# Streaming Operator Inference for Model Reduction of Large-Scale Dynamical Systems

arXiv: https://arxiv.org/abs/2601.12161 · HTML: https://mlsanity.com/paper/2601.12161/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 127 references that are in the map.
- First posted on arXiv 17 Jan 2026.

## Builds on (most cited first, 29 of 29)

- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems](https://mlsanity.com/paper/1912.08177/) (2019)
- [Data-driven reduced-order models via regularized operator inference for a single-injector combustion process](https://mlsanity.com/paper/2008.02862/) (2020)
- [Online dynamic mode decomposition for time-varying systems](https://mlsanity.com/paper/1707.02876/) (2017)
- [Reduced operator inference for nonlinear partial differential equations](https://mlsanity.com/paper/2102.00083/) (2021)
- [Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inference](https://mlsanity.com/paper/1908.11233/) (2019)
- [Bayesian operator inference for data-driven reduced-order modeling](https://mlsanity.com/paper/2204.10829/) (2022)
- [Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference](https://mlsanity.com/paper/2107.02597/) (2021)
- [Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systems](https://mlsanity.com/paper/2404.05040/) (2024)
- [Canonical and Noncanonical Hamiltonian Operator Inference](https://mlsanity.com/paper/2304.06262/) (2023)
- [Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inference](https://mlsanity.com/paper/2308.13819/) (2023)
- [A digital twin framework for civil engineering structures](https://mlsanity.com/paper/2308.01445/) (2023)
- [An Incremental Approach to Online Dynamic Mode Decomposition for Time-Varying Systems with Applications to EEG Data Modeling](https://mlsanity.com/paper/1908.01047/) (2019)
- [Streaming Compression of Scientific Data via weak-SINDy](https://mlsanity.com/paper/2308.14962/) (2023)
- [Domain decomposition for data-driven reduced modeling of large-scale systems](https://mlsanity.com/paper/2311.00883/) (2023)
- [Scientific Machine Learning Based Reduced-Order Models for Plasma Turbulence Simulations](https://mlsanity.com/paper/2401.05972/) (2024)
- [Active operator inference for learning low-dimensional dynamical-system models from noisy data](https://mlsanity.com/paper/2107.09256/) (2021)
- [Domain Decomposition-based coupling of Operator Inference reduced order models via the Schwarz alternating method](https://mlsanity.com/paper/2409.01433/) (2024)
- [Energy-Preserving Reduced Operator Inference for Efficient Design and Control](https://mlsanity.com/paper/2401.02889/) (2024)
- [Block-structured Operator Inference for coupled multiphysics model reduction](https://mlsanity.com/paper/2511.05389/) (2025)
- [Online Real-time Learning of Dynamical Systems from Noisy Streaming Data: A Koopman Operator Approach](https://mlsanity.com/paper/2212.05259/) (2022)
- [Nested Operator Inference for Adaptive Data-Driven Learning of Reduced-order Models](https://mlsanity.com/paper/2508.11542/) (2025)
- [Distributed computing for physics-based data-driven reduced modeling at scale: Application to a rotating detonation rocket engine](https://mlsanity.com/paper/2407.09994/) (2024)
- [Parallel Reduced Order Modeling for Digital Twins using High-Performance Computing Workflows](https://mlsanity.com/paper/2409.09080/) (2024)
- [Physically consistent predictive reduced-order modeling by enhancing Operator Inference with state constraints](https://mlsanity.com/paper/2502.03672/) (2025)
- [Symmetry-reduced model reduction of shift-equivariant systems via operator inference](https://mlsanity.com/paper/2507.18780/) (2025)
- [Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction](https://mlsanity.com/paper/2507.20463/) (2025)
- [Real-time Bayesian inference at extreme scale: A digital twin for tsunami early warning applied to the Cascadia subduction zone](https://mlsanity.com/paper/2504.16344/) (2025)
- [Performance Enhancement of the Recursive Least Squares Algorithms with Rank Two Updates](https://mlsanity.com/paper/2507.11095/) (2025)

## Built on by (most cited first, 2 of 2)

- [Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks](https://mlsanity.com/paper/2605.27756/) (2026)
- [Adaptive hybrid coupling with operator inference, the overlapping Schwarz alternating method and reinforcement learning](https://mlsanity.com/paper/2609.17837/) (2026)

## Abstract (arXiv)

Projection-based model reduction enables efficient simulation of complex dynamical systems by constructing low-dimensional surrogate models from high-dimensional data. The Operator Inference (OpInf) approach learns such reduced surrogate models through a two-step process: constructing a low-dimensional basis via Singular Value Decomposition (SVD) to compress the data, then solving a linear least-squares (LS) problem to infer reduced operators that govern the dynamics in this compressed space, all without access to the underlying code or full model operators, i.e., non-intrusively. Traditional OpInf operates as a batch learning method, where both the SVD and LS steps process all data simultaneously. This poses a barrier to deployment of the approach on large-scale applications where dataset sizes prevent the loading of all data into memory at once. Additionally, the traditional batch approach does not naturally allow model updates using new data acquired during online computation. To address these limitations, we propose Streaming OpInf, which learns reduced models from sequentially arriving data streams. Our approach employs incremental SVD for adaptive basis construction and recursive LS for streaming operator updates, eliminating the need to store complete data sets while enabling online model adaptation. The approach can flexibly combine different choices of streaming algorithms for numerical linear algebra: we systematically explore the impact of these choices both analytically and numerically to identify effective combinations for accurate reduced model learning. Numerical experiments on benchmark problems and a large-scale turbulent channel flow demonstrate that Streaming OpInf achieves accuracy comparable to batch OpInf while reducing memory requirements by over 99% and enabling dimension reductions exceeding 31,000x, resulting in orders-of-magnitude faster predictions.