Linear System Identification from Snapshot Data by Schrodinger bridge

Kohei Morimoto, Kenji Kashima
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:579-590, 2025.

Abstract

This paper proposes a system identification method for linear Gaussian systems from snapshot measurement data using Schrodinger bridges (SB). In many practical applications, such as single-cell RNA sequencing, only snapshot measurements of system state are available, making traditional system identification challenging. Our method employs an EM-like algorithm that alternates between trajectory estimation using SB and system parameter inference from the estimated trajectories. The Gaussian assumption for system states and noise allows us to exploit analytical solutions for the SB computation and parameter updates, enabling efficient computation. We also propose a data-driven method for estimating linear Gaussian SB, where marginal parameters are estimated incorporating dynamic constraints. In numerical simulation, we show our method achieves superior identification accuracy and time efficiency.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-morimoto25a, title = {Linear System Identification from Snapshot Data by Schrodinger bridge}, author = {Morimoto, Kohei and Kashima, Kenji}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {579--590}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/morimoto25a/morimoto25a.pdf}, url = {https://proceedings.mlr.press/v283/morimoto25a.html}, abstract = {This paper proposes a system identification method for linear Gaussian systems from snapshot measurement data using Schrodinger bridges (SB). In many practical applications, such as single-cell RNA sequencing, only snapshot measurements of system state are available, making traditional system identification challenging. Our method employs an EM-like algorithm that alternates between trajectory estimation using SB and system parameter inference from the estimated trajectories. The Gaussian assumption for system states and noise allows us to exploit analytical solutions for the SB computation and parameter updates, enabling efficient computation. We also propose a data-driven method for estimating linear Gaussian SB, where marginal parameters are estimated incorporating dynamic constraints. In numerical simulation, we show our method achieves superior identification accuracy and time efficiency.} }
Endnote
%0 Conference Paper %T Linear System Identification from Snapshot Data by Schrodinger bridge %A Kohei Morimoto %A Kenji Kashima %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-morimoto25a %I PMLR %P 579--590 %U https://proceedings.mlr.press/v283/morimoto25a.html %V 283 %X This paper proposes a system identification method for linear Gaussian systems from snapshot measurement data using Schrodinger bridges (SB). In many practical applications, such as single-cell RNA sequencing, only snapshot measurements of system state are available, making traditional system identification challenging. Our method employs an EM-like algorithm that alternates between trajectory estimation using SB and system parameter inference from the estimated trajectories. The Gaussian assumption for system states and noise allows us to exploit analytical solutions for the SB computation and parameter updates, enabling efficient computation. We also propose a data-driven method for estimating linear Gaussian SB, where marginal parameters are estimated incorporating dynamic constraints. In numerical simulation, we show our method achieves superior identification accuracy and time efficiency.
APA
Morimoto, K. & Kashima, K.. (2025). Linear System Identification from Snapshot Data by Schrodinger bridge. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:579-590 Available from https://proceedings.mlr.press/v283/morimoto25a.html.

Related Material