# Cost-effective Reduced-Order Modeling via Bayesian Active Learning

arXiv: https://arxiv.org/abs/2506.22645 · HTML: https://mlsanity.com/paper/2506.22645/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 27 Jun 2025.

## Builds on (most cited first, 14 of 14)

- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Active Learning on a Budget: Opposite Strategies Suit High and Low Budgets](https://mlsanity.com/paper/2202.02794/) (2022)
- [Towards Robust and Reproducible Active Learning Using Neural Networks](https://mlsanity.com/paper/2002.09564/) (2020)
- [Entropy-based Active Learning for Object Detection with Progressive Diversity Constraint](https://mlsanity.com/paper/2204.07965/) (2022)
- [Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulations](https://mlsanity.com/paper/2107.04556/) (2021)
- [Active Learning: Problem Settings and Recent Developments](https://mlsanity.com/paper/2012.04225/) (2020)
- [Bayesian operator inference for data-driven reduced-order modeling](https://mlsanity.com/paper/2204.10829/) (2022)
- [Quantifying the multi-objective cost of uncertainty](https://mlsanity.com/paper/2010.04653/) (2020)
- [Understanding Uncertainty-based Active Learning Under Model Mismatch](https://mlsanity.com/paper/2408.13690/) (2024)
- [Experimental Design via Generalized Mean Objective Cost of Uncertainty](https://mlsanity.com/paper/1805.01143/) (2018)
- [A Survey on Machine Learning Applied to Dynamic Physical Systems](https://mlsanity.com/paper/2009.09719/) (2020)

## Abstract (arXiv)

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.