Combining complex Langevin dynamics with score-based and energy-based diffusion models
Gert Aarts, Diaa E. Habibi, Lingxiao Wang and Kai Zhou
由于复杂动作或玻尔兹曼重量而导致标志问题理论有时可以在复杂的配置空间中使用随机过程进行数值解决。 然而,通过这种复杂的Langevin过程有效采样的概率分布并不为人所知,并且臭名昭着地难以理解。 在生成式AI中,扩散模型可以从数据中学习分布或其日志衍生物。 我们探索扩散模型学习复杂朗格文过程采样分布的能力,比较基于分数和基于能量的扩散模型,并推测可能的应用。
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...