论文标题
减轻哈伯德标志问题。机器学习的新颖应用
Mitigating the Hubbard Sign Problem. A Novel Application of Machine Learning
论文作者
论文摘要
许多引人入胜的系统遭受了严重的（复杂的动作）问题问题，使我们无法使用马尔可夫链蒙特卡洛模拟来计算它们。减轻符号问题的一种有希望的方法是将整合域向Lefschetz Thimbles转换。不幸的是，这遭受了较差的缩放，源于流动方程的数值整合和诱发的雅各布式的评估。在此程序中，我们提出了一种基于复杂价值的仿射耦合层的新的初步神经网络体系结构。该网络有效地进行了这样的转换，最终允许模拟具有严重符号问题的系统。我们在有限的化学电位上的哈伯德模型中测试了这种方法，对离子空间晶格上的相关电子很强地相关。
Many fascinating systems suffer from a severe (complex action) sign problem preventing us from calculating them with Markov Chain Monte Carlo simulations. One promising method to alleviate the sign problem is the transformation of the integration domain towards Lefschetz Thimbles. Unfortunately, this suffers from poor scaling originating in numerically integrating of flow equations and evaluation of an induced Jacobian. In this proceedings we present a new preliminary Neural Network architecture based on complex-valued affine coupling layers. This network performs such a transformation efficiently, ultimately allowing simulation of systems with a severe sign problem. We test this method within the Hubbard Model at finite chemical potential, modelling strongly correlated electrons on a spatial lattice of ions.
