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arXiv · 2506.22645

Cost-effective Reduced-Order Modeling via Bayesian Active Learning

Amir Hossein Rahmati·Nathan M. Urban·Byung-Jun Yoon·Xiaoning Qian
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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.

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Amir Hossein Rahmati, Nathan M. Urban, Byung-Jun Yoon, Xiaoning Qian. 2025-06-27. Cost-effective Reduced-Order Modeling via Bayesian Active Learning. https://arxiv.org/abs/2506.22645

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