Model reduction in time: Learning flow maps for reducing stochastic dynamical systems in time
Abstract
Predictions with dynamical systems can be computationally expensive---even with reduced models---because reaching future prediction times can require many sequential time integration steps. We propose Flow-Map First-Order Trajectory Matching (FM-FTM), a nonintrusive model reduction approach that accelerates ensemble predictions of stochastic dynamical systems by learning flow maps that replace multiple time-integration steps. Our method uses first-order trajectory matching (FTM) to learn a deterministic representation of the stochastic probability-current dynamics and then reduces its evolution over time into a flow map whose evaluation directly yields predictions over long time horizons. Numerical experiments on evolution problems with stochastic forcing demonstrate that FM-FTM accelerates ensemble predictions by up to two orders of magnitude while accurately predicting time marginals and ensemble statistics.
Related
- Lyapunov-Schmidt reduction for periodic orbits of implicit discrete dynamical systems
- Density Evolution for Stochastic Dynamical Systems Driven by α-Stable Processes: An Equation-Free Numerical Approach
- Low-Dimensional Reduction of Mean-Field Coupled Dynamical Systems with Units Described by Two Real Variables: Classification and Applications
- Distribution of hitting times for dissipative random dynamical systems on R^d , with application to stochastic gradient descent
- Geometric Methods for Stochastic Dynamical Systems: A Concise Introduction
BibTeX
@misc{jha2026model,
title = {{Model reduction in time: Learning flow maps for reducing stochastic dynamical systems in time}},
author = {Shreya Jha and Benjamin Peherstorfer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35504},
eprint = {2610.35504},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35504},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Model reduction in time: Learning flow maps for reducing stochastic dynamical systems in time
AU - Shreya Jha
AU - Benjamin Peherstorfer
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35504
UR - https://arxiv.org/abs/2610.35504
AB - Predictions with dynamical systems can be computationally expensive---even with reduced models---because reaching future prediction times can require many sequential time integration steps. We propose Flow-Map First-Order Trajectory Matching (FM-FTM), a nonintrusive model reduction approach that accelerates ensemble predictions of stochastic dynamical systems by learning flow maps that replace multiple time-integration steps. Our method uses first-order trajectory matching (FTM) to learn a deterministic representation of the stochastic probability-current dynamics and then reduces its evolution over time into a flow map whose evaluation directly yields predictions over long time horizons. Numerical experiments on evolution problems with stochastic forcing demonstrate that FM-FTM accelerates ensemble predictions by up to two orders of magnitude while accurately predicting time marginals and ensemble statistics.
ER -