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 k...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-04-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2023)057 |
| _version_ | 1797769719893196800 |
|---|---|
| author | Daniel Alvestad Rasmus Larsen Alexander Rothkopf |
| author_facet | Daniel Alvestad Rasmus Larsen Alexander Rothkopf |
| author_sort | Daniel Alvestad |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T21:12:05Z |
| format | Article |
| id | doaj.art-8a3a3eb315df46e1a17a9a7be8d12617 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T21:12:05Z |
| publishDate | 2023-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-8a3a3eb315df46e1a17a9a7be8d126172023-07-30T11:04:41ZengSpringerOpenJournal of High Energy Physics1029-84792023-04-012023414410.1007/JHEP04(2023)057Towards learning optimized kernels for complex LangevinDaniel Alvestad0Rasmus Larsen1Alexander Rothkopf2Department of Mathematics and Physics, University of StavangerDepartment of Mathematics and Physics, University of StavangerDepartment of Mathematics and Physics, University of StavangerAbstract 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.https://doi.org/10.1007/JHEP04(2023)057Lattice Quantum Field TheoryAlgorithms and Theoretical DevelopmentsStochastic Processes |
| spellingShingle | Daniel Alvestad Rasmus Larsen Alexander Rothkopf Towards learning optimized kernels for complex Langevin Journal of High Energy Physics Lattice Quantum Field Theory Algorithms and Theoretical Developments Stochastic Processes |
| title | Towards learning optimized kernels for complex Langevin |
| title_full | Towards learning optimized kernels for complex Langevin |
| title_fullStr | Towards learning optimized kernels for complex Langevin |
| title_full_unstemmed | Towards learning optimized kernels for complex Langevin |
| title_short | Towards learning optimized kernels for complex Langevin |
| title_sort | towards learning optimized kernels for complex langevin |
| topic | Lattice Quantum Field Theory Algorithms and Theoretical Developments Stochastic Processes |
| url | https://doi.org/10.1007/JHEP04(2023)057 |
| work_keys_str_mv | AT danielalvestad towardslearningoptimizedkernelsforcomplexlangevin AT rasmuslarsen towardslearningoptimizedkernelsforcomplexlangevin AT alexanderrothkopf towardslearningoptimizedkernelsforcomplexlangevin |