arXiv:2608. 16152v1 Announce Type: cross Abstract: We study resonance prediction in dispersive media, formulated as nonlinear spectral problems for volume integral operators.
arXiv:2608. 16873v2 Announce Type: replace 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.
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.
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.
arXiv:2606. 00401v1 Announce Type: cross Abstract: Simulating large molecular systems comprising thousands of atoms requires highly scalable methodologies.
arXiv:2607. 13566v1 Announce Type: cross Abstract: For low-dimensional problems ($d\leq3$), spectral methods can achieve exceptionally high accuracy.
arXiv:2608. 13504v1 Announce Type: new Abstract: We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data.
arXiv:2608. 11019v1 Announce Type: new Abstract: Modeling spatiotemporal dynamical systems governed by partial differential equations (PDEs) poses two major challenges: it either requires expensive physics-based simulators that entail iterative numerical solving at high computational cost, or it depends on abundant training data, yet purely data-driven models often generalize poorly to downstream dynamic operating conditions.
arXiv:2606. 11518v1 Announce Type: cross Abstract: Fourier neural operators (FNOs) are effective and efficient surrogates for approximating solutions of PDEs and generalize across discretizations.
arXiv:2606. 00322v1 Announce Type: new Abstract: We introduce a perturbative approach for nonparametric instrumental variable (NPIV) estimation.
arXiv:2604. 20141v2 Announce Type: replace Abstract: We introduce Fourier Weak SINDy, a minimal noise-robust and interpretable derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for data-driven test function selection.
arXiv:2501. 10870v2 Announce Type: replace-cross Abstract: The principal objective of this work is twofold within nonparametric regression settings: (1) to establish the minimax optimal convergence rates for fixed-bandwidth Gaussian kernel spectral algorithms when the true regression function resides in a Sobolev space, and (2) to apply Gaussian spectral algorithms for achieving robust and adaptive transfer learning under concept shift.