# Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challenges

arXiv: https://arxiv.org/abs/2602.11378 · HTML: https://mlsanity.com/paper/2602.11378/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 72 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Builds on (most cited first, 21 of 21)

- [Model Reduction and Neural Networks for Parametric PDEs](https://mlsanity.com/paper/2005.03180/) (2020)
- [A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs](https://mlsanity.com/paper/2001.04001/) (2020)
- [Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems](https://mlsanity.com/paper/1912.08177/) (2019)
- [Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics](https://mlsanity.com/paper/1912.11114/) (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)
- [Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions](https://mlsanity.com/paper/2211.06786/) (2022)
- [Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference](https://mlsanity.com/paper/2110.07653/) (2021)
- [Learning physics-based reduced-order models for a single-injector combustion process](https://mlsanity.com/paper/1908.03620/) (2019)
- [Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inference](https://mlsanity.com/paper/1908.11233/) (2019)
- [Learning Nonlinear Projections for Reduced-Order Modeling of Dynamical Systems using Constrained Autoencoders](https://mlsanity.com/paper/2307.15288/) (2023)
- [Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows](https://mlsanity.com/paper/2010.06701/) (2020)
- [On-the-fly Reduced Order Modeling of Passive and Reactive Species via Time-Dependent Manifolds](https://mlsanity.com/paper/2101.03847/) (2021)
- [Optimizing Oblique Projections for Nonlinear Systems using Trajectories](https://mlsanity.com/paper/2106.01211/) (2021)
- [Model Reduction for Nonlinear Systems by Balanced Truncation of State and Gradient Covariance](https://mlsanity.com/paper/2207.14387/) (2022)
- [Lookahead data-gathering strategies for online adaptive model reduction of transport-dominated problems](https://mlsanity.com/paper/2307.14874/) (2023)
- [A globally convergent method to accelerate topology optimization using on-the-fly model reduction](https://mlsanity.com/paper/2004.05756/) (2020)
- [On GROUSE and Incremental SVD](https://mlsanity.com/paper/1307.5494/) (2013)
- [Nested Operator Inference for Adaptive Data-Driven Learning of Reduced-order Models](https://mlsanity.com/paper/2508.11542/) (2025)
- [Non-intrusive Balancing Transformation of Highly Stiff Systems with Lightly-damped Impulse Response](https://mlsanity.com/paper/2109.10408/) (2021)
- [Data-driven Balanced Truncation for Predictive Model Order Reduction of Aeroacoustic Response](https://mlsanity.com/paper/2304.13900/) (2023)

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

- [History-aware adaptive reduced-order models via incremental singular value decomposition](https://mlsanity.com/paper/2605.28684/) (2026)
- [In-context learning from self-generated trajectories for adaptive model reduction](https://mlsanity.com/paper/2607.02937/) (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 Reduced Order Models (ROMs) are often deployed as static surrogates, which limits their practical utility once a system leaves the training manifold. We formalize and study adaptive non-intrusive ROMs that update both the latent subspace and the reduced dynamics online. Building on ideas from static non-intrusive ROMs, specifically, Operator Inference (OpInf) and the recently-introduced Non-intrusive Trajectory-based optimization of Reduced-Order Models (NiTROM), we propose three formulations: Adaptive OpInf (sequential basis/operator refits), Adaptive NiTROM (joint Riemannian optimization of encoder/decoder and polynomial dynamics), and a hybrid that initializes NiTROM with an OpInf update. We describe the online data window, adaptation window, and computational budget, and analyze cost scaling. On a transiently perturbed lid-driven cavity flow, static Galerkin/OpInf/NiTROM drift or destabilize when forecasting beyond training. In contrast, Adaptive OpInf robustly suppresses amplitude drift with modest cost; Adaptive NiTROM is shown to attain near-exact energy tracking under frequent updates but is sensitive to its initialization and optimization depth; the hybrid is most reliable under regime changes and minimal offline data, yielding physically coherent fields and bounded energy. We argue that predictive claims for ROMs must be cost-aware and transparent, with clear separation of training/adaptation/deployment regimes and explicit reporting of online budgets and full-order model queries. This work provides a practical template for building self-correcting, non-intrusive ROMs that remain effective as the dynamics evolve well beyond the initial manifold.