arXiv:2608. 16152v1 Announce Type: cross Abstract: We study resonance prediction in dispersive media, formulated as nonlinear spectral problems for volume integral operators.
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The paper introduces a method that combines Fourier Neural Operators with wavelet-based encodings to learn and predict multiple eigenmodes of the elastic wave equation in metamaterials. By encoding PDE inputs with wavelets, the model can deterministically select eigenmodes for both continuous and binary geometries, and it explains how prediction accuracy depends on geometric discontinuities. The surrogate model achieves a three‑order‑of‑magnitude speedup over finite element analysis while maintaining high fidelity, offering a powerful tool for accelerating metamaterial design.
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.
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.
Learning functional relationships from noisy data is a central problem in scientific inference. Spectral methods approximate unknown functions by expanding them in a basis and estimating the corresponding coefficients from data, but the stability of these coefficients under noise remains poorly understood.
We identify a diagonal saturation principle in modal inverse problems: when truncation noise is isotropic, the Bayes-optimal Tikhonov shape is a closed-form power law Gamma_k proportional to lambda_k^...
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.