基于核的机器学习方法计算多体格林函数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
摘要：
提出了一种基于核岭回归（KRR）的监督学习方法，并结合遗传算法（GAs）计算多体格林函数理论中的准粒子能量。这些表示材料的电子激发的能量是一组非线性方程的解，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，我们使用KRR作为自适应代理模型，减少了显式计算的SE的数量。转换成一个全球性的优化问题与适当定义的适应度函数的准粒子能量的标准不动点问题，应用遗传算法产生唯一的物理相关的解决方案。我们证明了我们的方法的适用性的一组分子从$GW$ 100数据集，这是已知的表现出一个特别有问题的结构的SE。KRR-GA模型的结果在小于0.01 eV的范围内与参考标准实施一致，同时将所需的SE评估的数量大致减少了十倍。
英文摘要：
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.
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