# Nested Operator Inference for Adaptive Data-Driven Learning of Reduced-order Models

arXiv: https://arxiv.org/abs/2508.11542 · HTML: https://mlsanity.com/paper/2508.11542/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 15 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [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)
- [Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms](https://mlsanity.com/paper/2002.09726/) (2020)
- [Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference](https://mlsanity.com/paper/2110.07653/) (2021)
- [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)
- [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)
- [Operator inference with roll outs for learning reduced models from scarce and low-quality data](https://mlsanity.com/paper/2212.01418/) (2022)
- [Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inference](https://mlsanity.com/paper/2308.13819/) (2023)
- [Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories](https://mlsanity.com/paper/2103.01362/) (2021)
- [Energy-Preserving Reduced Operator Inference for Efficient Design and Control](https://mlsanity.com/paper/2401.02889/) (2024)

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

- [Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challenges](https://mlsanity.com/paper/2602.11378/) (2026)
- [Streaming Operator Inference for Model Reduction of Large-Scale Dynamical Systems](https://mlsanity.com/paper/2601.12161/) (2026)
- [Active learning for data-driven reduced models of parametric differential systems with Bayesian operator inference](https://mlsanity.com/paper/2601.00038/) (2025)

## Abstract (arXiv)

This paper presents a data-driven, nested Operator Inference (OpInf) approach for learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems. The approach exploits the inherent hierarchy within the reduced space to iteratively construct initial guesses for the OpInf learning problem that prioritize the interactions of the dominant modes. The initial guess computed for any target reduced dimension corresponds to a ROM with provably smaller or equal snapshot reconstruction error than with standard OpInf. Moreover, our nested OpInf algorithm can be warm-started from previously learned models, enabling versatile application scenarios involving dynamic basis and model form updates. We demonstrate the performance of our algorithm on a cubic heat conduction problem, with nested OpInf achieving a four times smaller error than standard OpInf at a comparable offline time. Further, we apply nested OpInf to a large-scale, parameterized model of the Greenland ice sheet where, despite model form approximation errors, it learns a ROM with, on average, 3% error and computational speed-up factor above 19,000.