标题： 生成模型在伊辛系统中的热力学保真度 显示英文标题

标题： Thermodynamic Fidelity of Generative Models for Ising System

摘要： 机器学习已成为科学和工程中建模的核心技术，要么作为物理基础模型的补充，要么作为其替代品。 最近，人们投入了大量努力来开发能够预测场量的模型，但目前最先进的模型在描述复杂物理现象方面的局限性尚不明确。 我们研究了生成扩散模型和生成对抗网络（GAN）描述伊辛模型的能力。 我们发现，使用围绕临界温度的多个温度下的平衡构型通过Metropolis蒙特卡洛方法训练的扩散模型可以捕捉相变过程中的平均热力学变量，并能外推到更高和更低的温度。 该模型还捕捉了与涨落相关的物理性质的整体趋势（比热和磁化率），但在非遍历的低温下和临界温度下的非平凡无标度相关性除外，尽管与蒙特卡洛模拟相比，临界指数有一些差异。 GAN在热力学性质上的表现较差，并且在没有仔细训练的情况下容易出现模式崩溃。 这项研究突显了生成模型在捕捉某些物理系统相关复杂现象方面的潜力和局限性。 显示英文摘要

摘要： Machine learning has become a central technique for modeling in science and engineering, either complementing or as surrogates to physics-based models. Significant efforts have recently been devoted to models capable of predicting field quantities but the limitations of current state-of-the-art models in describing complex physics are not well understood. We characterize the ability of generative diffusion models and generative adversarial networks (GAN) to describe the Ising model. We find diffusion models trained using equilibrium configurations obtained using Metropolis Monte Carlo for a range of temperatures around the critical temperature can capture average thermodynamic variables across the phase transformation and extrapolate to higher and lower temperatures. The model also captures the overall trends of physical properties associated with fluctuations (specific heat and susceptibility) except at the non-ergodic low temperatures and non-trivial scale-free correlations at the critical temperature, albeit with some difference in the critical exponent compared to Monte Carlo simulations. GANs perform more poorly on thermodynamic properties and are susceptible to mode-collapse without careful training. This investigation highlights the potential and limitations of generative models in capturing the complex phenomena associated with certain physical systems.