arXiv:2607. 14193v1 Announce Type: cross Abstract: The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber $\kappa^2$ complex.
By Boyuan Deng, Kshitiz Upadhyay, Michael Shields
arXiv:2607. 25790v1 Announce Type: cross Abstract: This paper proposes a novel physics-guided spectral deep operator network, termed SpectONet, for solving Euler-Bernoulli beam (EBB) vibration problems.
By Shivani Saini, Ramesh Kumar Vats, Arup Kumar Sahoo
arXiv:2608. 16873v1 Announce Type: new Abstract: High-fidelity finite-element simulations can provide accurate numerical predictions for side-branch resonators, but large simulation datasets are expensive to generate and purely data-driven surrogates may become unreliable when simulation-labelled data are scarce.
By Jiaming Li
The paper presents a data‑efficient machine learning framework that incorporates a low‑cost analytical model to enhance predictions of sound‑reduction frequencies in Helmholtz resonators. Two strategies are explored: (1) using the analytical model as a baseline and learning only the discrepancy with limited high‑fidelity simulation data, and (2) distilling the analytical mapping into a learned prior and calibrating it with scarce simulation data. Experiments on rectangular side‑branch resonators show that both approaches significantly reduce prediction error compared to direct learning, achieving mean absolute errors as low as 0.371 Hz with full‑model fine‑tuning.
By Jiaming Li
High-fidelity finite-element simulations can provide accurate numerical predictions for side-branch resonators, but large simulation datasets are expensive to generate and purely data-driven surrogates may become unreliable when simulation-labelled data are scarce. This study develops an analytical-prior learning framework that reuses a low-cost analytical model to improve data efficiency under limited high-fidelity simulation budgets.
arXiv:2609.35938v1 Announce Type: new
Abstract: This paper proposes an interpretable neural operator framework, the Kernel Operator Network (KernelOnet), which incorporates kernel functions explicitl...
By Yuan Guo, Hanshu Chen, Qiang Xi, Timon Rabczuk, Zhuojia Fu