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
The paper explores how to use gradients of simulator outputs with respect to input parameters to improve Bayesian inference for expensive simulators. By incorporating gradient information into Gaussian process surrogate models, the authors show that Bayesian optimization can converge faster under a limited simulation budget. They find that reverse‑mode differentiation yields efficiency gains, while forward‑mode does not offset its computational cost, especially when the number of parameters exceeds the output dimensionality.
By \v{S}imon Sold\'at, V\'aclav \v{S}m\'idl
arXiv:2512.12749v3 Announce Type: replace-cross
Abstract: Learning surrogate models for physical systems with latent uncertainty remains challenging in data-scarce regimes: deterministic neural opera...
By Sahil Bhola, Karthik Duraisamy
arXiv:2602.01176v2 Announce Type: replace
Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physica...
By Olaf Yunus Laitinen Imanov
The paper introduces a scalable method for uncertainty quantification in neural networks by applying a low‑rank generalized Laplace approximation within a data‑informed active subspace. It constructs a local Gaussian posterior around pretrained weights, calibrates the prior variance via empirical Bayes, and compares two posterior scalings: standard Bayesian and mean‑loss scaling. The study finds that mean‑loss scaling yields a more stable, lower‑dimensional subspace and produces calibrated, coherent predictive confidence intervals, whereas standard scaling can cause posterior variance contraction and degrade predictive coherence.
By Wouter N. Edeling, Peter V. Coveney
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: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:2503. 05598v2 Announce Type: replace-cross Abstract: This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation.
By Prashant K. Jha
arXiv:2609.36712v1 Announce Type: cross
Abstract: Accurately learning nonlinear dynamics from a finite-duration experiment requires the efficient collection of informative data. We address this chall...
By Juncal Arbelaiz, Anushri Arora, Jonathan W. Pillow
arXiv:2609.26021v1 Announce Type: new
Abstract: Dynamic black-box optimization presents significant challenges for Bayesian Optimization (BO), as the objective function evolves over time, causing opt...
By Merlin Angel Kelly, Rishan Patel, Alexander Thomas, Ziyue Zhu, Zikun Quan, Tom Carlson, Youngjun Cho
arXiv:2606. 09949v1 Announce Type: cross Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE solvers.
By Pierre Cesar (DATAMOVE), Sofya Dymchenko (DATAMOVE), Abhishek Purandare (DATAMOVE), Bruno Raffin (DATAMOVE)
Accurately learning nonlinear dynamics from a finite-duration experiment requires the efficient collection of informative data. We address this challenge for stochastic controlled nonlinear dynamical...