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Combining complex Langevin dynamics with score-based and energy-based diffusion models
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Diaa Eddin Habibi,
Lingxiao Wang ,
Kai Zhou
Journal of High Energy Physics, Volume: 2025, Issue: 12, Start page: 160
Swansea University Authors:
Gert Aarts , Diaa Eddin Habibi
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DOI (Published version): 10.1007/jhep12(2025)160
Abstract
Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by this complex Langevin process is not known a priori and notori...
| Published in: | Journal of High Energy Physics |
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| ISSN: | 1029-8479 |
| Published: |
Springer Nature
2025
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa71204 |
| Abstract: |
Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by this complex Langevin process is not known a priori and notoriously hard to understand. In generative AI, diffusion models can learn distributions, or their log derivatives, from data. We explore the ability of diffusion models to learn the distributions sampled by a complex Langevin process, comparing score-based and energy-based diffusion models, and speculate about possible applications. |
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| Keywords: |
Algorithms and Theoretical Developments; Non-Zero Temperature and Density; Other Lattice Field Theories |
| College: |
Faculty of Science and Engineering |
| Funders: |
GA thanks KZ and his group for the kind hospitality at CUHK-Shenzhen during the completion of this work. This visit was supported in part by the Royal Society International Exchanges 2024 Global Round 2 IES\R2\242215. GA is further supported by STFC Consolidated Grant ST/X000648/1. DEH is supported by the UKRI AIMLAC CDT EP/S023992/1. LW thanks the DEEP-IN working group at RIKEN-iTHEMS for its support in the preparation of this paper. LW is also supported by the RIKEN TRIP initiative (RIKEN Quantum), JSPS KAKENHI Grant No. 25H01560, and JST-BOOST Grant No. JPMJBY24H9. KZ is supported by the CUHK-Shenzhen university development fund under grant No. UDF01003041 and UDF03003041, Shenzhen Peacock fund under No. 2023TC0179 and NSFC grant under No. 92570117. We acknowledge the support of the Supercomputing Wales and AccelerateAI projects, which are part-funded by the European Regional Development Fund (ERDF) via Welsh Government. Article funded by SCOAP3. |
| Issue: |
12 |
| Start Page: |
160 |