Active Learning with Bayesian Multi-Fidelity Laplace Neural Operators for Oscillatory Parametric PDEs

תקציר מקורי באנגליתarXiv: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 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 vi