发表机构
Potsdam Institute for Climate Impact Research; Technical University Berlin（波茨坦气候影响研究所; 柏林工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种保持动力学的拼车路径网络约简方法，证明在路径长度依赖的决策下可将网络约简为加权活动节点网络，并探讨了等价性在全局优化下的破坏，为路径过程分析提供通用框架。
AI 中文摘要
在具有分布式需求的系统中，降低拼车路径的复杂性是一个核心挑战。我们在此表明，此类动力学允许一种精确的粗粒化表示：对于一大类其决策仅依赖于路径长度的路由算法，整个网络可以约简为一个由最短路径距离加权的有效活动节点网络，而不会改变由此产生的轨迹，直至随机简并性破缺。因此，该约简定义了一个生成相同路径动力学的网络表示的等价类。我们进一步证明，对于全局优化的调度器，这种等价性会通过简并放大而被系统地违反，但在精确可解区域之外仍保持定量准确。我们的结果确定了何时可以在不损失动力学保真度的情况下整合掉空间结构，为分析相互作用的路径过程提供了一个通用框架。
英文摘要
Reducing the complexity of ride-pooling paths is a central challenge in systems with distributed demand. Here we show that such dynamics admit an exact coarse-grained representation: for a broad class of routing algorithms whose decisions depend only on path lengths, the full network can be reduced to an effective network of active nodes weighted by shortest-path distances without altering the resulting trajectories, up to stochastic degeneracy breaking. The reduction therefore defines an equivalence class of network representations generating identical path dynamics. We further demonstrate that for globally optimizing dispatchers this equivalence is systematically violated through degeneracy amplification, yet remains quantitatively accurate beyond the exactly solvable regime. Our results identify when spatial structure can be integrated out without loss of dynamical fidelity, providing a general framework for the analysis of interacting path processes.
