Machine learning, with its remarkable ability for retrieving information and identifying patterns from data, has emerged as a powerful tool for discovering governing equations. It has been increasingly informed by physics, and more recently by thermodynamics, to further uncover the thermodynamic structure underlying the evolution equations, i.e., the thermodynamic potentials driving the system and the operators governing the kinetics. However, despite its great success, the inverse problem of thermodynamic model discovery from macroscopic data is in many cases non-unique, meaning that multiple pairs of potentials and operators can give rise to the same macroscopic dynamics, which significantly hinders the physical interpretability of the learned models. In this work, we consider the problem of deriving the macroscopic (continuum) equations from microscopic (particle) data, and encode knowledge from statistical mechanics to resolve this non-uniqueness for the first time. The proposed machine learning framework, named as Statistical-Physics-Informed Neural Networks (Stat-PINNs), is here developed for purely dissipative isothermal systems. Interestingly, it only uses data from short-time particle simulations to learn the thermodynamic structure, which can in turn be used to predict long-time macroscopic evolutions. We demonstrate the approach for particle systems with Arrhenius-type interactions, common to a wide range of phenomena, such as defect diffusion in solids, surface absorption, and chemical reactions. Our results from Stat-PINNs can successfully recover the known analytic solution for the case with long-range interactions and discover the hitherto unknown potential and operator governing the short-range interaction cases. We compare our results with direct particle simulations and an analogous approach that solely excludes statistical mechanics, and observe that, in addition to recovering the unique thermodynamic structure, statistical mechanics relations can increase the robustness and predictive capability of the learning strategy.

中文翻译：

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统计物理信息神经网络 （Stat-PINN）：一种用于粗粒度耗散动力学的机器学习策略


机器学习具有从数据中检索信息和识别模式的卓越能力，已成为发现控制方程的强大工具。物理学和热力学越来越多地为它提供信息，以进一步揭示演化方程背后的热力学结构，即驱动系统的热力学势和控制动力学的算子。然而，尽管取得了巨大的成功，但从宏观数据中发现热力学模型的逆问题在许多情况下是非唯一的，这意味着多对势和算子可以产生相同的宏观动力学，这严重阻碍了学习模型的物理可解释性。在这项工作中，我们考虑了从微观（粒子）数据推导出宏观（连续体）方程的问题，并编码了来自统计力学的知识，以首次解决这种非唯一性。所提出的机器学习框架，称为统计物理信息神经网络 （Stat-PINN），是为纯耗散等温系统开发的。有趣的是，它只使用来自短时粒子模拟的数据来学习热力学结构，而热力学结构又可以用于预测长期宏观演化。我们展示了具有 Arrhenius 型相互作用的粒子系统的方法，该方法在各种现象中都很常见，例如固体中的缺陷扩散、表面吸收和化学反应。我们来自 Stat-PINNs 的结果可以成功地恢复具有长程交互作用的案例的已知解析解，并发现迄今为止未知的势能和运算符来控制短程交互作用案例。 我们将我们的结果与直接粒子模拟和仅排除统计力学的类似方法进行了比较，并观察到，除了恢复独特的热力学结构外，统计力学关系还可以提高学习策略的稳健性和预测能力。