Learning Long-Term Stable Operator Inference Reduced-Order Models of Fluid Flows through Online Spatial Filtering
Abstract
This paper introduces an online evolve--filter--relax (EFR) strategy for long-term stability of Operator Inference (OpInf) reduced-order models (ROMs) of complex fluid flow simulations. The main novelty of the new EFR-OpInf strategy is the use of online (i.e., at the learned ROM online evaluation level) spatial filtering inspired from large eddy simulation to significantly improve long-term stability and predictive performance of standard OpInf. Furthermore, the EFR-OpInf strategy reduces, and in some cases even eliminates, the need for standard L2 regularization, while providing physical interpretability for the OpInf hyperparameters. The EFR-OpInf framework is modular, readily integrated into existing OpInf workflows, and accommodates a user-selected ROM filtering strategy. We demonstrate the EFR-OpInf's effectiveness using a fully non-intrusive projection-based ROM filter, a ROM differential filter, and a hybrid projection-differential ROM filter. The new EFR-OpInf models are evaluated on a high-Péclet-number convection--diffusion--reaction problem that embeds the variation in one parameter and two unsteady Navier--Stokes problems that focus on predictions beyond a training horizon: a transitional two-dimensional flow past a cylinder and a three-dimensional turbulent minimal channel flow. Across these three scenarios, EFR-OpInf can reduce prediction errors by up to an order of magnitude relative to standard OpInf. Moreover, EFR-OpInf remains stable over long prediction horizons in cases where standard OpInf diverges. Depending on the ROM filter used, EFR-OpInf's computational cost is comparable to that of standard OpInf.
Related
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BibTeX
@misc{moore2026learning,
title = {{Learning Long-Term Stable Operator Inference Reduced-Order Models of Fluid Flows through Online Spatial Filtering}},
author = {Ian Moore and Ping-Hsuan Tsai and Anthony Gruber and Ionuţ Farcaş and Christopher Wentland and Irina Tezaur and Traian Iliescu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14812},
eprint = {2609.14812},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14812},
}
RIS
TY - UNPB
TI - Learning Long-Term Stable Operator Inference Reduced-Order Models of Fluid Flows through Online Spatial Filtering
AU - Ian Moore
AU - Ping-Hsuan Tsai
AU - Anthony Gruber
AU - Ionuţ Farcaş
AU - Christopher Wentland
AU - Irina Tezaur
AU - Traian Iliescu
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14812
UR - https://arxiv.org/abs/2609.14812
AB - This paper introduces an online evolve--filter--relax (EFR) strategy for long-term stability of Operator Inference (OpInf) reduced-order models (ROMs) of complex fluid flow simulations. The main novelty of the new EFR-OpInf strategy is the use of online (i.e., at the learned ROM online evaluation level) spatial filtering inspired from large eddy simulation to significantly improve long-term stability and predictive performance of standard OpInf. Furthermore, the EFR-OpInf strategy reduces, and in some cases even eliminates, the need for standard L^2 regularization, while providing physical interpretability for the OpInf hyperparameters. The EFR-OpInf framework is modular, readily integrated into existing OpInf workflows, and accommodates a user-selected ROM filtering strategy. We demonstrate the EFR-OpInf's effectiveness using a fully non-intrusive projection-based ROM filter, a ROM differential filter, and a hybrid projection-differential ROM filter. The new EFR-OpInf models are evaluated on a high-Péclet-number convection--diffusion--reaction problem that embeds the variation in one parameter and two unsteady Navier--Stokes problems that focus on predictions beyond a training horizon: a transitional two-dimensional flow past a cylinder and a three-dimensional turbulent minimal channel flow. Across these three scenarios, EFR-OpInf can reduce prediction errors by up to an order of magnitude relative to standard OpInf. Moreover, EFR-OpInf remains stable over long prediction horizons in cases where standard OpInf diverges. Depending on the ROM filter used, EFR-OpInf's computational cost is comparable to that of standard OpInf.
ER -