The paper presents an active learning framework that enhances data-driven reduced-order models (ROMs) for parametric dynamical systems by intelligently selecting training parameters. Using a Bayesian linear regression version of operator inference, the method quantifies prediction uncertainty to guide sequential adaptive sampling, aiming to improve ROM stability and accuracy across the parameter domain. Numerical experiments on nonlinear PDE systems show that this adaptive strategy outperforms random sampling under the same computational budget.
By Shane A. McQuarrie, Mengwu Guo, Anirban Chaudhuri
arXiv:2607. 06252v1 Announce Type: cross Abstract: Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations.
By Fabian Schneider, Tapio Helin, Leila Taghizadeh
arXiv:2607. 29225v1 Announce Type: new Abstract: Bayesian Optimization (BO) is widely adopted for data-efficient optimization in scientific and engineering applications, yet its computational cost is rarely evaluated alongside optimization performance.
By Panagiotis Krokidas, Christoforos Rekatsinas, Vassilis Sioros, Grigorios M. Chatziathanasiou, Efi-Maria Papia, George Giannakopoulos
arXiv:2606. 20417v1 Announce Type: new Abstract: Inverse problems for differential equations arise throughout science and engineering, where one seeks to infer unknown model parameters from noisy or incomplete observations.
By Christian Jimenez-Beltran, Aretha L. Teckentrup, Antonio Vergari, Konstantinos C. Zygalakis
IQS-BO introduces an in‑context query selection method for Bayesian optimisation that learns to choose evaluation points via supervised learning on synthetic priors. The approach uses a Prior‑data Fitted Network (PFN) to predict, in a single forward pass, the probability that each candidate maximises the objective, thereby amortising the decision step and eliminating the need for costly surrogate refitting or acquisition maximisation. Experiments show that IQS‑BO matches or surpasses traditional Gaussian‑process‑based BO and other in‑context methods on both synthetic and real‑world benchmarks, and that a mixture prior combining GP samples with challenging function types further improves performance.
By Luca Geminiani, Nadja Klein
arXiv:2511. 16340v2 Announce Type: replace Abstract: Efficient Gaussian process (GP) inference is critical for sequential decision-making tasks such as active learning, online prediction, and Bayesian optimization.
By Alan Yufei Dong, Jihao Andreas Lin, Jos\'e Miguel Hern\'andez-Lobato