The solution of the path structured multimarginal Schr\"{o}dinger bridge problem (MSBP) is the most-likely measure-valued trajectory consistent with a sequence of observed probability measures or distributional snapshots. We leverage recent algorithmic advances in solving such structured MSBPs for learning stochastic hardware resource usage by control software. The solution enables predicting the time-varying distribution of hardware resource availability at a desired time with guaranteed linear convergence. We demonstrate the efficacy of our probabilistic learning approach in a model predictive control software execution case study. The method exhibits rapid convergence to an accurate prediction of hardware resource utilization of the controller. The method can be broadly applied to any software to predict cyber-physical context-dependent performance at arbitrary time.

解决路径结构化多边际Schr"{o}dinger桥问题的解是与一系列观测概率测度或分布快照一致的最可能的测度值轨迹，我们利用了最近在解决这类结构化MSBP时的算法进展，以控制软件学习随机硬件资源使用情况，该解使得能够预测在所需时间点硬件资源可用性的时变分布，并保证线性收敛，我们在模型预测控制软件执行案例研究中展示了我们的概率学习方法的效力，该方法在控制器的硬件资源利用率准确预测上表现出快速收敛性，这种方法可以广泛应用于任何软件，以在任意时间预测网络物理环境下的性能。

基于路径结构的多边缘Schrödinger桥方法用于概率学习控制软件对硬件资源使用