用莫比乌斯分布建模节点移动密度，更准确且更简洁。
Off the Normal Path: Learning Spatial Density Models of Node Mobility
- 用莫比乌斯分布保持空间对称性，提升模型表达能力。
- 在圆盘区域上，模型密度预测精度优于传统混合密度网络和归一化流。
- 结果可解释性强，适合用于网络优化与参数扫描加速。
我们研究二维地形上移动节点稳态密度函数的建模问题。此类模型有助于网络设计与优化，例如加速参数扫描中的密度计算。本文评估了现成的混合密度网络和两类归一化流在圆盘区域上的适用性，并引入莫比乌斯分布以保留空间对称关系。实验表明，莫比乌斯混合模型能以更少参数准确描述稳态密度分布，性能优于或相当替代方法。
原文摘要 · Abstract (English)
We consider the problem of learning models of spatial density functions, representing the steady-state density of mobile nodes moving on a two-dimensional terrain. Deriving such models can assist in network design and optimization problems, e.g., by accelerating the computation of the density function during a parameter sweep. We address the question of applicability of off-the-shelf mixture density network models and of, two varieties of, normalizing flows for the description of mobile node density over a disk. We introduce the use of Möbius distributions to retain symmetric spatial relations. Our results indicate that mixtures of Möbius distributions provide interpretable, parsimonious models for the studied steady state density distributions, that match or outperform the alternatives.
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