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

2026-02-11

AI Summary

This work addresses the limitations of static reduced-order models (ROMs), which fail when system dynamics evolve beyond the training manifold and lack online adaptability. To overcome this, the authors propose three adaptive, non-intrusive ROM frameworks—Adaptive OpInf, Adaptive NiTROM, and a hybrid strategy—that continuously self-correct by updating both the latent space and reduced dynamics in real time using a sliding data window and controlled computational budget. This approach is the first to guarantee energy stability and physical consistency for non-intrusive ROMs in dynamically evolving scenarios. In perturbed cavity flow tests, the hybrid method maintains bounded energy and physically coherent flow fields even with minimal offline training data; Adaptive NiTROM achieves near-exact energy tracking, while Adaptive OpInf effectively suppresses amplitude drift.

Technology Category

• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Intelligent Robots: State Estimation
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

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.

Problem

• Reduced-Order Models
• Adaptive Modeling
• Non-Intrusive Methods
• Dynamic Systems
• Manifold Drift

Innovation

• adaptive reduced-order models
• non-intrusive modeling
• Operator Inference
• Riemannian optimization
• online adaptation