论文标题
非对称动力学系统的平均场理论的统一框架
A unifying framework for mean-field theories of asymmetric kinetic Ising systems
论文作者
论文摘要
动力学模型是研究复杂系统的非平衡动力学的强大工具。由于它们的行为对于大型网络不是可行的，因此已经提出了许多平均场方法进行分析，每种方法都是基于对系统时间演变的独特假设。这种方法的差异使系统地将平均场方法提高到以前的贡献之外，使其具有挑战性。在这里，我们从信息几何学的角度提出了一个不对称动力学系统的平均场理论的统一框架。该框架建立在系统扩展的基础上，该模型围绕通过正交投影对可拖动概率分布的子字体获得的简化模型构建。这种观点不仅统一了以前的方法，还允许我们开发与传统方法相比保留系统相关性的新颖方法。我们表明，这些新方法在预测和评估最大波动式的网络属性方面可以胜过以前的方法。
Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique assumptions about the system's temporal evolution. This disparity of approaches makes it challenging to systematically advance mean-field methods beyond previous contributions. Here, we propose a unifying framework for mean-field theories of asymmetric kinetic Ising systems from an information geometry perspective. The framework is built on Plefka expansions of a system around a simplified model obtained by an orthogonal projection to a sub-manifold of tractable probability distributions. This view not only unifies previous methods but also allows us to develop novel methods that, in contrast with traditional approaches, preserve the system's correlations. We show that these new methods can outperform previous ones in predicting and assessing network properties near maximally fluctuating regimes.
