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
The paper introduces Gradient-based Sample Selection Bayesian Optimization (GSSBO), a method that builds the Gaussian process surrogate on a strategically chosen subset of samples rather than the full dataset. By using gradient information to eliminate redundant points while keeping diversity and representativeness, GSSBO achieves sublinear regret bounds and reduces the cubic computational cost of standard BO. Experiments on synthetic and real-world tasks show that this approach maintains comparable optimization performance while significantly cutting GP fitting time and resource usage.
By Qiyu Wei, Haowei Wang, Zirui Cao, Songhao Wang, Richard Allmendinger, Mauricio A \'Alvarez
arXiv:2502.00550v2 Announce Type: replace
Abstract: Surrogate models of parametric dynamical systems are essential for many-query and real-time predictions in engineering applications such as design...
By Bongseok Kim, Haoyang Zheng, Michael Penwarden, Guang Lin
arXiv:2610.22763v1 Announce Type: new
Abstract: Bayesian optimization (BO) over discrete spaces is challenging due to missing gradients and the sparsity of valid solutions. Latent-space BO sidesteps...
By Tommaso Ancilli, Thomas Wedenig, Henry Moss, Robert Peharz
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
By Ricardo Baptista, Hojjat Kaveh, Andrew M. Stuart
arXiv:2606. 16138v1 Announce Type: cross Abstract: Recovering dynamical systems from noisy observations is a recurring challenge across scientific domains, including neuroscience and physics.
By Henry D. Smith, Brian L. Trippe, Scott W. Linderman
arXiv:2606. 08438v1 Announce Type: cross Abstract: Bayesian optimization (BO) is a widely used approach for black-box optimization that uses a Gaussian process (GP) as a surrogate and guides sequential evaluations via an acquisition function, with the ultimate goal of locating the global optimum $\mathbf{x}^{\star}$.
By Yilin Zheng, Haowei Wang, Szu Hui Ng, Enlu Zhou