Active Learning

This work develops an active learning framework to intelligently enrich data-driven reduced-order models (ROMs) of parametric dynamical systems, which can serve as the foundation of virtual assets in a digital twin. Data-driven ROMs are explainable, computationally efficient scientific machine learning models that aim to preserve the underlying physics of complex dynamical simulations. Since the quality of data-driven ROMs is sensitive to the quality of the limited training data, we seek to identify training parameters for which using the associated training data results in the best possible parametric ROM. Our approach uses the operator inference methodology, a regression-based strategy which can be tailored to particular parametric structure for a large class of problems. We establish a probabilistic version of parametric operator inference, casting the learning problem as a Bayesian linear regression. Prediction uncertainties stemming from the resulting probabilistic ROM solutions are used to design a sequential adaptive sampling scheme to select new training parameter vectors that promote ROM stability and accuracy globally in the parameter domain. We conduct numerical experiments for several nonlinear parametric systems of partial differential equations and compare the results to ROMs trained on random parameter samples. The results demonstrate that the proposed adaptive sampling strategy consistently yields more stable and accurate ROMs than random sampling does under the same computational budget.

Active learning (AL) aims to build high-quality labeled datasets by iteratively selecting the most informative samples from an unlabeled pool under limited annotation budgets. However, in fine-grained image classification, assessing this informativeness reliably is especially challenging due to subtle differences between classes. In this paper, we introduce a novel active learning method, combining discrepancy-confusion uncertainty and calibration diversity for active fine-grained image classification (DECERN), to effectively perceive the distinctiveness between fine-grained images and evaluate the sample value. DECERN introduces a multifaceted informativeness measure that combines discrepancy-confusion uncertainty and calibration diversity. The discrepancy-confusion uncertainty quantifies the structural stability and category directionality of fine-grained unlabeled data during local feature fusion. Subsequently, uncertainty-weighted clustering is performed to diversify the uncertainty samples. Then we calibrate the diversity to maximize the global diversity of the selected sample while maintaining its local representativeness. Extensive experiments conducted on 7 fine-grained image datasets across 39 distinct experimental settings demonstrate that our method achieves superior performance compared to state-of-the-art methods.

The scalability of pool-based active learning is limited by the computational cost of evaluating large unlabeled datasets, a challenge that is particularly acute in virtual screening for drug discovery. While active learning strategies such as Bayesian Active Learning by Disagreement (BALD) prioritize informative samples, it remains computationally intensive when scaled to libraries containing billions samples. In this work, we introduce BALD-GFlowNet, a generative active learning framework that circumvents this issue. Our method leverages Generative Flow Networks (GFlowNets) to directly sample objects in proportion to the BALD reward. By replacing traditional pool-based acquisition with generative sampling, BALD-GFlowNet achieves scalability that is independent of the size of the unlabeled pool. In our virtual screening experiment, we show that BALD-GFlowNet achieves a performance comparable to that of standard BALD baseline while generating more structurally diverse molecules, offering a promising direction for efficient and scalable molecular discovery.

Surrogate models of parametric dynamical systems are essential for many-query and real-time predictions in engineering applications such as design optimization and digital twins. However, generating high-fidelity (HF) training data over a broad range of parameters and operating conditions remains computationally expensive. To address this challenge, we propose a Bayesian multi-fidelity Laplace neural operator (MF-LNO) for uncertainty-aware active learning of oscillatory parametric PDEs. Specifically, the proposed Bayesian MF-LNO iteratively calibrates the discrepancy between low- and high-fidelity data, where predictive uncertainty guides the adaptive acquisition of informative HF trajectories. Such predictive uncertainty is quantified via replica-exchange stochastic gradient Langevin dynamics (reSGLD), whose broad posterior exploration enables uncertainty to serve as an error indicator for adaptive HF sample acquisition. Numerical experiments on the Lorenz system, Duffing oscillator, and beam dynamics demonstrate that uncertainty-guided HF sample acquisition consistently outperforms random sampling, while the proposed Bayesian MF-LNO achieves higher prediction accuracy than MF-DeepONet with predictive uncertainty quantification. These results demonstrate that Bayesian multi-fidelity LNOs, combined with uncertainty-guided active learning, provide a data-efficient framework for operator learning in engineering dynamical systems.

Although generative models hold promise for discovering molecules with optimized desired properties, they often fail to suggest synthesizable molecules that improve upon the properties of the structures represented in the training distribution. We find that this limitation arises not only from the molecule generation process itself, but also from the poor generalization capabilities of molecular property predictors. We address this challenge by creating a closed-loop molecule generation pipeline with iterative retraining on new quantum chemical simulation data. Compared against static, single-pass generative modeling approaches, only our closed-loop iterative workflow generates molecules with properties extending beyond the training distribution (up to 0.44 standard deviations beyond the original range) and achieves a 79% improvement in out-of-distribution molecule classification accuracy. Furthermore, by conditioning molecular generation on thermodynamic stability data obtained during the iterative loop, the proportion of stable and hence potentially synthesizable molecules generated is 3.5x higher than the next-best model.

Continuous sign language recognition (CSLR) is a key technology for accessibility, yet its development remains limited by the high cost of annotating continuous video streams. Active learning offers a path toward mitigating this cost, but standard acquisition functions are not designed for weakly aligned sign language videos, where sign executions are interleaved with rest poses, irregular pauses, sign-like motion, and temporally redundant frames. This temporal redundancy can undermine sample selection, as acquisition scores may be influenced by timesteps from regions that are not associated with the decoded gloss sequence, distorting the video's estimated informativeness. In this work, we show that modern CSLR models already contain a mechanism for identifying gloss-level temporal evidence: the CTC decoder. Although typically used only during inference, its alignment peaks indicate where the model localizes each predicted gloss in the feature sequence, providing a source of temporal structure for active learning acquisition functions at zero additional labeling cost. Thus, we introduce RAIDAL (Redundancy-Aware Information Density Active Learning), which repurposes the CTC decoder to restrict representation-based scoring to decoder-aligned gloss regions, rather than exposing the acquisition function to the entire unfiltered video. Across three datasets and two architectures, RAIDAL achieves its strongest data-efficiency gains over competing baselines in large-vocabulary, budget-limited settings, while remaining competitive in the smaller-vocabulary, large-budget setting. The code used in this work is publicly available at github.com/verlab/RAIDAL.