# Path Structured Multimarginal Schr"odinger Bridge for Probabilistic Learning of Hardware Resource Usage by Control Software

arXiv: https://arxiv.org/abs/2310.00604 · HTML: https://mlsanity.com/paper/2310.00604/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 42 references that are in the map.
- First posted on arXiv 1 Oct 2023.

## Builds on (most cited first, 9 of 9)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Multi-marginal optimal transport: theory and applications](https://mlsanity.com/paper/1406.0026/) (2014)
- [An Optimal Transport approach for the Schr"odinger bridge problem and convergence of Sinkhorn algorithm](https://mlsanity.com/paper/1911.06850/) (2019)
- [The data-driven Schroedinger bridge](https://mlsanity.com/paper/1806.01364/) (2018)
- [Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm](https://mlsanity.com/paper/1710.08234/) (2017)
- [Accelerating the Sinkhorn algorithm for sparse multi-marginal optimal transport by fast Fourier transforms](https://mlsanity.com/paper/2208.03120/) (2022)
- [Density-based Stochastic Reachability Computation for Occupancy Prediction in Automated Driving](https://mlsanity.com/paper/2006.12581/) (2020)

## Built on by (most cited first, 3 of 3)

- [Stochastic Learning of Computational Resource Usage as Graph Structured Multimarginal Schr"odinger Bridge](https://mlsanity.com/paper/2405.12463/) (2024)
- [Optimal Multimarginal Schr"odinger Bridge: Minimum Spanning Tree over Measure-valued Vertices](https://mlsanity.com/paper/2509.10626/) (2025)
- [Generative Profiling for Soft Real-Time Systems and its Applications to Resource Allocation](https://mlsanity.com/paper/2604.01441/) (2026)

## Abstract (arXiv)

The solution of the path structured multimarginal Schr"odinger 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.