代表材料电子激发的能量是对一组非线性方程的解决方案，其中包含$ GW $近似中的电子自能（SE）。由于该SE的频率依赖性，标准方法在计算上是昂贵的，并且可能会产生非物理解决方案，特别是对于较大的系统。在我们提出的模型中，我们将KRR用作自适应替代模型，从而减少了SE的显式计算数量。通过适当定义的健身函数，将找到准粒子能量的标准定点问题转换为全局优化问题，GA的应用可独特地产生与物理相关的解决方案。我们证明了我们的方法适用于从$ GW $ 100数据集中的一组分子中，众所周知，这些数据表现出特别有问题的SE结构。 KRR-GA模型的结果与参考标准实现在不到0.01 eV的范围内同意，同时将所需的SE评估的数量大约减少了十倍。
We present a Kernel Ridge Regression (KRR) based supervised learning method combined with Genetic Algorithms (GAs) for the calculation of quasiparticle energies within Many-Body Green's Functions Theory. These energies representing electronic excitations of a material are solutions to a set of non-linear equations, containing the electron self-energy (SE) in the $GW$ approximation. Due to the frequency-dependence of this SE, standard approaches are computationally expensive and may yield non-physical solutions, in particular for larger systems. In our proposed model, we use KRR as a self-adaptive surrogate model which reduces the number of explicit calculations of the SE. Transforming the standard fixed-point problem of finding quasiparticle energies into a global optimization problem with a suitably defined fitness function, application of the GA yields uniquely the physically relevant solution. We demonstrate the applicability of our method for a set of molecules from the $GW$100 dataset, which are known to exhibit a particularly problematic structure of the SE. Results of the KRR-GA model agree within less than 0.01 eV with the reference standard implementation, while reducing the number of required SE evaluations roughly by a factor of ten.
