发表机构
Kuban State University（库班国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多簇开放系统，从聚合快照恢复转移算子，提出最小作用先验方法，精确保持平衡，优于平滑方法，并揭示聚合观测的信息极限。
AI 中文摘要
许多开放系统仅通过聚合快照被观测，而在状态间移动物体的规则仍然隐藏。本文研究从两个相邻快照恢复多簇开放系统转移算子的逆问题。一致算子填充一个仿射流形：数据固定聚合流量并留下内部路由自由，因此每种恢复方法都承诺一个选择某个算子的先验。以零参考进行Tikhonov正则化给出每个源单纯形上的均匀流出，这低估了惯性系统中的保留。我们提出算子轨迹上的最小作用，在该作用下规则的变化尽可能小，只要数据允许。在离散时间中，这作为概率陈述是精确的：作用通过在高斯参考（趋向完全保留）下的似然为轨迹定价，因此最小作用选择与平衡一致的最可能轨迹。因果构造通过在约束的零空间内仅移动算子来保持平衡精确，我们将其与最优传输、Perron-Frobenius粗粒化和薛定谔桥联系起来。两个实例承载它：俄罗斯劳动力市场和辐射阻尼相对论电子系综。该构造将平衡保持到机器精度，而时间平滑在劳动力序列上使其损坏百分之十二，在物理序列中损坏百分之六十。谱间隙从聚合快照不可识别，但可从微观轨迹获得，其中Ulam方法以百分之六以内的误差再现Landau-Lifshitz速率。在短劳动力序列上，在常规显著性水平下，没有方法在点精度上优于朴素预测。其价值是结构性的：一个可解释的算子、一个精确保持的平衡，以及聚合观测的显式信息极限。
英文摘要
Many open systems are observed only through aggregate snapshots, while the rule that moves objects between states stays hidden. This paper studies the inverse problem of recovering the transfer operator of a multicluster open system from two adjacent snapshots. The consistent operators fill an affine manifold: the data fix the aggregate flows and leave the internal routing free, so every recovery method commits to a prior that selects one operator. Tikhonov regularisation with a zero reference gives the uniform outflow on each source simplex, which underestimates retention in an inertial system. We propose least action on the operator trajectory, under which the rule changes as little as the data permit. In discrete time this is exact as a probability statement: the action prices a trajectory by its likelihood under a Gaussian reference drawn toward full retention, so least action selects the most probable trajectory consistent with the balance. A causal construction keeps the balance exact by moving the operator only inside the null space of the constraints, and we relate it to optimal transport, to Perron-Frobenius coarse-graining, and to the Schrödinger bridge. Two instantiations carry it: the Russian labour market and a radiation-damped relativistic electron ensemble. The construction holds the balance to machine precision where temporal smoothing corrupts it by twelve percent on the labour series and sixty percent in the physical one. The spectral gap is non-identifiable from aggregate snapshots but available from micro-trajectories, where Ulam's method reproduces the Landau-Lifshitz rate to within six percent. On the short labour series no method beats the naive forecast in point accuracy at conventional significance levels. The value is structural: an interpretable operator, an exactly preserved balance, and an explicit information limit of aggregate observation.
Comments42 pages, 10 figures, 5 tables. Extended version of an article accepted in Mathematical Modeling and Computational Methods (BMSTU). Code and data: doi:10.5281/zenodo.21140416. Preprint record: doi:10.5281/zenodo.21758814
