Towards learning optimized kernels for complex Langevin

Abstract

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.