Cost-effective Reduced-Order Modeling via Bayesian Active Learning

2025-06-27

AI Summary

High-fidelity full-order models (FOMs) are computationally prohibitive, while conventional reduced-order modeling (ROM) relies heavily on large volumes of simulation data. To address this, we propose a Bayesian active learning–driven ROM paradigm. Methodologically, we innovatively integrate uncertainty-aware Bayesian proper orthogonal decomposition (POD) basis construction with variational inference, establishing a joint adaptive sampling–reduction optimization framework: predictive uncertainty guides sequential active sampling, enabling dynamic refinement of both the low-dimensional manifold and the surrogate model. In temperature field evolution prediction, our approach reduces high-fidelity simulations by ~60% compared to random or grid-based sampling, while improving generalization accuracy at fine temporal resolution. Our key contribution is the first deep embedding of Bayesian uncertainty quantification into the POD-based ROM pipeline, achieving synergistic gains in data efficiency and model fidelity.

Technology Category

• Machine Learning: Active Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Machine Learning surrogates have been developed to accelerate solving systems dynamics of complex processes in different science and engineering applications. To faithfully capture governing systems dynamics, these methods rely on large training datasets, hence restricting their applicability in real-world problems. In this work, we propose BayPOD-AL, an active learning framework based on an uncertainty-aware Bayesian proper orthogonal decomposition (POD) approach, which aims to effectively learn reduced-order models from high-fidelity full-order models representing complex systems. Experimental results on predicting the temperature evolution over a rod demonstrate BayPOD-AL's effectiveness in suggesting the informative data and reducing computational cost related to constructing a training dataset compared to other uncertainty-guided active learning strategies. Furthermore, we demonstrate BayPOD-AL's generalizability and efficiency by evaluating its performance on a dataset of higher temporal resolution than the training dataset.

Problem

• Reducing computational cost in reduced-order modeling
• Improving data efficiency in learning system dynamics
• Enhancing generalizability of machine learning surrogates

Innovation

• Bayesian active learning for reduced-order modeling
• Uncertainty-aware Proper Orthogonal Decomposition approach
• Efficient data selection to reduce computational costs