Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challenges
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908829056237568 |
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| author | Hedayat, Amirpasha Padovan, Alberto Duraisamy, Karthik |
| author_facet | Hedayat, Amirpasha Padovan, Alberto Duraisamy, Karthik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11378 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challenges Hedayat, Amirpasha Padovan, Alberto Duraisamy, Karthik Machine Learning Computational Engineering, Finance, and Science Numerical Analysis Computational Physics 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. |
| title | Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challenges |
| topic | Machine Learning Computational Engineering, Finance, and Science Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2602.11378 |