Many complex systems are composed of interacting parts, and the underlying laws are usually simple and universal. While graph neural networks provide a useful relational inductive bias for modeling such systems, generalization to new system instances of the same type is less studied. In this work we trained graph neural networks to fit time series from an example nonlinear dynamical system, the belief propagation algorithm. We found simple interpretations of the learned representation and model components, and they are consistent with core properties of the probabilistic inference algorithm. We successfully identified a `graph translator' between the statistical interactions in belief propagation and parameters of the corresponding trained network, and showed that it enables two types of novel generalization: to recover the underlying structure of a new system instance based solely on time series observations, or to construct a new network from this structure directly. Our results demonstrated a path towards understanding both dynamics and structure of a complex system and how such understanding can be used for generalization.
翻译:许多复杂的系统由互动部分组成,而基本的法律通常是简单和普遍的。虽然图形神经网络为模拟这些系统的模型提供了有用的感应偏差,但对类似类型的新系统实例的概括性研究较少。在这项工作中,我们训练了图形神经网络,以适应一个非线性动态系统的典型时间序列,即信仰传播算法。我们发现对所学的表述和模型组成部分的简单解释,它们与概率推算算法的核心特性是一致的。我们成功地确定了信仰传播中的统计互动和相应培训网络参数之间的“绘图翻译”功能,并表明它能够实现两种新型的新的概括性:完全基于时间序列观察的新系统实例的基本结构,或者直接从这个结构中构建一个新的网络。我们的结果展示了理解复杂系统的动态和结构以及如何将这种理解用于概括化的路径。