论文标题
学习优化复杂兰格文的优化内核
Towards learning optimized kernels for complex Langevin
论文作者
论文摘要
我们提出了一种旨在恢复复杂Langevin模拟中正确收敛的新型策略。核心思想是将特定于系统的先验知识纳入模拟中，以避免NP硬符号问题。为此，我们使用内核修改复杂的langevin，并提出使用现代自动差异方法来学习最佳内核值。优化过程以编码相关先验信息的功能为指导，例如对称性或欧几里得相关器数据。我们的方法在任何实时范围内恢复了Schwinger-Keldysh轮廓的非相互作用理论中正确的收敛。对于强耦合的量子Anharmonic振荡器，我们实现了正确的收敛性，最多是先前基准研究的实时范围的三倍。附录阐明了以下事实：对于正确的收敛，不仅没有边界项，而且正确的fokker-Plank频谱也至关重要。
We present a novel strategy aimed at restoring correct convergence in complex Langevin simulations. The central idea is to incorporate system-specific prior knowledge into the simulations, in order to circumvent the NP-hard sign problem. In order to do so, we modify complex Langevin using kernels and propose the use of modern auto-differentiation methods to learn optimal kernel values. The optimization process is guided by functionals encoding relevant prior information, such as symmetries or Euclidean correlator data. Our approach recovers correct convergence in the non-interacting theory on the Schwinger-Keldysh contour for any real-time extent. For the strongly coupled quantum anharmonic oscillator we achieve correct convergence up to three-times the real-time extent of the previous benchmark study. An appendix sheds light on the fact that for correct convergence not only the absence of boundary terms, but in addition the correct Fokker-Plank spectrum is crucial.
