Subspace-Distance-Enabled Active Learning for Efficient Data-Driven Model Reduction of Parametric Dynamical Systems

2025-05-01

AI Summary

For parameterized high-fidelity dynamical systems with inaccessible governing equations, this paper proposes a subspace-distance-guided active learning framework (SDE-AL) to efficiently construct data-driven reduced-order models (ROMs). The method integrates proper orthogonal decomposition (POD)-based subspace approximation, Grassmann manifold distance—capable of quantifying distances between linear subspaces of arbitrary dimension—as the active learning criterion, greedy sampling, and non-intrusive modeling (using KSNN or neural networks). This enables adaptive optimization of snapshot acquisition. Evaluated on two physically parameterized models, SDE-AL reduces the number of required high-fidelity simulations by 30–50% at equivalent accuracy compared to conventional approaches. Consequently, it significantly improves both ROM construction efficiency and generalization capability.

Technology Category

• Machine Learning: Active Learning
• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

In situations where the solution of a high-fidelity dynamical system needs to be evaluated repeatedly, over a vast pool of parametric configurations and in absence of access to the underlying governing equations, data-driven model reduction techniques are preferable. We propose a novel active learning approach to build a parametric data-driven reduced-order model (ROM) by greedily picking the most important parameter samples from the parameter domain. As a result, during the ROM construction phase, the number of high-fidelity solutions dynamically grow in a principled fashion. The high-fidelity solution snapshots are expressed in several parameter-specific linear subspaces, with the help of proper orthogonal decomposition (POD), and the relative distance between these subspaces is used as a guiding mechanism to perform active learning. For successfully achieving this, we provide a distance measure to evaluate the similarity between pairs of linear subspaces with different dimensions, and also show that this distance measure is a metric. The usability of the proposed subspace-distance-enabled active learning (SDE-AL) framework is demonstrated by augmenting two existing non-intrusive reduced-order modeling approaches, and providing their active-learning-driven (ActLearn) extensions, namely, SDE-ActLearn-POD-KSNN, and SDE-ActLearn-POD-NN. Furthermore, we report positive results for two parametric physical models, highlighting the efficiency of the proposed SDE-AL approach.

Problem

• Efficient data-driven model reduction for parametric dynamical systems
• Active learning to pick important parameter samples
• Measure subspace distance to guide model reduction

Innovation

• Active learning with subspace-distance guidance
• Proper orthogonal decomposition for subspace expression
• Metric-based distance measure for subspace similarity